Track a circular trajectory by solving a QP and using quadprog solver (using CLF approach)

Question

Pallov Anand on 24 Apr 2023

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https://se.mathworks.com/matlabcentral/answers/1952363-track-a-circular-trajectory-by-solving-a-qp-and-using-quadprog-solver-using-clf-approach

Edited: Torsten on 24 Apr 2023

Hi, I am trying to track a circular trajectory i.e. xd = R * cos(t); yd = R * sin(t) using a single integrator and QUADPROG solver. Below is my code:

clc

close all

clear all

t_span = 80;

dt = 0.02;

t = 0:dt:t_span;

number_of_robots = 1;

options = optimoptions('quadprog','Display','off');

x = zeros(1, length(t), number_of_robots);

y = zeros(1, length(t), number_of_robots);

x(1,1,1) = 6;

y(1,1,1) = 8;

Xc1 = 2;

Yc1 = 2;

alpha = 5;

r = 2;

for n = 1:length(t)

for z =1:number_of_robots

if z == 1

xd(1,:,z) = r * cos(t) + Xc1;

yd(1,:,z) = r * sin(t) + Yc1;

elseif z==2

xd(1,:,z) = r * sin(t).*(1-cos(t)) + Xc2;

yd(1,:,z) = r * cos(t).*(1-cos(t)) + Yc2;

end

X_r(:,n, z) = [x(:,n,z); y(:,n,z)];

Xd(:,n, z) = [xd(:,n,z); yd(:,n,z)];

H = eye(2);

f(:,n,z) = [0;0];

A = - 2 * [xd(1,n,z) - x(1,n,z), yd(1,n,z) - y(1,n,z)];

b = - alpha * ( (xd(1,n,z) - x(1,n,z))^2 + (yd(1,n,z) - y(1,n,z))^2 );

u(:,n,z) = quadprog(H,f(:,n,z),A, b,[],[],[],[],[],options);

x(1, n+1, z) = x(1,n,z) + dt * (u(1,n,z));

y(1, n+1, z) = y(1,n,z) + dt * (u(2,n,z));

disp(['Current time = ', num2str(n*dt)])

end

Current time = 0.02 Current time = 0.04 Current time = 0.06 Current time = 0.08 Current time = 0.1 Current time = 0.12 Current time = 0.14 Current time = 0.16 Current time = 0.18 Current time = 0.2 Current time = 0.22 Current time = 0.24 Current time = 0.26 Current time = 0.28 Current time = 0.3 Current time = 0.32 Current time = 0.34 Current time = 0.36 Current time = 0.38 Current time = 0.4 Current time = 0.42 Current time = 0.44 Current time = 0.46 Current time = 0.48 Current time = 0.5 Current time = 0.52 Current time = 0.54 Current time = 0.56 Current time = 0.58 Current time = 0.6 Current time = 0.62 Current time = 0.64 Current time = 0.66 Current time = 0.68 Current time = 0.7 Current time = 0.72 Current time = 0.74 Current time = 0.76 Current time = 0.78 Current time = 0.8 Current time = 0.82 Current time = 0.84 Current time = 0.86 Current time = 0.88 Current time = 0.9 Current time = 0.92 Current time = 0.94 Current time = 0.96 Current time = 0.98 Current time = 1 Current time = 1.02 Current time = 1.04 Current time = 1.06 Current time = 1.08 Current time = 1.1 Current time = 1.12 Current time = 1.14 Current time = 1.16 Current time = 1.18 Current time = 1.2 Current time = 1.22 Current time = 1.24 Current time = 1.26 Current time = 1.28 Current time = 1.3 Current time = 1.32 Current time = 1.34 Current time = 1.36 Current time = 1.38 Current time = 1.4 Current time = 1.42 Current time = 1.44 Current time = 1.46 Current time = 1.48 Current time = 1.5 Current time = 1.52 Current time = 1.54 Current time = 1.56 Current time = 1.58 Current time = 1.6 Current time = 1.62 Current time = 1.64 Current time = 1.66 Current time = 1.68 Current time = 1.7 Current time = 1.72 Current time = 1.74 Current time = 1.76 Current time = 1.78 Current time = 1.8 Current time = 1.82 Current time = 1.84 Current time = 1.86 Current time = 1.88 Current time = 1.9 Current time = 1.92 Current time = 1.94 Current time = 1.96 Current time = 1.98 Current time = 2 Current time = 2.02 Current time = 2.04 Current time = 2.06 Current time = 2.08 Current time = 2.1 Current time = 2.12 Current time = 2.14 Current time = 2.16 Current time = 2.18 Current time = 2.2 Current time = 2.22 Current time = 2.24 Current time = 2.26 Current time = 2.28 Current time = 2.3 Current time = 2.32 Current time = 2.34 Current time = 2.36 Current time = 2.38 Current time = 2.4 Current time = 2.42 Current time = 2.44 Current time = 2.46 Current time = 2.48 Current time = 2.5 Current time = 2.52 Current time = 2.54 Current time = 2.56 Current time = 2.58 Current time = 2.6 Current time = 2.62 Current time = 2.64 Current time = 2.66 Current time = 2.68 Current time = 2.7 Current time = 2.72 Current time = 2.74 Current time = 2.76 Current time = 2.78 Current time = 2.8 Current time = 2.82 Current time = 2.84 Current time = 2.86 Current time = 2.88 Current time = 2.9 Current time = 2.92 Current time = 2.94 Current time = 2.96 Current time = 2.98 Current time = 3 Current time = 3.02 Current time = 3.04 Current time = 3.06 Current time = 3.08 Current time = 3.1 Current time = 3.12 Current time = 3.14 Current time = 3.16 Current time = 3.18 Current time = 3.2 Current time = 3.22 Current time = 3.24 Current time = 3.26 Current time = 3.28 Current time = 3.3 Current time = 3.32 Current time = 3.34 Current time = 3.36 Current time = 3.38 Current time = 3.4 Current time = 3.42 Current time = 3.44 Current time = 3.46 Current time = 3.48 Current time = 3.5 Current time = 3.52 Current time = 3.54 Current time = 3.56 Current time = 3.58 Current time = 3.6 Current time = 3.62 Current time = 3.64 Current time = 3.66 Current time = 3.68 Current time = 3.7 Current time = 3.72 Current time = 3.74 Current time = 3.76 Current time = 3.78 Current time = 3.8 Current time = 3.82 Current time = 3.84 Current time = 3.86 Current time = 3.88 Current time = 3.9 Current time = 3.92 Current time = 3.94 Current time = 3.96 Current time = 3.98 Current time = 4 Current time = 4.02 Current time = 4.04 Current time = 4.06 Current time = 4.08 Current time = 4.1 Current time = 4.12 Current time = 4.14 Current time = 4.16 Current time = 4.18 Current time = 4.2 Current time = 4.22 Current time = 4.24 Current time = 4.26 Current time = 4.28 Current time = 4.3 Current time = 4.32 Current time = 4.34 Current time = 4.36 Current time = 4.38 Current time = 4.4 Current time = 4.42 Current time = 4.44 Current time = 4.46 Current time = 4.48 Current time = 4.5 Current time = 4.52 Current time = 4.54 Current time = 4.56 Current time = 4.58 Current time = 4.6 Current time = 4.62 Current time = 4.64 Current time = 4.66 Current time = 4.68 Current time = 4.7 Current time = 4.72 Current time = 4.74 Current time = 4.76 Current time = 4.78 Current time = 4.8 Current time = 4.82 Current time = 4.84 Current time = 4.86 Current time = 4.88 Current time = 4.9 Current time = 4.92 Current time = 4.94 Current time = 4.96 Current time = 4.98 Current time = 5 Current time = 5.02 Current time = 5.04 Current time = 5.06 Current time = 5.08 Current time = 5.1 Current time = 5.12 Current time = 5.14 Current time = 5.16 Current time = 5.18 Current time = 5.2 Current time = 5.22 Current time = 5.24 Current time = 5.26 Current time = 5.28 Current time = 5.3 Current time = 5.32 Current time = 5.34 Current time = 5.36 Current time = 5.38 Current time = 5.4 Current time = 5.42 Current time = 5.44 Current time = 5.46 Current time = 5.48 Current time = 5.5 Current time = 5.52 Current time = 5.54 Current time = 5.56 Current time = 5.58 Current time = 5.6 Current time = 5.62 Current time = 5.64 Current time = 5.66 Current time = 5.68 Current time = 5.7 Current time = 5.72 Current time = 5.74 Current time = 5.76 Current time = 5.78 Current time = 5.8 Current time = 5.82 Current time = 5.84 Current time = 5.86 Current time = 5.88 Current time = 5.9 Current time = 5.92 Current time = 5.94 Current time = 5.96 Current time = 5.98 Current time = 6 Current time = 6.02 Current time = 6.04 Current time = 6.06 Current time = 6.08 Current time = 6.1 Current time = 6.12 Current time = 6.14 Current time = 6.16 Current time = 6.18 Current time = 6.2 Current time = 6.22 Current time = 6.24 Current time = 6.26 Current time = 6.28 Current time = 6.3 Current time = 6.32 Current time = 6.34 Current time = 6.36 Current time = 6.38 Current time = 6.4 Current time = 6.42 Current time = 6.44 Current time = 6.46 Current time = 6.48 Current time = 6.5 Current time = 6.52 Current time = 6.54 Current time = 6.56 Current time = 6.58 Current time = 6.6 Current time = 6.62 Current time = 6.64 Current time = 6.66 Current time = 6.68 Current time = 6.7 Current time = 6.72 Current time = 6.74 Current time = 6.76 Current time = 6.78 Current time = 6.8 Current time = 6.82 Current time = 6.84 Current time = 6.86 Current time = 6.88 Current time = 6.9 Current time = 6.92 Current time = 6.94 Current time = 6.96 Current time = 6.98 Current time = 7 Current time = 7.02 Current time = 7.04 Current time = 7.06 Current time = 7.08 Current time = 7.1 Current time = 7.12 Current time = 7.14 Current time = 7.16 Current time = 7.18 Current time = 7.2 Current time = 7.22 Current time = 7.24 Current time = 7.26 Current time = 7.28 Current time = 7.3 Current time = 7.32 Current time = 7.34 Current time = 7.36 Current time = 7.38 Current time = 7.4 Current time = 7.42 Current time = 7.44 Current time = 7.46 Current time = 7.48 Current time = 7.5 Current time = 7.52 Current time = 7.54 Current time = 7.56 Current time = 7.58 Current time = 7.6 Current time = 7.62 Current time = 7.64 Current time = 7.66 Current time = 7.68 Current time = 7.7 Current time = 7.72 Current time = 7.74 Current time = 7.76 Current time = 7.78 Current time = 7.8 Current time = 7.82 Current time = 7.84 Current time = 7.86 Current time = 7.88 Current time = 7.9 Current time = 7.92 Current time = 7.94 Current time = 7.96 Current time = 7.98 Current time = 8 Current time = 8.02 Current time = 8.04 Current time = 8.06 Current time = 8.08 Current time = 8.1 Current time = 8.12 Current time = 8.14 Current time = 8.16 Current time = 8.18 Current time = 8.2 Current time = 8.22 Current time = 8.24 Current time = 8.26 Current time = 8.28 Current time = 8.3 Current time = 8.32 Current time = 8.34 Current time = 8.36 Current time = 8.38 Current time = 8.4 Current time = 8.42 Current time = 8.44 Current time = 8.46 Current time = 8.48 Current time = 8.5 Current time = 8.52 Current time = 8.54 Current time = 8.56 Current time = 8.58 Current time = 8.6 Current time = 8.62 Current time = 8.64 Current time = 8.66 Current time = 8.68 Current time = 8.7 Current time = 8.72 Current time = 8.74 Current time = 8.76 Current time = 8.78 Current time = 8.8 Current time = 8.82 Current time = 8.84 Current time = 8.86 Current time = 8.88 Current time = 8.9 Current time = 8.92 Current time = 8.94 Current time = 8.96 Current time = 8.98 Current time = 9 Current time = 9.02 Current time = 9.04 Current time = 9.06 Current time = 9.08 Current time = 9.1 Current time = 9.12 Current time = 9.14 Current time = 9.16 Current time = 9.18 Current time = 9.2 Current time = 9.22 Current time = 9.24 Current time = 9.26 Current time = 9.28 Current time = 9.3 Current time = 9.32 Current time = 9.34 Current time = 9.36 Current time = 9.38 Current time = 9.4 Current time = 9.42 Current time = 9.44 Current time = 9.46 Current time = 9.48 Current time = 9.5 Current time = 9.52 Current time = 9.54 Current time = 9.56 Current time = 9.58 Current time = 9.6 Current time = 9.62 Current time = 9.64 Current time = 9.66 Current time = 9.68 Current time = 9.7 Current time = 9.72 Current time = 9.74 Current time = 9.76 Current time = 9.78 Current time = 9.8 Current time = 9.82 Current time = 9.84 Current time = 9.86 Current time = 9.88 Current time = 9.9 Current time = 9.92 Current time = 9.94 Current time = 9.96 Current time = 9.98 Current time = 10 Current time = 10.02 Current time = 10.04 Current time = 10.06 Current time = 10.08 Current time = 10.1 Current time = 10.12 Current time = 10.14 Current time = 10.16 Current time = 10.18 Current time = 10.2 Current time = 10.22 Current time = 10.24 Current time = 10.26 Current time = 10.28 Current time = 10.3 Current time = 10.32 Current time = 10.34 Current time = 10.36 Current time = 10.38 Current time = 10.4 Current time = 10.42 Current time = 10.44 Current time = 10.46 Current time = 10.48 Current time = 10.5 Current time = 10.52 Current time = 10.54 Current time = 10.56 Current time = 10.58 Current time = 10.6 Current time = 10.62 Current time = 10.64 Current time = 10.66 Current time = 10.68 Current time = 10.7 Current time = 10.72 Current time = 10.74 Current time = 10.76 Current time = 10.78 Current time = 10.8 Current time = 10.82 Current time = 10.84 Current time = 10.86 Current time = 10.88 Current time = 10.9 Current time = 10.92 Current time = 10.94 Current time = 10.96 Current time = 10.98 Current time = 11 Current time = 11.02 Current time = 11.04 Current time = 11.06 Current time = 11.08 Current time = 11.1 Current time = 11.12 Current time = 11.14 Current time = 11.16 Current time = 11.18 Current time = 11.2 Current time = 11.22 Current time = 11.24 Current time = 11.26 Current time = 11.28 Current time = 11.3 Current time = 11.32 Current time = 11.34 Current time = 11.36 Current time = 11.38 Current time = 11.4 Current time = 11.42 Current time = 11.44 Current time = 11.46 Current time = 11.48 Current time = 11.5 Current time = 11.52 Current time = 11.54 Current time = 11.56 Current time = 11.58 Current time = 11.6 Current time = 11.62 Current time = 11.64 Current time = 11.66 Current time = 11.68 Current time = 11.7 Current time = 11.72 Current time = 11.74 Current time = 11.76 Current time = 11.78 Current time = 11.8 Current time = 11.82 Current time = 11.84 Current time = 11.86 Current time = 11.88 Current time = 11.9 Current time = 11.92 Current time = 11.94 Current time = 11.96 Current time = 11.98 Current time = 12 Current time = 12.02 Current time = 12.04 Current time = 12.06 Current time = 12.08 Current time = 12.1 Current time = 12.12 Current time = 12.14 Current time = 12.16 Current time = 12.18 Current time = 12.2 Current time = 12.22 Current time = 12.24 Current time = 12.26 Current time = 12.28 Current time = 12.3 Current time = 12.32 Current time = 12.34 Current time = 12.36 Current time = 12.38 Current time = 12.4 Current time = 12.42 Current time = 12.44 Current time = 12.46 Current time = 12.48 Current time = 12.5 Current time = 12.52 Current time = 12.54 Current time = 12.56 Current time = 12.58 Current time = 12.6 Current time = 12.62 Current time = 12.64 Current time = 12.66 Current time = 12.68 Current time = 12.7 Current time = 12.72 Current time = 12.74 Current time = 12.76 Current time = 12.78 Current time = 12.8 Current time = 12.82 Current time = 12.84 Current time = 12.86 Current time = 12.88 Current time = 12.9 Current time = 12.92 Current time = 12.94 Current time = 12.96 Current time = 12.98 Current time = 13 Current time = 13.02 Current time = 13.04 Current time = 13.06 Current time = 13.08 Current time = 13.1 Current time = 13.12 Current time = 13.14 Current time = 13.16 Current time = 13.18 Current time = 13.2 Current time = 13.22 Current time = 13.24 Current time = 13.26 Current time = 13.28 Current time = 13.3 Current time = 13.32 Current time = 13.34 Current time = 13.36 Current time = 13.38 Current time = 13.4 Current time = 13.42 Current time = 13.44 Current time = 13.46 Current time = 13.48 Current time = 13.5 Current time = 13.52 Current time = 13.54 Current time = 13.56 Current time = 13.58 Current time = 13.6 Current time = 13.62 Current time = 13.64 Current time = 13.66 Current time = 13.68 Current time = 13.7 Current time = 13.72 Current time = 13.74 Current time = 13.76 Current time = 13.78 Current time = 13.8 Current time = 13.82 Current time = 13.84 Current time = 13.86 Current time = 13.88 Current time = 13.9 Current time = 13.92 Current time = 13.94 Current time = 13.96 Current time = 13.98 Current time = 14 Current time = 14.02 Current time = 14.04 Current time = 14.06 Current time = 14.08 Current time = 14.1 Current time = 14.12 Current time = 14.14 Current time = 14.16 Current time = 14.18 Current time = 14.2 Current time = 14.22 Current time = 14.24 Current time = 14.26 Current time = 14.28 Current time = 14.3 Current time = 14.32 Current time = 14.34 Current time = 14.36 Current time = 14.38 Current time = 14.4 Current time = 14.42 Current time = 14.44 Current time = 14.46 Current time = 14.48 Current time = 14.5 Current time = 14.52 Current time = 14.54 Current time = 14.56 Current time = 14.58 Current time = 14.6 Current time = 14.62 Current time = 14.64 Current time = 14.66 Current time = 14.68 Current time = 14.7 Current time = 14.72 Current time = 14.74 Current time = 14.76 Current time = 14.78 Current time = 14.8 Current time = 14.82 Current time = 14.84 Current time = 14.86 Current time = 14.88 Current time = 14.9 Current time = 14.92 Current time = 14.94 Current time = 14.96 Current time = 14.98 Current time = 15 Current time = 15.02 Current time = 15.04 Current time = 15.06 Current time = 15.08 Current time = 15.1 Current time = 15.12 Current time = 15.14 Current time = 15.16 Current time = 15.18 Current time = 15.2 Current time = 15.22 Current time = 15.24 Current time = 15.26 Current time = 15.28 Current time = 15.3 Current time = 15.32 Current time = 15.34 Current time = 15.36 Current time = 15.38 Current time = 15.4 Current time = 15.42 Current time = 15.44 Current time = 15.46 Current time = 15.48 Current time = 15.5 Current time = 15.52 Current time = 15.54 Current time = 15.56 Current time = 15.58 Current time = 15.6 Current time = 15.62 Current time = 15.64 Current time = 15.66 Current time = 15.68 Current time = 15.7 Current time = 15.72 Current time = 15.74 Current time = 15.76 Current time = 15.78 Current time = 15.8 Current time = 15.82 Current time = 15.84 Current time = 15.86 Current time = 15.88 Current time = 15.9 Current time = 15.92 Current time = 15.94 Current time = 15.96 Current time = 15.98 Current time = 16 Current time = 16.02 Current time = 16.04 Current time = 16.06 Current time = 16.08 Current time = 16.1 Current time = 16.12 Current time = 16.14 Current time = 16.16 Current time = 16.18 Current time = 16.2 Current time = 16.22 Current time = 16.24 Current time = 16.26 Current time = 16.28 Current time = 16.3 Current time = 16.32 Current time = 16.34 Current time = 16.36 Current time = 16.38 Current time = 16.4 Current time = 16.42 Current time = 16.44 Current time = 16.46 Current time = 16.48 Current time = 16.5 Current time = 16.52 Current time = 16.54 Current time = 16.56 Current time = 16.58 Current time = 16.6 Current time = 16.62 Current time = 16.64 Current time = 16.66 Current time = 16.68 Current time = 16.7 Current time = 16.72 Current time = 16.74 Current time = 16.76 Current time = 16.78 Current time = 16.8 Current time = 16.82 Current time = 16.84 Current time = 16.86 Current time = 16.88 Current time = 16.9 Current time = 16.92 Current time = 16.94 Current time = 16.96 Current time = 16.98 Current time = 17 Current time = 17.02 Current time = 17.04 Current time = 17.06 Current time = 17.08 Current time = 17.1 Current time = 17.12 Current time = 17.14 Current time = 17.16 Current time = 17.18 Current time = 17.2 Current time = 17.22 Current time = 17.24 Current time = 17.26 Current time = 17.28 Current time = 17.3 Current time = 17.32 Current time = 17.34 Current time = 17.36 Current time = 17.38 Current time = 17.4 Current time = 17.42 Current time = 17.44 Current time = 17.46 Current time = 17.48 Current time = 17.5 Current time = 17.52 Current time = 17.54 Current time = 17.56 Current time = 17.58 Current time = 17.6 Current time = 17.62 Current time = 17.64 Current time = 17.66 Current time = 17.68 Current time = 17.7 Current time = 17.72 Current time = 17.74 Current time = 17.76 Current time = 17.78 Current time = 17.8 Current time = 17.82 Current time = 17.84 Current time = 17.86 Current time = 17.88 Current time = 17.9 Current time = 17.92 Current time = 17.94 Current time = 17.96 Current time = 17.98 Current time = 18 Current time = 18.02 Current time = 18.04 Current time = 18.06 Current time = 18.08 Current time = 18.1 Current time = 18.12 Current time = 18.14 Current time = 18.16 Current time = 18.18 Current time = 18.2 Current time = 18.22 Current time = 18.24 Current time = 18.26 Current time = 18.28 Current time = 18.3 Current time = 18.32 Current time = 18.34 Current time = 18.36 Current time = 18.38 Current time = 18.4 Current time = 18.42 Current time = 18.44 Current time = 18.46 Current time = 18.48 Current time = 18.5 Current time = 18.52 Current time = 18.54 Current time = 18.56 Current time = 18.58 Current time = 18.6 Current time = 18.62 Current time = 18.64 Current time = 18.66 Current time = 18.68 Current time = 18.7 Current time = 18.72 Current time = 18.74 Current time = 18.76 Current time = 18.78 Current time = 18.8 Current time = 18.82 Current time = 18.84 Current time = 18.86 Current time = 18.88 Current time = 18.9 Current time = 18.92 Current time = 18.94 Current time = 18.96 Current time = 18.98 Current time = 19 Current time = 19.02 Current time = 19.04 Current time = 19.06 Current time = 19.08 Current time = 19.1 Current time = 19.12 Current time = 19.14 Current time = 19.16 Current time = 19.18 Current time = 19.2 Current time = 19.22 Current time = 19.24 Current time = 19.26 Current time = 19.28 Current time = 19.3 Current time = 19.32 Current time = 19.34 Current time = 19.36 Current time = 19.38 Current time = 19.4 Current time = 19.42 Current time = 19.44 Current time = 19.46 Current time = 19.48 Current time = 19.5 Current time = 19.52 Current time = 19.54 Current time = 19.56 Current time = 19.58 Current time = 19.6 Current time = 19.62 Current time = 19.64 Current time = 19.66 Current time = 19.68 Current time = 19.7 Current time = 19.72 Current time = 19.74 Current time = 19.76 Current time = 19.78 Current time = 19.8 Current time = 19.82 Current time = 19.84 Current time = 19.86 Current time = 19.88 Current time = 19.9 Current time = 19.92 Current time = 19.94 Current time = 19.96 Current time = 19.98 Current time = 20 Current time = 20.02 Current time = 20.04 Current time = 20.06 Current time = 20.08 Current time = 20.1 Current time = 20.12 Current time = 20.14 Current time = 20.16 Current time = 20.18 Current time = 20.2 Current time = 20.22 Current time = 20.24 Current time = 20.26 Current time = 20.28 Current time = 20.3 Current time = 20.32 Current time = 20.34 Current time = 20.36 Current time = 20.38 Current time = 20.4 Current time = 20.42 Current time = 20.44 Current time = 20.46 Current time = 20.48 Current time = 20.5 Current time = 20.52 Current time = 20.54 Current time = 20.56 Current time = 20.58 Current time = 20.6 Current time = 20.62 Current time = 20.64 Current time = 20.66 Current time = 20.68 Current time = 20.7 Current time = 20.72 Current time = 20.74 Current time = 20.76 Current time = 20.78 Current time = 20.8 Current time = 20.82 Current time = 20.84 Current time = 20.86 Current time = 20.88 Current time = 20.9 Current time = 20.92 Current time = 20.94 Current time = 20.96 Current time = 20.98 Current time = 21 Current time = 21.02 Current time = 21.04 Current time = 21.06 Current time = 21.08 Current time = 21.1 Current time = 21.12 Current time = 21.14 Current time = 21.16 Current time = 21.18 Current time = 21.2 Current time = 21.22 Current time = 21.24 Current time = 21.26 Current time = 21.28 Current time = 21.3 Current time = 21.32 Current time = 21.34 Current time = 21.36 Current time = 21.38 Current time = 21.4 Current time = 21.42 Current time = 21.44 Current time = 21.46 Current time = 21.48 Current time = 21.5 Current time = 21.52 Current time = 21.54 Current time = 21.56 Current time = 21.58 Current time = 21.6 Current time = 21.62 Current time = 21.64 Current time = 21.66 Current time = 21.68 Current time = 21.7 Current time = 21.72 Current time = 21.74 Current time = 21.76 Current time = 21.78 Current time = 21.8 Current time = 21.82 Current time = 21.84 Current time = 21.86 Current time = 21.88 Current time = 21.9 Current time = 21.92 Current time = 21.94 Current time = 21.96 Current time = 21.98 Current time = 22 Current time = 22.02 Current time = 22.04 Current time = 22.06 Current time = 22.08 Current time = 22.1 Current time = 22.12 Current time = 22.14 Current time = 22.16 Current time = 22.18 Current time = 22.2 Current time = 22.22 Current time = 22.24 Current time = 22.26 Current time = 22.28 Current time = 22.3 Current time = 22.32 Current time = 22.34 Current time = 22.36 Current time = 22.38 Current time = 22.4 Current time = 22.42 Current time = 22.44 Current time = 22.46 Current time = 22.48 Current time = 22.5 Current time = 22.52 Current time = 22.54 Current time = 22.56 Current time = 22.58 Current time = 22.6 Current time = 22.62 Current time = 22.64 Current time = 22.66 Current time = 22.68 Current time = 22.7 Current time = 22.72 Current time = 22.74 Current time = 22.76 Current time = 22.78 Current time = 22.8 Current time = 22.82 Current time = 22.84 Current time = 22.86 Current time = 22.88 Current time = 22.9 Current time = 22.92 Current time = 22.94 Current time = 22.96 Current time = 22.98 Current time = 23 Current time = 23.02 Current time = 23.04 Current time = 23.06 Current time = 23.08 Current time = 23.1 Current time = 23.12 Current time = 23.14 Current time = 23.16 Current time = 23.18 Current time = 23.2 Current time = 23.22 Current time = 23.24 Current time = 23.26 Current time = 23.28 Current time = 23.3 Current time = 23.32 Current time = 23.34 Current time = 23.36 Current time = 23.38 Current time = 23.4 Current time = 23.42 Current time = 23.44 Current time = 23.46 Current time = 23.48 Current time = 23.5 Current time = 23.52 Current time = 23.54 Current time = 23.56 Current time = 23.58 Current time = 23.6 Current time = 23.62 Current time = 23.64 Current time = 23.66 Current time = 23.68 Current time = 23.7 Current time = 23.72 Current time = 23.74 Current time = 23.76 Current time = 23.78 Current time = 23.8 Current time = 23.82 Current time = 23.84 Current time = 23.86 Current time = 23.88 Current time = 23.9 Current time = 23.92 Current time = 23.94 Current time = 23.96 Current time = 23.98 Current time = 24 Current time = 24.02 Current time = 24.04 Current time = 24.06 Current time = 24.08 Current time = 24.1 Current time = 24.12 Current time = 24.14 Current time = 24.16 Current time = 24.18 Current time = 24.2 Current time = 24.22 Current time = 24.24 Current time = 24.26 Current time = 24.28 Current time = 24.3 Current time = 24.32 Current time = 24.34 Current time = 24.36 Current time = 24.38 Current time = 24.4 Current time = 24.42 Current time = 24.44 Current time = 24.46 Current time = 24.48 Current time = 24.5 Current time = 24.52 Current time = 24.54 Current time = 24.56 Current time = 24.58 Current time = 24.6 Current time = 24.62 Current time = 24.64 Current time = 24.66 Current time = 24.68 Current time = 24.7 Current time = 24.72 Current time = 24.74 Current time = 24.76 Current time = 24.78 Current time = 24.8 Current time = 24.82 Current time = 24.84 Current time = 24.86 Current time = 24.88 Current time = 24.9 Current time = 24.92 Current time = 24.94 Current time = 24.96 Current time = 24.98 Current time = 25 Current time = 25.02 Current time = 25.04 Current time = 25.06 Current time = 25.08 Current time = 25.1 Current time = 25.12 Current time = 25.14 Current time = 25.16 Current time = 25.18 Current time = 25.2 Current time = 25.22 Current time = 25.24 Current time = 25.26 Current time = 25.28 Current time = 25.3 Current time = 25.32 Current time = 25.34 Current time = 25.36 Current time = 25.38 Current time = 25.4 Current time = 25.42 Current time = 25.44 Current time = 25.46 Current time = 25.48 Current time = 25.5 Current time = 25.52 Current time = 25.54 Current time = 25.56 Current time = 25.58 Current time = 25.6 Current time = 25.62 Current time = 25.64 Current time = 25.66 Current time = 25.68 Current time = 25.7 Current time = 25.72 Current time = 25.74 Current time = 25.76 Current time = 25.78 Current time = 25.8 Current time = 25.82 Current time = 25.84 Current time = 25.86 Current time = 25.88 Current time = 25.9 Current time = 25.92 Current time = 25.94 Current time = 25.96 Current time = 25.98 Current time = 26 Current time = 26.02 Current time = 26.04 Current time = 26.06 Current time = 26.08 Current time = 26.1 Current time = 26.12 Current time = 26.14 Current time = 26.16 Current time = 26.18 Current time = 26.2 Current time = 26.22 Current time = 26.24 Current time = 26.26 Current time = 26.28 Current time = 26.3 Current time = 26.32 Current time = 26.34 Current time = 26.36 Current time = 26.38 Current time = 26.4 Current time = 26.42 Current time = 26.44 Current time = 26.46 Current time = 26.48 Current time = 26.5 Current time = 26.52 Current time = 26.54 Current time = 26.56 Current time = 26.58 Current time = 26.6 Current time = 26.62 Current time = 26.64 Current time = 26.66 Current time = 26.68 Current time = 26.7 Current time = 26.72 Current time = 26.74 Current time = 26.76 Current time = 26.78 Current time = 26.8 Current time = 26.82 Current time = 26.84 Current time = 26.86 Current time = 26.88 Current time = 26.9 Current time = 26.92 Current time = 26.94 Current time = 26.96 Current time = 26.98 Current time = 27 Current time = 27.02 Current time = 27.04 Current time = 27.06 Current time = 27.08 Current time = 27.1 Current time = 27.12 Current time = 27.14 Current time = 27.16 Current time = 27.18 Current time = 27.2 Current time = 27.22 Current time = 27.24 Current time = 27.26 Current time = 27.28 Current time = 27.3 Current time = 27.32 Current time = 27.34 Current time = 27.36 Current time = 27.38 Current time = 27.4 Current time = 27.42 Current time = 27.44 Current time = 27.46 Current time = 27.48 Current time = 27.5 Current time = 27.52 Current time = 27.54 Current time = 27.56 Current time = 27.58 Current time = 27.6 Current time = 27.62 Current time = 27.64 Current time = 27.66 Current time = 27.68 Current time = 27.7 Current time = 27.72 Current time = 27.74 Current time = 27.76 Current time = 27.78 Current time = 27.8 Current time = 27.82 Current time = 27.84 Current time = 27.86 Current time = 27.88 Current time = 27.9 Current time = 27.92 Current time = 27.94 Current time = 27.96 Current time = 27.98 Current time = 28 Current time = 28.02 Current time = 28.04 Current time = 28.06 Current time = 28.08 Current time = 28.1 Current time = 28.12 Current time = 28.14 Current time = 28.16 Current time = 28.18 Current time = 28.2 Current time = 28.22 Current time = 28.24 Current time = 28.26 Current time = 28.28 Current time = 28.3 Current time = 28.32 Current time = 28.34 Current time = 28.36 Current time = 28.38 Current time = 28.4 Current time = 28.42 Current time = 28.44 Current time = 28.46 Current time = 28.48 Current time = 28.5 Current time = 28.52 Current time = 28.54 Current time = 28.56 Current time = 28.58 Current time = 28.6 Current time = 28.62 Current time = 28.64 Current time = 28.66 Current time = 28.68 Current time = 28.7 Current time = 28.72 Current time = 28.74 Current time = 28.76 Current time = 28.78 Current time = 28.8 Current time = 28.82 Current time = 28.84 Current time = 28.86 Current time = 28.88 Current time = 28.9 Current time = 28.92 Current time = 28.94 Current time = 28.96 Current time = 28.98 Current time = 29 Current time = 29.02 Current time = 29.04 Current time = 29.06 Current time = 29.08 Current time = 29.1 Current time = 29.12 Current time = 29.14 Current time = 29.16 Current time = 29.18 Current time = 29.2 Current time = 29.22 Current time = 29.24 Current time = 29.26 Current time = 29.28 Current time = 29.3 Current time = 29.32 Current time = 29.34 Current time = 29.36 Current time = 29.38 Current time = 29.4 Current time = 29.42 Current time = 29.44 Current time = 29.46 Current time = 29.48 Current time = 29.5 Current time = 29.52 Current time = 29.54 Current time = 29.56 Current time = 29.58 Current time = 29.6 Current time = 29.62 Current time = 29.64 Current time = 29.66 Current time = 29.68 Current time = 29.7 Current time = 29.72 Current time = 29.74 Current time = 29.76 Current time = 29.78 Current time = 29.8 Current time = 29.82 Current time = 29.84 Current time = 29.86 Current time = 29.88 Current time = 29.9 Current time = 29.92 Current time = 29.94 Current time = 29.96 Current time = 29.98 Current time = 30 Current time = 30.02 Current time = 30.04 Current time = 30.06 Current time = 30.08 Current time = 30.1 Current time = 30.12 Current time = 30.14 Current time = 30.16 Current time = 30.18 Current time = 30.2 Current time = 30.22 Current time = 30.24 Current time = 30.26 Current time = 30.28 Current time = 30.3 Current time = 30.32 Current time = 30.34 Current time = 30.36 Current time = 30.38 Current time = 30.4 Current time = 30.42 Current time = 30.44 Current time = 30.46 Current time = 30.48 Current time = 30.5 Current time = 30.52 Current time = 30.54 Current time = 30.56 Current time = 30.58 Current time = 30.6 Current time = 30.62 Current time = 30.64 Current time = 30.66 Current time = 30.68 Current time = 30.7 Current time = 30.72 Current time = 30.74 Current time = 30.76 Current time = 30.78 Current time = 30.8 Current time = 30.82 Current time = 30.84 Current time = 30.86 Current time = 30.88 Current time = 30.9 Current time = 30.92 Current time = 30.94 Current time = 30.96 Current time = 30.98 Current time = 31 Current time = 31.02 Current time = 31.04 Current time = 31.06 Current time = 31.08 Current time = 31.1 Current time = 31.12 Current time = 31.14 Current time = 31.16 Current time = 31.18 Current time = 31.2 Current time = 31.22 Current time = 31.24 Current time = 31.26 Current time = 31.28 Current time = 31.3 Current time = 31.32 Current time = 31.34 Current time = 31.36 Current time = 31.38 Current time = 31.4 Current time = 31.42 Current time = 31.44 Current time = 31.46 Current time = 31.48 Current time = 31.5 Current time = 31.52 Current time = 31.54 Current time = 31.56 Current time = 31.58 Current time = 31.6 Current time = 31.62 Current time = 31.64 Current time = 31.66 Current time = 31.68 Current time = 31.7 Current time = 31.72 Current time = 31.74 Current time = 31.76 Current time = 31.78 Current time = 31.8 Current time = 31.82 Current time = 31.84 Current time = 31.86 Current time = 31.88 Current time = 31.9 Current time = 31.92 Current time = 31.94 Current time = 31.96 Current time = 31.98 Current time = 32 Current time = 32.02 Current time = 32.04 Current time = 32.06 Current time = 32.08 Current time = 32.1 Current time = 32.12 Current time = 32.14 Current time = 32.16 Current time = 32.18 Current time = 32.2 Current time = 32.22 Current time = 32.24 Current time = 32.26 Current time = 32.28 Current time = 32.3 Current time = 32.32 Current time = 32.34 Current time = 32.36 Current time = 32.38 Current time = 32.4 Current time = 32.42 Current time = 32.44 Current time = 32.46 Current time = 32.48 Current time = 32.5 Current time = 32.52 Current time = 32.54 Current time = 32.56 Current time = 32.58 Current time = 32.6 Current time = 32.62 Current time = 32.64 Current time = 32.66 Current time = 32.68 Current time = 32.7 Current time = 32.72 Current time = 32.74 Current time = 32.76 Current time = 32.78 Current time = 32.8 Current time = 32.82 Current time = 32.84 Current time = 32.86 Current time = 32.88 Current time = 32.9 Current time = 32.92 Current time = 32.94 Current time = 32.96 Current time = 32.98 Current time = 33 Current time = 33.02 Current time = 33.04 Current time = 33.06 Current time = 33.08 Current time = 33.1 Current time = 33.12 Current time = 33.14 Current time = 33.16 Current time = 33.18 Current time = 33.2 Current time = 33.22 Current time = 33.24 Current time = 33.26 Current time = 33.28 Current time = 33.3 Current time = 33.32 Current time = 33.34 Current time = 33.36 Current time = 33.38 Current time = 33.4 Current time = 33.42 Current time = 33.44 Current time = 33.46 Current time = 33.48 Current time = 33.5 Current time = 33.52 Current time = 33.54 Current time = 33.56 Current time = 33.58 Current time = 33.6 Current time = 33.62 Current time = 33.64 Current time = 33.66 Current time = 33.68 Current time = 33.7 Current time = 33.72 Current time = 33.74 Current time = 33.76 Current time = 33.78 Current time = 33.8 Current time = 33.82 Current time = 33.84 Current time = 33.86 Current time = 33.88 Current time = 33.9 Current time = 33.92 Current time = 33.94 Current time = 33.96 Current time = 33.98 Current time = 34 Current time = 34.02 Current time = 34.04 Current time = 34.06 Current time = 34.08 Current time = 34.1 Current time = 34.12 Current time = 34.14 Current time = 34.16 Current time = 34.18 Current time = 34.2 Current time = 34.22 Current time = 34.24 Current time = 34.26 Current time = 34.28 Current time = 34.3 Current time = 34.32 Current time = 34.34 Current time = 34.36 Current time = 34.38 Current time = 34.4 Current time = 34.42 Current time = 34.44 Current time = 34.46 Current time = 34.48 Current time = 34.5 Current time = 34.52 Current time = 34.54 Current time = 34.56 Current time = 34.58 Current time = 34.6 Current time = 34.62 Current time = 34.64 Current time = 34.66 Current time = 34.68 Current time = 34.7 Current time = 34.72 Current time = 34.74 Current time = 34.76 Current time = 34.78 Current time = 34.8 Current time = 34.82 Current time = 34.84 Current time = 34.86 Current time = 34.88 Current time = 34.9 Current time = 34.92 Current time = 34.94 Current time = 34.96 Current time = 34.98 Current time = 35 Current time = 35.02 Current time = 35.04 Current time = 35.06 Current time = 35.08 Current time = 35.1 Current time = 35.12 Current time = 35.14 Current time = 35.16 Current time = 35.18 Current time = 35.2 Current time = 35.22 Current time = 35.24 Current time = 35.26 Current time = 35.28 Current time = 35.3 Current time = 35.32 Current time = 35.34 Current time = 35.36 Current time = 35.38 Current time = 35.4 Current time = 35.42 Current time = 35.44 Current time = 35.46 Current time = 35.48 Current time = 35.5 Current time = 35.52 Current time = 35.54 Current time = 35.56 Current time = 35.58 Current time = 35.6 Current time = 35.62 Current time = 35.64 Current time = 35.66 Current time = 35.68 Current time = 35.7 Current time = 35.72 Current time = 35.74 Current time = 35.76 Current time = 35.78 Current time = 35.8 Current time = 35.82 Current time = 35.84 Current time = 35.86 Current time = 35.88 Current time = 35.9 Current time = 35.92 Current time = 35.94 Current time = 35.96 Current time = 35.98 Current time = 36 Current time = 36.02 Current time = 36.04 Current time = 36.06 Current time = 36.08 Current time = 36.1 Current time = 36.12 Current time = 36.14 Current time = 36.16 Current time = 36.18 Current time = 36.2 Current time = 36.22 Current time = 36.24 Current time = 36.26 Current time = 36.28 Current time = 36.3 Current time = 36.32 Current time = 36.34 Current time = 36.36 Current time = 36.38 Current time = 36.4 Current time = 36.42 Current time = 36.44 Current time = 36.46 Current time = 36.48 Current time = 36.5 Current time = 36.52 Current time = 36.54 Current time = 36.56 Current time = 36.58 Current time = 36.6 Current time = 36.62 Current time = 36.64 Current time = 36.66 Current time = 36.68 Current time = 36.7 Current time = 36.72 Current time = 36.74 Current time = 36.76 Current time = 36.78 Current time = 36.8 Current time = 36.82 Current time = 36.84 Current time = 36.86 Current time = 36.88 Current time = 36.9 Current time = 36.92 Current time = 36.94 Current time = 36.96 Current time = 36.98 Current time = 37 Current time = 37.02 Current time = 37.04 Current time = 37.06 Current time = 37.08 Current time = 37.1 Current time = 37.12 Current time = 37.14 Current time = 37.16 Current time = 37.18 Current time = 37.2 Current time = 37.22 Current time = 37.24 Current time = 37.26 Current time = 37.28 Current time = 37.3 Current time = 37.32 Current time = 37.34 Current time = 37.36 Current time = 37.38 Current time = 37.4 Current time = 37.42 Current time = 37.44 Current time = 37.46 Current time = 37.48 Current time = 37.5 Current time = 37.52 Current time = 37.54 Current time = 37.56 Current time = 37.58 Current time = 37.6 Current time = 37.62 Current time = 37.64 Current time = 37.66 Current time = 37.68 Current time = 37.7 Current time = 37.72 Current time = 37.74 Current time = 37.76 Current time = 37.78 Current time = 37.8 Current time = 37.82 Current time = 37.84 Current time = 37.86 Current time = 37.88 Current time = 37.9 Current time = 37.92 Current time = 37.94 Current time = 37.96 Current time = 37.98 Current time = 38 Current time = 38.02 Current time = 38.04 Current time = 38.06 Current time = 38.08 Current time = 38.1 Current time = 38.12 Current time = 38.14 Current time = 38.16 Current time = 38.18 Current time = 38.2 Current time = 38.22 Current time = 38.24 Current time = 38.26 Current time = 38.28 Current time = 38.3 Current time = 38.32 Current time = 38.34 Current time = 38.36 Current time = 38.38 Current time = 38.4 Current time = 38.42 Current time = 38.44 Current time = 38.46 Current time = 38.48 Current time = 38.5 Current time = 38.52 Current time = 38.54 Current time = 38.56 Current time = 38.58 Current time = 38.6 Current time = 38.62 Current time = 38.64 Current time = 38.66 Current time = 38.68 Current time = 38.7 Current time = 38.72 Current time = 38.74 Current time = 38.76 Current time = 38.78 Current time = 38.8 Current time = 38.82 Current time = 38.84 Current time = 38.86 Current time = 38.88 Current time = 38.9 Current time = 38.92 Current time = 38.94 Current time = 38.96 Current time = 38.98 Current time = 39 Current time = 39.02 Current time = 39.04 Current time = 39.06 Current time = 39.08 Current time = 39.1 Current time = 39.12 Current time = 39.14 Current time = 39.16 Current time = 39.18 Current time = 39.2 Current time = 39.22 Current time = 39.24 Current time = 39.26 Current time = 39.28 Current time = 39.3 Current time = 39.32 Current time = 39.34 Current time = 39.36 Current time = 39.38 Current time = 39.4 Current time = 39.42 Current time = 39.44 Current time = 39.46 Current time = 39.48 Current time = 39.5 Current time = 39.52 Current time = 39.54 Current time = 39.56 Current time = 39.58 Current time = 39.6 Current time = 39.62 Current time = 39.64 Current time = 39.66 Current time = 39.68 Current time = 39.7 Current time = 39.72 Current time = 39.74 Current time = 39.76 Current time = 39.78 Current time = 39.8 Current time = 39.82 Current time = 39.84 Current time = 39.86 Current time = 39.88 Current time = 39.9 Current time = 39.92 Current time = 39.94 Current time = 39.96 Current time = 39.98 Current time = 40 Current time = 40.02 Current time = 40.04 Current time = 40.06 Current time = 40.08 Current time = 40.1 Current time = 40.12 Current time = 40.14 Current time = 40.16 Current time = 40.18 Current time = 40.2 Current time = 40.22 Current time = 40.24 Current time = 40.26 Current time = 40.28 Current time = 40.3 Current time = 40.32 Current time = 40.34 Current time = 40.36 Current time = 40.38 Current time = 40.4 Current time = 40.42 Current time = 40.44 Current time = 40.46 Current time = 40.48 Current time = 40.5 Current time = 40.52 Current time = 40.54 Current time = 40.56 Current time = 40.58 Current time = 40.6 Current time = 40.62 Current time = 40.64 Current time = 40.66 Current time = 40.68 Current time = 40.7 Current time = 40.72 Current time = 40.74 Current time = 40.76 Current time = 40.78 Current time = 40.8 Current time = 40.82 Current time = 40.84 Current time = 40.86 Current time = 40.88 Current time = 40.9 Current time = 40.92 Current time = 40.94 Current time = 40.96 Current time = 40.98 Current time = 41 Current time = 41.02 Current time = 41.04 Current time = 41.06 Current time = 41.08 Current time = 41.1 Current time = 41.12 Current time = 41.14 Current time = 41.16 Current time = 41.18 Current time = 41.2 Current time = 41.22 Current time = 41.24 Current time = 41.26 Current time = 41.28 Current time = 41.3 Current time = 41.32 Current time = 41.34 Current time = 41.36 Current time = 41.38 Current time = 41.4 Current time = 41.42 Current time = 41.44 Current time = 41.46 Current time = 41.48 Current time = 41.5 Current time = 41.52 Current time = 41.54 Current time = 41.56 Current time = 41.58 Current time = 41.6 Current time = 41.62 Current time = 41.64 Current time = 41.66 Current time = 41.68 Current time = 41.7 Current time = 41.72 Current time = 41.74 Current time = 41.76 Current time = 41.78 Current time = 41.8 Current time = 41.82 Current time = 41.84 Current time = 41.86 Current time = 41.88 Current time = 41.9 Current time = 41.92 Current time = 41.94 Current time = 41.96 Current time = 41.98 Current time = 42 Current time = 42.02 Current time = 42.04 Current time = 42.06 Current time = 42.08 Current time = 42.1 Current time = 42.12 Current time = 42.14 Current time = 42.16 Current time = 42.18 Current time = 42.2 Current time = 42.22 Current time = 42.24 Current time = 42.26 Current time = 42.28 Current time = 42.3 Current time = 42.32 Current time = 42.34 Current time = 42.36 Current time = 42.38 Current time = 42.4 Current time = 42.42 Current time = 42.44 Current time = 42.46 Current time = 42.48 Current time = 42.5 Current time = 42.52 Current time = 42.54 Current time = 42.56 Current time = 42.58 Current time = 42.6 Current time = 42.62 Current time = 42.64 Current time = 42.66 Current time = 42.68 Current time = 42.7 Current time = 42.72 Current time = 42.74 Current time = 42.76 Current time = 42.78 Current time = 42.8 Current time = 42.82 Current time = 42.84 Current time = 42.86 Current time = 42.88 Current time = 42.9 Current time = 42.92 Current time = 42.94 Current time = 42.96 Current time = 42.98 Current time = 43 Current time = 43.02 Current time = 43.04 Current time = 43.06 Current time = 43.08 Current time = 43.1 Current time = 43.12 Current time = 43.14 Current time = 43.16 Current time = 43.18 Current time = 43.2 Current time = 43.22 Current time = 43.24 Current time = 43.26 Current time = 43.28 Current time = 43.3 Current time = 43.32 Current time = 43.34 Current time = 43.36 Current time = 43.38 Current time = 43.4 Current time = 43.42 Current time = 43.44 Current time = 43.46 Current time = 43.48 Current time = 43.5 Current time = 43.52 Current time = 43.54 Current time = 43.56 Current time = 43.58 Current time = 43.6 Current time = 43.62 Current time = 43.64 Current time = 43.66 Current time = 43.68 Current time = 43.7 Current time = 43.72 Current time = 43.74 Current time = 43.76 Current time = 43.78 Current time = 43.8 Current time = 43.82 Current time = 43.84 Current time = 43.86 Current time = 43.88 Current time = 43.9 Current time = 43.92 Current time = 43.94 Current time = 43.96 Current time = 43.98 Current time = 44 Current time = 44.02 Current time = 44.04 Current time = 44.06 Current time = 44.08 Current time = 44.1 Current time = 44.12 Current time = 44.14 Current time = 44.16 Current time = 44.18 Current time = 44.2 Current time = 44.22 Current time = 44.24 Current time = 44.26 Current time = 44.28 Current time = 44.3 Current time = 44.32 Current time = 44.34 Current time = 44.36 Current time = 44.38 Current time = 44.4 Current time = 44.42 Current time = 44.44 Current time = 44.46 Current time = 44.48 Current time = 44.5 Current time = 44.52 Current time = 44.54 Current time = 44.56 Current time = 44.58 Current time = 44.6 Current time = 44.62 Current time = 44.64 Current time = 44.66 Current time = 44.68 Current time = 44.7 Current time = 44.72 Current time = 44.74 Current time = 44.76 Current time = 44.78 Current time = 44.8 Current time = 44.82 Current time = 44.84 Current time = 44.86 Current time = 44.88 Current time = 44.9 Current time = 44.92 Current time = 44.94 Current time = 44.96 Current time = 44.98 Current time = 45 Current time = 45.02 Current time = 45.04 Current time = 45.06 Current time = 45.08 Current time = 45.1 Current time = 45.12 Current time = 45.14 Current time = 45.16 Current time = 45.18 Current time = 45.2 Current time = 45.22 Current time = 45.24 Current time = 45.26 Current time = 45.28 Current time = 45.3 Current time = 45.32 Current time = 45.34 Current time = 45.36 Current time = 45.38 Current time = 45.4 Current time = 45.42 Current time = 45.44 Current time = 45.46 Current time = 45.48 Current time = 45.5 Current time = 45.52 Current time = 45.54 Current time = 45.56 Current time = 45.58 Current time = 45.6 Current time = 45.62 Current time = 45.64 Current time = 45.66 Current time = 45.68 Current time = 45.7 Current time = 45.72 Current time = 45.74 Current time = 45.76 Current time = 45.78 Current time = 45.8 Current time = 45.82 Current time = 45.84 Current time = 45.86 Current time = 45.88 Current time = 45.9 Current time = 45.92 Current time = 45.94 Current time = 45.96 Current time = 45.98 Current time = 46 Current time = 46.02 Current time = 46.04 Current time = 46.06 Current time = 46.08 Current time = 46.1 Current time = 46.12 Current time = 46.14 Current time = 46.16 Current time = 46.18 Current time = 46.2 Current time = 46.22 Current time = 46.24 Current time = 46.26 Current time = 46.28 Current time = 46.3 Current time = 46.32 Current time = 46.34 Current time = 46.36 Current time = 46.38 Current time = 46.4 Current time = 46.42 Current time = 46.44 Current time = 46.46 Current time = 46.48 Current time = 46.5 Current time = 46.52 Current time = 46.54 Current time = 46.56 Current time = 46.58 Current time = 46.6 Current time = 46.62 Current time = 46.64 Current time = 46.66 Current time = 46.68 Current time = 46.7 Current time = 46.72 Current time = 46.74 Current time = 46.76 Current time = 46.78 Current time = 46.8 Current time = 46.82 Current time = 46.84 Current time = 46.86 Current time = 46.88 Current time = 46.9 Current time = 46.92 Current time = 46.94 Current time = 46.96 Current time = 46.98 Current time = 47 Current time = 47.02 Current time = 47.04 Current time = 47.06 Current time = 47.08 Current time = 47.1 Current time = 47.12 Current time = 47.14 Current time = 47.16 Current time = 47.18 Current time = 47.2 Current time = 47.22 Current time = 47.24 Current time = 47.26 Current time = 47.28 Current time = 47.3 Current time = 47.32 Current time = 47.34 Current time = 47.36 Current time = 47.38 Current time = 47.4 Current time = 47.42 Current time = 47.44 Current time = 47.46 Current time = 47.48 Current time = 47.5 Current time = 47.52 Current time = 47.54 Current time = 47.56 Current time = 47.58 Current time = 47.6 Current time = 47.62 Current time = 47.64 Current time = 47.66 Current time = 47.68 Current time = 47.7 Current time = 47.72 Current time = 47.74 Current time = 47.76 Current time = 47.78 Current time = 47.8 Current time = 47.82 Current time = 47.84 Current time = 47.86 Current time = 47.88 Current time = 47.9 Current time = 47.92 Current time = 47.94 Current time = 47.96 Current time = 47.98 Current time = 48 Current time = 48.02 Current time = 48.04 Current time = 48.06 Current time = 48.08 Current time = 48.1 Current time = 48.12 Current time = 48.14 Current time = 48.16 Current time = 48.18 Current time = 48.2 Current time = 48.22 Current time = 48.24 Current time = 48.26 Current time = 48.28 Current time = 48.3 Current time = 48.32 Current time = 48.34 Current time = 48.36 Current time = 48.38 Current time = 48.4 Current time = 48.42 Current time = 48.44 Current time = 48.46 Current time = 48.48 Current time = 48.5 Current time = 48.52 Current time = 48.54 Current time = 48.56 Current time = 48.58 Current time = 48.6 Current time = 48.62 Current time = 48.64 Current time = 48.66 Current time = 48.68 Current time = 48.7 Current time = 48.72 Current time = 48.74 Current time = 48.76 Current time = 48.78 Current time = 48.8 Current time = 48.82 Current time = 48.84 Current time = 48.86 Current time = 48.88 Current time = 48.9 Current time = 48.92 Current time = 48.94 Current time = 48.96 Current time = 48.98 Current time = 49 Current time = 49.02 Current time = 49.04 Current time = 49.06 Current time = 49.08 Current time = 49.1 Current time = 49.12 Current time = 49.14 Current time = 49.16 Current time = 49.18 Current time = 49.2 Current time = 49.22 Current time = 49.24 Current time = 49.26 Current time = 49.28 Current time = 49.3 Current time = 49.32 Current time = 49.34 Current time = 49.36 Current time = 49.38 Current time = 49.4 Current time = 49.42 Current time = 49.44 Current time = 49.46 Current time = 49.48 Current time = 49.5 Current time = 49.52 Current time = 49.54 Current time = 49.56 Current time = 49.58 Current time = 49.6 Current time = 49.62 Current time = 49.64 Current time = 49.66 Current time = 49.68 Current time = 49.7 Current time = 49.72 Current time = 49.74 Current time = 49.76 Current time = 49.78 Current time = 49.8 Current time = 49.82 Current time = 49.84 Current time = 49.86 Current time = 49.88 Current time = 49.9 Current time = 49.92 Current time = 49.94 Current time = 49.96 Current time = 49.98 Current time = 50 Current time = 50.02 Current time = 50.04 Current time = 50.06 Current time = 50.08 Current time = 50.1 Current time = 50.12 Current time = 50.14 Current time = 50.16 Current time = 50.18 Current time = 50.2 Current time = 50.22 Current time = 50.24 Current time = 50.26 Current time = 50.28 Current time = 50.3 Current time = 50.32 Current time = 50.34 Current time = 50.36 Current time = 50.38 Current time = 50.4 Current time = 50.42 Current time = 50.44 Current time = 50.46 Current time = 50.48 Current time = 50.5 Current time = 50.52 Current time = 50.54 Current time = 50.56 Current time = 50.58 Current time = 50.6 Current time = 50.62 Current time = 50.64 Current time = 50.66 Current time = 50.68 Current time = 50.7 Current time = 50.72 Current time = 50.74 Current time = 50.76 Current time = 50.78 Current time = 50.8 Current time = 50.82 Current time = 50.84 Current time = 50.86 Current time = 50.88 Current time = 50.9 Current time = 50.92 Current time = 50.94 Current time = 50.96 Current time = 50.98 Current time = 51 Current time = 51.02 Current time = 51.04 Current time = 51.06 Current time = 51.08 Current time = 51.1 Current time = 51.12 Current time = 51.14 Current time = 51.16 Current time = 51.18 Current time = 51.2 Current time = 51.22 Current time = 51.24 Current time = 51.26 Current time = 51.28 Current time = 51.3 Current time = 51.32 Current time = 51.34 Current time = 51.36 Current time = 51.38 Current time = 51.4 Current time = 51.42 Current time = 51.44 Current time = 51.46 Current time = 51.48 Current time = 51.5 Current time = 51.52 Current time = 51.54 Current time = 51.56 Current time = 51.58 Current time = 51.6 Current time = 51.62 Current time = 51.64 Current time = 51.66 Current time = 51.68 Current time = 51.7 Current time = 51.72 Current time = 51.74 Current time = 51.76 Current time = 51.78 Current time = 51.8 Current time = 51.82 Current time = 51.84 Current time = 51.86 Current time = 51.88 Current time = 51.9 Current time = 51.92 Current time = 51.94 Current time = 51.96 Current time = 51.98 Current time = 52 Current time = 52.02 Current time = 52.04 Current time = 52.06 Current time = 52.08 Current time = 52.1 Current time = 52.12 Current time = 52.14 Current time = 52.16 Current time = 52.18 Current time = 52.2 Current time = 52.22 Current time = 52.24 Current time = 52.26 Current time = 52.28 Current time = 52.3 Current time = 52.32 Current time = 52.34 Current time = 52.36 Current time = 52.38 Current time = 52.4 Current time = 52.42 Current time = 52.44 Current time = 52.46 Current time = 52.48 Current time = 52.5 Current time = 52.52 Current time = 52.54 Current time = 52.56 Current time = 52.58 Current time = 52.6 Current time = 52.62 Current time = 52.64 Current time = 52.66 Current time = 52.68 Current time = 52.7 Current time = 52.72 Current time = 52.74 Current time = 52.76 Current time = 52.78 Current time = 52.8 Current time = 52.82 Current time = 52.84 Current time = 52.86 Current time = 52.88 Current time = 52.9 Current time = 52.92 Current time = 52.94 Current time = 52.96 Current time = 52.98 Current time = 53 Current time = 53.02 Current time = 53.04 Current time = 53.06 Current time = 53.08 Current time = 53.1 Current time = 53.12 Current time = 53.14 Current time = 53.16 Current time = 53.18 Current time = 53.2 Current time = 53.22 Current time = 53.24 Current time = 53.26 Current time = 53.28 Current time = 53.3 Current time = 53.32 Current time = 53.34 Current time = 53.36 Current time = 53.38 Current time = 53.4 Current time = 53.42 Current time = 53.44 Current time = 53.46 Current time = 53.48 Current time = 53.5 Current time = 53.52 Current time = 53.54 Current time = 53.56 Current time = 53.58 Current time = 53.6 Current time = 53.62 Current time = 53.64 Current time = 53.66 Current time = 53.68 Current time = 53.7 Current time = 53.72 Current time = 53.74 Current time = 53.76 Current time = 53.78 Current time = 53.8 Current time = 53.82 Current time = 53.84 Current time = 53.86 Current time = 53.88 Current time = 53.9 Current time = 53.92 Current time = 53.94 Current time = 53.96 Current time = 53.98 Current time = 54 Current time = 54.02 Current time = 54.04 Current time = 54.06 Current time = 54.08 Current time = 54.1 Current time = 54.12 Current time = 54.14 Current time = 54.16 Current time = 54.18 Current time = 54.2 Current time = 54.22 Current time = 54.24 Current time = 54.26 Current time = 54.28 Current time = 54.3 Current time = 54.32 Current time = 54.34 Current time = 54.36 Current time = 54.38 Current time = 54.4 Current time = 54.42 Current time = 54.44 Current time = 54.46 Current time = 54.48 Current time = 54.5 Current time = 54.52 Current time = 54.54 Current time = 54.56 Current time = 54.58 Current time = 54.6 Current time = 54.62 Current time = 54.64 Current time = 54.66 Current time = 54.68 Current time = 54.7 Current time = 54.72 Current time = 54.74 Current time = 54.76 Current time = 54.78 Current time = 54.8 Current time = 54.82 Current time = 54.84 Current time = 54.86 Current time = 54.88 Current time = 54.9 Current time = 54.92 Current time = 54.94 Current time = 54.96 Current time = 54.98 Current time = 55 Current time = 55.02 Current time = 55.04 Current time = 55.06 Current time = 55.08 Current time = 55.1 Current time = 55.12 Current time = 55.14 Current time = 55.16 Current time = 55.18 Current time = 55.2 Current time = 55.22 Current time = 55.24 Current time = 55.26 Current time = 55.28 Current time = 55.3 Current time = 55.32 Current time = 55.34 Current time = 55.36 Current time = 55.38 Current time = 55.4 Current time = 55.42 Current time = 55.44 Current time = 55.46 Current time = 55.48 Current time = 55.5 Current time = 55.52 Current time = 55.54 Current time = 55.56 Current time = 55.58 Current time = 55.6 Current time = 55.62 Current time = 55.64 Current time = 55.66 Current time = 55.68 Current time = 55.7 Current time = 55.72 Current time = 55.74 Current time = 55.76 Current time = 55.78 Current time = 55.8 Current time = 55.82 Current time = 55.84 Current time = 55.86 Current time = 55.88 Current time = 55.9 Current time = 55.92 Current time = 55.94 Current time = 55.96 Current time = 55.98 Current time = 56 Current time = 56.02 Current time = 56.04 Current time = 56.06 Current time = 56.08 Current time = 56.1 Current time = 56.12 Current time = 56.14 Current time = 56.16 Current time = 56.18 Current time = 56.2 Current time = 56.22 Current time = 56.24 Current time = 56.26 Current time = 56.28 Current time = 56.3 Current time = 56.32 Current time = 56.34 Current time = 56.36 Current time = 56.38 Current time = 56.4 Current time = 56.42 Current time = 56.44 Current time = 56.46 Current time = 56.48 Current time = 56.5 Current time = 56.52 Current time = 56.54 Current time = 56.56 Current time = 56.58 Current time = 56.6 Current time = 56.62 Current time = 56.64 Current time = 56.66 Current time = 56.68 Current time = 56.7 Current time = 56.72 Current time = 56.74 Current time = 56.76 Current time = 56.78 Current time = 56.8 Current time = 56.82 Current time = 56.84 Current time = 56.86 Current time = 56.88 Current time = 56.9 Current time = 56.92 Current time = 56.94 Current time = 56.96 Current time = 56.98 Current time = 57 Current time = 57.02 Current time = 57.04 Current time = 57.06 Current time = 57.08 Current time = 57.1 Current time = 57.12 Current time = 57.14 Current time = 57.16 Current time = 57.18 Current time = 57.2 Current time = 57.22 Current time = 57.24 Current time = 57.26 Current time = 57.28 Current time = 57.3 Current time = 57.32 Current time = 57.34 Current time = 57.36 Current time = 57.38 Current time = 57.4 Current time = 57.42 Current time = 57.44 Current time = 57.46 Current time = 57.48 Current time = 57.5 Current time = 57.52 Current time = 57.54 Current time = 57.56 Current time = 57.58 Current time = 57.6 Current time = 57.62 Current time = 57.64 Current time = 57.66 Current time = 57.68 Current time = 57.7 Current time = 57.72 Current time = 57.74 Current time = 57.76 Current time = 57.78 Current time = 57.8 Current time = 57.82 Current time = 57.84 Current time = 57.86 Current time = 57.88 Current time = 57.9 Current time = 57.92 Current time = 57.94 Current time = 57.96 Current time = 57.98 Current time = 58 Current time = 58.02 Current time = 58.04 Current time = 58.06 Current time = 58.08 Current time = 58.1 Current time = 58.12 Current time = 58.14 Current time = 58.16 Current time = 58.18 Current time = 58.2 Current time = 58.22 Current time = 58.24 Current time = 58.26 Current time = 58.28 Cur...

figure(1)

plot(xd, yd);

hold on

plot(x, y);

It is supposed to track the desired circular. But the actual x and y trajectories are varying by varying alpha. Can anyone help me with this.

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Answer 1

Sam Chak on 24 Apr 2023

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https://se.mathworks.com/matlabcentral/answers/1952363-track-a-circular-trajectory-by-solving-a-qp-and-using-quadprog-solver-using-clf-approach#answer_1222254

Open in MATLAB Online

Hi @Pallov Anand

Sufficiently increasing the value of alpha

reduces the tracking error between the x-y trajectory and the desired circular path.

t_span = 80;

dt = 0.008;

t = 0:dt:t_span;

numbots = 1;

options = optimoptions('quadprog', 'Display', 'off');

x = zeros(1, length(t), numbots);

y = zeros(1, length(t), numbots);

x(1,1,1) = 6; % initial x-coordinate

y(1,1,1) = 8; % initial y-coordinate

Xc1 = 3; % center, x-coordinate

Yc1 = 5; % center, y-coordinate

alpha = 13;

r = 2;

for n = 1:length(t)

for z = 1:numbots

if z == 1

xd(1,:,z) = r*cos(t) + Xc1;

yd(1,:,z) = r*sin(t) + Yc1;

elseif z == 2

xd(1,:,z) = r*sin(t).*(1 - cos(t)) + Xc2;

yd(1,:,z) = r*cos(t).*(1 - cos(t)) + Yc2;

end

X_r(:,n, z) = [ x(:,n,z); y(:,n,z)];

Xd(:,n, z) = [xd(:,n,z); yd(:,n,z)];

H = eye(2);

f(:,n,z) = [0; 0];

A = - 2*[xd(1,n,z) - x(1,n,z), yd(1,n,z) - y(1,n,z)];

b = - alpha*( ( xd(1,n,z) - x(1,n,z) )^2 + ( yd(1,n,z) - y(1,n,z) )^2 );

u(:,n,z) = quadprog(H, f(:,n,z), A, b, [], [], [], [], [], options);

x(1,n+1,z) = x(1,n,z) + dt*u(1,n,z);

y(1,n+1,z) = y(1,n,z) + dt*u(2,n,z);

disp(['Current time = ', num2str(n*dt)])

end

Current time = 0.008 Current time = 0.016 Current time = 0.024 Current time = 0.032 Current time = 0.04 Current time = 0.048 Current time = 0.056 Current time = 0.064 Current time = 0.072 Current time = 0.08 Current time = 0.088 Current time = 0.096 Current time = 0.104 Current time = 0.112 Current time = 0.12 Current time = 0.128 Current time = 0.136 Current time = 0.144 Current time = 0.152 Current time = 0.16 Current time = 0.168 Current time = 0.176 Current time = 0.184 Current time = 0.192 Current time = 0.2 Current time = 0.208 Current time = 0.216 Current time = 0.224 Current time = 0.232 Current time = 0.24 Current time = 0.248 Current time = 0.256 Current time = 0.264 Current time = 0.272 Current time = 0.28 Current time = 0.288 Current time = 0.296 Current time = 0.304 Current time = 0.312 Current time = 0.32 Current time = 0.328 Current time = 0.336 Current time = 0.344 Current time = 0.352 Current time = 0.36 Current time = 0.368 Current time = 0.376 Current time = 0.384 Current time = 0.392 Current time = 0.4 Current time = 0.408 Current time = 0.416 Current time = 0.424 Current time = 0.432 Current time = 0.44 Current time = 0.448 Current time = 0.456 Current time = 0.464 Current time = 0.472 Current time = 0.48 Current time = 0.488 Current time = 0.496 Current time = 0.504 Current time = 0.512 Current time = 0.52 Current time = 0.528 Current time = 0.536 Current time = 0.544 Current time = 0.552 Current time = 0.56 Current time = 0.568 Current time = 0.576 Current time = 0.584 Current time = 0.592 Current time = 0.6 Current time = 0.608 Current time = 0.616 Current time = 0.624 Current time = 0.632 Current time = 0.64 Current time = 0.648 Current time = 0.656 Current time = 0.664 Current time = 0.672 Current time = 0.68 Current time = 0.688 Current time = 0.696 Current time = 0.704 Current time = 0.712 Current time = 0.72 Current time = 0.728 Current time = 0.736 Current time = 0.744 Current time = 0.752 Current time = 0.76 Current time = 0.768 Current time = 0.776 Current time = 0.784 Current time = 0.792 Current time = 0.8 Current time = 0.808 Current time = 0.816 Current time = 0.824 Current time = 0.832 Current time = 0.84 Current time = 0.848 Current time = 0.856 Current time = 0.864 Current time = 0.872 Current time = 0.88 Current time = 0.888 Current time = 0.896 Current time = 0.904 Current time = 0.912 Current time = 0.92 Current time = 0.928 Current time = 0.936 Current time = 0.944 Current time = 0.952 Current time = 0.96 Current time = 0.968 Current time = 0.976 Current time = 0.984 Current time = 0.992 Current time = 1 Current time = 1.008 Current time = 1.016 Current time = 1.024 Current time = 1.032 Current time = 1.04 Current time = 1.048 Current time = 1.056 Current time = 1.064 Current time = 1.072 Current time = 1.08 Current time = 1.088 Current time = 1.096 Current time = 1.104 Current time = 1.112 Current time = 1.12 Current time = 1.128 Current time = 1.136 Current time = 1.144 Current time = 1.152 Current time = 1.16 Current time = 1.168 Current time = 1.176 Current time = 1.184 Current time = 1.192 Current time = 1.2 Current time = 1.208 Current time = 1.216 Current time = 1.224 Current time = 1.232 Current time = 1.24 Current time = 1.248 Current time = 1.256 Current time = 1.264 Current time = 1.272 Current time = 1.28 Current time = 1.288 Current time = 1.296 Current time = 1.304 Current time = 1.312 Current time = 1.32 Current time = 1.328 Current time = 1.336 Current time = 1.344 Current time = 1.352 Current time = 1.36 Current time = 1.368 Current time = 1.376 Current time = 1.384 Current time = 1.392 Current time = 1.4 Current time = 1.408 Current time = 1.416 Current time = 1.424 Current time = 1.432 Current time = 1.44 Current time = 1.448 Current time = 1.456 Current time = 1.464 Current time = 1.472 Current time = 1.48 Current time = 1.488 Current time = 1.496 Current time = 1.504 Current time = 1.512 Current time = 1.52 Current time = 1.528 Current time = 1.536 Current time = 1.544 Current time = 1.552 Current time = 1.56 Current time = 1.568 Current time = 1.576 Current time = 1.584 Current time = 1.592 Current time = 1.6 Current time = 1.608 Current time = 1.616 Current time = 1.624 Current time = 1.632 Current time = 1.64 Current time = 1.648 Current time = 1.656 Current time = 1.664 Current time = 1.672 Current time = 1.68 Current time = 1.688 Current time = 1.696 Current time = 1.704 Current time = 1.712 Current time = 1.72 Current time = 1.728 Current time = 1.736 Current time = 1.744 Current time = 1.752 Current time = 1.76 Current time = 1.768 Current time = 1.776 Current time = 1.784 Current time = 1.792 Current time = 1.8 Current time = 1.808 Current time = 1.816 Current time = 1.824 Current time = 1.832 Current time = 1.84 Current time = 1.848 Current time = 1.856 Current time = 1.864 Current time = 1.872 Current time = 1.88 Current time = 1.888 Current time = 1.896 Current time = 1.904 Current time = 1.912 Current time = 1.92 Current time = 1.928 Current time = 1.936 Current time = 1.944 Current time = 1.952 Current time = 1.96 Current time = 1.968 Current time = 1.976 Current time = 1.984 Current time = 1.992 Current time = 2 Current time = 2.008 Current time = 2.016 Current time = 2.024 Current time = 2.032 Current time = 2.04 Current time = 2.048 Current time = 2.056 Current time = 2.064 Current time = 2.072 Current time = 2.08 Current time = 2.088 Current time = 2.096 Current time = 2.104 Current time = 2.112 Current time = 2.12 Current time = 2.128 Current time = 2.136 Current time = 2.144 Current time = 2.152 Current time = 2.16 Current time = 2.168 Current time = 2.176 Current time = 2.184 Current time = 2.192 Current time = 2.2 Current time = 2.208 Current time = 2.216 Current time = 2.224 Current time = 2.232 Current time = 2.24 Current time = 2.248 Current time = 2.256 Current time = 2.264 Current time = 2.272 Current time = 2.28 Current time = 2.288 Current time = 2.296 Current time = 2.304 Current time = 2.312 Current time = 2.32 Current time = 2.328 Current time = 2.336 Current time = 2.344 Current time = 2.352 Current time = 2.36 Current time = 2.368 Current time = 2.376 Current time = 2.384 Current time = 2.392 Current time = 2.4 Current time = 2.408 Current time = 2.416 Current time = 2.424 Current time = 2.432 Current time = 2.44 Current time = 2.448 Current time = 2.456 Current time = 2.464 Current time = 2.472 Current time = 2.48 Current time = 2.488 Current time = 2.496 Current time = 2.504 Current time = 2.512 Current time = 2.52 Current time = 2.528 Current time = 2.536 Current time = 2.544 Current time = 2.552 Current time = 2.56 Current time = 2.568 Current time = 2.576 Current time = 2.584 Current time = 2.592 Current time = 2.6 Current time = 2.608 Current time = 2.616 Current time = 2.624 Current time = 2.632 Current time = 2.64 Current time = 2.648 Current time = 2.656 Current time = 2.664 Current time = 2.672 Current time = 2.68 Current time = 2.688 Current time = 2.696 Current time = 2.704 Current time = 2.712 Current time = 2.72 Current time = 2.728 Current time = 2.736 Current time = 2.744 Current time = 2.752 Current time = 2.76 Current time = 2.768 Current time = 2.776 Current time = 2.784 Current time = 2.792 Current time = 2.8 Current time = 2.808 Current time = 2.816 Current time = 2.824 Current time = 2.832 Current time = 2.84 Current time = 2.848 Current time = 2.856 Current time = 2.864 Current time = 2.872 Current time = 2.88 Current time = 2.888 Current time = 2.896 Current time = 2.904 Current time = 2.912 Current time = 2.92 Current time = 2.928 Current time = 2.936 Current time = 2.944 Current time = 2.952 Current time = 2.96 Current time = 2.968 Current time = 2.976 Current time = 2.984 Current time = 2.992 Current time = 3 Current time = 3.008 Current time = 3.016 Current time = 3.024 Current time = 3.032 Current time = 3.04 Current time = 3.048 Current time = 3.056 Current time = 3.064 Current time = 3.072 Current time = 3.08 Current time = 3.088 Current time = 3.096 Current time = 3.104 Current time = 3.112 Current time = 3.12 Current time = 3.128 Current time = 3.136 Current time = 3.144 Current time = 3.152 Current time = 3.16 Current time = 3.168 Current time = 3.176 Current time = 3.184 Current time = 3.192 Current time = 3.2 Current time = 3.208 Current time = 3.216 Current time = 3.224 Current time = 3.232 Current time = 3.24 Current time = 3.248 Current time = 3.256 Current time = 3.264 Current time = 3.272 Current time = 3.28 Current time = 3.288 Current time = 3.296 Current time = 3.304 Current time = 3.312 Current time = 3.32 Current time = 3.328 Current time = 3.336 Current time = 3.344 Current time = 3.352 Current time = 3.36 Current time = 3.368 Current time = 3.376 Current time = 3.384 Current time = 3.392 Current time = 3.4 Current time = 3.408 Current time = 3.416 Current time = 3.424 Current time = 3.432 Current time = 3.44 Current time = 3.448 Current time = 3.456 Current time = 3.464 Current time = 3.472 Current time = 3.48 Current time = 3.488 Current time = 3.496 Current time = 3.504 Current time = 3.512 Current time = 3.52 Current time = 3.528 Current time = 3.536 Current time = 3.544 Current time = 3.552 Current time = 3.56 Current time = 3.568 Current time = 3.576 Current time = 3.584 Current time = 3.592 Current time = 3.6 Current time = 3.608 Current time = 3.616 Current time = 3.624 Current time = 3.632 Current time = 3.64 Current time = 3.648 Current time = 3.656 Current time = 3.664 Current time = 3.672 Current time = 3.68 Current time = 3.688 Current time = 3.696 Current time = 3.704 Current time = 3.712 Current time = 3.72 Current time = 3.728 Current time = 3.736 Current time = 3.744 Current time = 3.752 Current time = 3.76 Current time = 3.768 Current time = 3.776 Current time = 3.784 Current time = 3.792 Current time = 3.8 Current time = 3.808 Current time = 3.816 Current time = 3.824 Current time = 3.832 Current time = 3.84 Current time = 3.848 Current time = 3.856 Current time = 3.864 Current time = 3.872 Current time = 3.88 Current time = 3.888 Current time = 3.896 Current time = 3.904 Current time = 3.912 Current time = 3.92 Current time = 3.928 Current time = 3.936 Current time = 3.944 Current time = 3.952 Current time = 3.96 Current time = 3.968 Current time = 3.976 Current time = 3.984 Current time = 3.992 Current time = 4 Current time = 4.008 Current time = 4.016 Current time = 4.024 Current time = 4.032 Current time = 4.04 Current time = 4.048 Current time = 4.056 Current time = 4.064 Current time = 4.072 Current time = 4.08 Current time = 4.088 Current time = 4.096 Current time = 4.104 Current time = 4.112 Current time = 4.12 Current time = 4.128 Current time = 4.136 Current time = 4.144 Current time = 4.152 Current time = 4.16 Current time = 4.168 Current time = 4.176 Current time = 4.184 Current time = 4.192 Current time = 4.2 Current time = 4.208 Current time = 4.216 Current time = 4.224 Current time = 4.232 Current time = 4.24 Current time = 4.248 Current time = 4.256 Current time = 4.264 Current time = 4.272 Current time = 4.28 Current time = 4.288 Current time = 4.296 Current time = 4.304 Current time = 4.312 Current time = 4.32 Current time = 4.328 Current time = 4.336 Current time = 4.344 Current time = 4.352 Current time = 4.36 Current time = 4.368 Current time = 4.376 Current time = 4.384 Current time = 4.392 Current time = 4.4 Current time = 4.408 Current time = 4.416 Current time = 4.424 Current time = 4.432 Current time = 4.44 Current time = 4.448 Current time = 4.456 Current time = 4.464 Current time = 4.472 Current time = 4.48 Current time = 4.488 Current time = 4.496 Current time = 4.504 Current time = 4.512 Current time = 4.52 Current time = 4.528 Current time = 4.536 Current time = 4.544 Current time = 4.552 Current time = 4.56 Current time = 4.568 Current time = 4.576 Current time = 4.584 Current time = 4.592 Current time = 4.6 Current time = 4.608 Current time = 4.616 Current time = 4.624 Current time = 4.632 Current time = 4.64 Current time = 4.648 Current time = 4.656 Current time = 4.664 Current time = 4.672 Current time = 4.68 Current time = 4.688 Current time = 4.696 Current time = 4.704 Current time = 4.712 Current time = 4.72 Current time = 4.728 Current time = 4.736 Current time = 4.744 Current time = 4.752 Current time = 4.76 Current time = 4.768 Current time = 4.776 Current time = 4.784 Current time = 4.792 Current time = 4.8 Current time = 4.808 Current time = 4.816 Current time = 4.824 Current time = 4.832 Current time = 4.84 Current time = 4.848 Current time = 4.856 Current time = 4.864 Current time = 4.872 Current time = 4.88 Current time = 4.888 Current time = 4.896 Current time = 4.904 Current time = 4.912 Current time = 4.92 Current time = 4.928 Current time = 4.936 Current time = 4.944 Current time = 4.952 Current time = 4.96 Current time = 4.968 Current time = 4.976 Current time = 4.984 Current time = 4.992 Current time = 5 Current time = 5.008 Current time = 5.016 Current time = 5.024 Current time = 5.032 Current time = 5.04 Current time = 5.048 Current time = 5.056 Current time = 5.064 Current time = 5.072 Current time = 5.08 Current time = 5.088 Current time = 5.096 Current time = 5.104 Current time = 5.112 Current time = 5.12 Current time = 5.128 Current time = 5.136 Current time = 5.144 Current time = 5.152 Current time = 5.16 Current time = 5.168 Current time = 5.176 Current time = 5.184 Current time = 5.192 Current time = 5.2 Current time = 5.208 Current time = 5.216 Current time = 5.224 Current time = 5.232 Current time = 5.24 Current time = 5.248 Current time = 5.256 Current time = 5.264 Current time = 5.272 Current time = 5.28 Current time = 5.288 Current time = 5.296 Current time = 5.304 Current time = 5.312 Current time = 5.32 Current time = 5.328 Current time = 5.336 Current time = 5.344 Current time = 5.352 Current time = 5.36 Current time = 5.368 Current time = 5.376 Current time = 5.384 Current time = 5.392 Current time = 5.4 Current time = 5.408 Current time = 5.416 Current time = 5.424 Current time = 5.432 Current time = 5.44 Current time = 5.448 Current time = 5.456 Current time = 5.464 Current time = 5.472 Current time = 5.48 Current time = 5.488 Current time = 5.496 Current time = 5.504 Current time = 5.512 Current time = 5.52 Current time = 5.528 Current time = 5.536 Current time = 5.544 Current time = 5.552 Current time = 5.56 Current time = 5.568 Current time = 5.576 Current time = 5.584 Current time = 5.592 Current time = 5.6 Current time = 5.608 Current time = 5.616 Current time = 5.624 Current time = 5.632 Current time = 5.64 Current time = 5.648 Current time = 5.656 Current time = 5.664 Current time = 5.672 Current time = 5.68 Current time = 5.688 Current time = 5.696 Current time = 5.704 Current time = 5.712 Current time = 5.72 Current time = 5.728 Current time = 5.736 Current time = 5.744 Current time = 5.752 Current time = 5.76 Current time = 5.768 Current time = 5.776 Current time = 5.784 Current time = 5.792 Current time = 5.8 Current time = 5.808 Current time = 5.816 Current time = 5.824 Current time = 5.832 Current time = 5.84 Current time = 5.848 Current time = 5.856 Current time = 5.864 Current time = 5.872 Current time = 5.88 Current time = 5.888 Current time = 5.896 Current time = 5.904 Current time = 5.912 Current time = 5.92 Current time = 5.928 Current time = 5.936 Current time = 5.944 Current time = 5.952 Current time = 5.96 Current time = 5.968 Current time = 5.976 Current time = 5.984 Current time = 5.992 Current time = 6 Current time = 6.008 Current time = 6.016 Current time = 6.024 Current time = 6.032 Current time = 6.04 Current time = 6.048 Current time = 6.056 Current time = 6.064 Current time = 6.072 Current time = 6.08 Current time = 6.088 Current time = 6.096 Current time = 6.104 Current time = 6.112 Current time = 6.12 Current time = 6.128 Current time = 6.136 Current time = 6.144 Current time = 6.152 Current time = 6.16 Current time = 6.168 Current time = 6.176 Current time = 6.184 Current time = 6.192 Current time = 6.2 Current time = 6.208 Current time = 6.216 Current time = 6.224 Current time = 6.232 Current time = 6.24 Current time = 6.248 Current time = 6.256 Current time = 6.264 Current time = 6.272 Current time = 6.28 Current time = 6.288 Current time = 6.296 Current time = 6.304 Current time = 6.312 Current time = 6.32 Current time = 6.328 Current time = 6.336 Current time = 6.344 Current time = 6.352 Current time = 6.36 Current time = 6.368 Current time = 6.376 Current time = 6.384 Current time = 6.392 Current time = 6.4 Current time = 6.408 Current time = 6.416 Current time = 6.424 Current time = 6.432 Current time = 6.44 Current time = 6.448 Current time = 6.456 Current time = 6.464 Current time = 6.472 Current time = 6.48 Current time = 6.488 Current time = 6.496 Current time = 6.504 Current time = 6.512 Current time = 6.52 Current time = 6.528 Current time = 6.536 Current time = 6.544 Current time = 6.552 Current time = 6.56 Current time = 6.568 Current time = 6.576 Current time = 6.584 Current time = 6.592 Current time = 6.6 Current time = 6.608 Current time = 6.616 Current time = 6.624 Current time = 6.632 Current time = 6.64 Current time = 6.648 Current time = 6.656 Current time = 6.664 Current time = 6.672 Current time = 6.68 Current time = 6.688 Current time = 6.696 Current time = 6.704 Current time = 6.712 Current time = 6.72 Current time = 6.728 Current time = 6.736 Current time = 6.744 Current time = 6.752 Current time = 6.76 Current time = 6.768 Current time = 6.776 Current time = 6.784 Current time = 6.792 Current time = 6.8 Current time = 6.808 Current time = 6.816 Current time = 6.824 Current time = 6.832 Current time = 6.84 Current time = 6.848 Current time = 6.856 Current time = 6.864 Current time = 6.872 Current time = 6.88 Current time = 6.888 Current time = 6.896 Current time = 6.904 Current time = 6.912 Current time = 6.92 Current time = 6.928 Current time = 6.936 Current time = 6.944 Current time = 6.952 Current time = 6.96 Current time = 6.968 Current time = 6.976 Current time = 6.984 Current time = 6.992 Current time = 7 Current time = 7.008 Current time = 7.016 Current time = 7.024 Current time = 7.032 Current time = 7.04 Current time = 7.048 Current time = 7.056 Current time = 7.064 Current time = 7.072 Current time = 7.08 Current time = 7.088 Current time = 7.096 Current time = 7.104 Current time = 7.112 Current time = 7.12 Current time = 7.128 Current time = 7.136 Current time = 7.144 Current time = 7.152 Current time = 7.16 Current time = 7.168 Current time = 7.176 Current time = 7.184 Current time = 7.192 Current time = 7.2 Current time = 7.208 Current time = 7.216 Current time = 7.224 Current time = 7.232 Current time = 7.24 Current time = 7.248 Current time = 7.256 Current time = 7.264 Current time = 7.272 Current time = 7.28 Current time = 7.288 Current time = 7.296 Current time = 7.304 Current time = 7.312 Current time = 7.32 Current time = 7.328 Current time = 7.336 Current time = 7.344 Current time = 7.352 Current time = 7.36 Current time = 7.368 Current time = 7.376 Current time = 7.384 Current time = 7.392 Current time = 7.4 Current time = 7.408 Current time = 7.416 Current time = 7.424 Current time = 7.432 Current time = 7.44 Current time = 7.448 Current time = 7.456 Current time = 7.464 Current time = 7.472 Current time = 7.48 Current time = 7.488 Current time = 7.496 Current time = 7.504 Current time = 7.512 Current time = 7.52 Current time = 7.528 Current time = 7.536 Current time = 7.544 Current time = 7.552 Current time = 7.56 Current time = 7.568 Current time = 7.576 Current time = 7.584 Current time = 7.592 Current time = 7.6 Current time = 7.608 Current time = 7.616 Current time = 7.624 Current time = 7.632 Current time = 7.64 Current time = 7.648 Current time = 7.656 Current time = 7.664 Current time = 7.672 Current time = 7.68 Current time = 7.688 Current time = 7.696 Current time = 7.704 Current time = 7.712 Current time = 7.72 Current time = 7.728 Current time = 7.736 Current time = 7.744 Current time = 7.752 Current time = 7.76 Current time = 7.768 Current time = 7.776 Current time = 7.784 Current time = 7.792 Current time = 7.8 Current time = 7.808 Current time = 7.816 Current time = 7.824 Current time = 7.832 Current time = 7.84 Current time = 7.848 Current time = 7.856 Current time = 7.864 Current time = 7.872 Current time = 7.88 Current time = 7.888 Current time = 7.896 Current time = 7.904 Current time = 7.912 Current time = 7.92 Current time = 7.928 Current time = 7.936 Current time = 7.944 Current time = 7.952 Current time = 7.96 Current time = 7.968 Current time = 7.976 Current time = 7.984 Current time = 7.992 Current time = 8 Current time = 8.008 Current time = 8.016 Current time = 8.024 Current time = 8.032 Current time = 8.04 Current time = 8.048 Current time = 8.056 Current time = 8.064 Current time = 8.072 Current time = 8.08 Current time = 8.088 Current time = 8.096 Current time = 8.104 Current time = 8.112 Current time = 8.12 Current time = 8.128 Current time = 8.136 Current time = 8.144 Current time = 8.152 Current time = 8.16 Current time = 8.168 Current time = 8.176 Current time = 8.184 Current time = 8.192 Current time = 8.2 Current time = 8.208 Current time = 8.216 Current time = 8.224 Current time = 8.232 Current time = 8.24 Current time = 8.248 Current time = 8.256 Current time = 8.264 Current time = 8.272 Current time = 8.28 Current time = 8.288 Current time = 8.296 Current time = 8.304 Current time = 8.312 Current time = 8.32 Current time = 8.328 Current time = 8.336 Current time = 8.344 Current time = 8.352 Current time = 8.36 Current time = 8.368 Current time = 8.376 Current time = 8.384 Current time = 8.392 Current time = 8.4 Current time = 8.408 Current time = 8.416 Current time = 8.424 Current time = 8.432 Current time = 8.44 Current time = 8.448 Current time = 8.456 Current time = 8.464 Current time = 8.472 Current time = 8.48 Current time = 8.488 Current time = 8.496 Current time = 8.504 Current time = 8.512 Current time = 8.52 Current time = 8.528 Current time = 8.536 Current time = 8.544 Current time = 8.552 Current time = 8.56 Current time = 8.568 Current time = 8.576 Current time = 8.584 Current time = 8.592 Current time = 8.6 Current time = 8.608 Current time = 8.616 Current time = 8.624 Current time = 8.632 Current time = 8.64 Current time = 8.648 Current time = 8.656 Current time = 8.664 Current time = 8.672 Current time = 8.68 Current time = 8.688 Current time = 8.696 Current time = 8.704 Current time = 8.712 Current time = 8.72 Current time = 8.728 Current time = 8.736 Current time = 8.744 Current time = 8.752 Current time = 8.76 Current time = 8.768 Current time = 8.776 Current time = 8.784 Current time = 8.792 Current time = 8.8 Current time = 8.808 Current time = 8.816 Current time = 8.824 Current time = 8.832 Current time = 8.84 Current time = 8.848 Current time = 8.856 Current time = 8.864 Current time = 8.872 Current time = 8.88 Current time = 8.888 Current time = 8.896 Current time = 8.904 Current time = 8.912 Current time = 8.92 Current time = 8.928 Current time = 8.936 Current time = 8.944 Current time = 8.952 Current time = 8.96 Current time = 8.968 Current time = 8.976 Current time = 8.984 Current time = 8.992 Current time = 9 Current time = 9.008 Current time = 9.016 Current time = 9.024 Current time = 9.032 Current time = 9.04 Current time = 9.048 Current time = 9.056 Current time = 9.064 Current time = 9.072 Current time = 9.08 Current time = 9.088 Current time = 9.096 Current time = 9.104 Current time = 9.112 Current time = 9.12 Current time = 9.128 Current time = 9.136 Current time = 9.144 Current time = 9.152 Current time = 9.16 Current time = 9.168 Current time = 9.176 Current time = 9.184 Current time = 9.192 Current time = 9.2 Current time = 9.208 Current time = 9.216 Current time = 9.224 Current time = 9.232 Current time = 9.24 Current time = 9.248 Current time = 9.256 Current time = 9.264 Current time = 9.272 Current time = 9.28 Current time = 9.288 Current time = 9.296 Current time = 9.304 Current time = 9.312 Current time = 9.32 Current time = 9.328 Current time = 9.336 Current time = 9.344 Current time = 9.352 Current time = 9.36 Current time = 9.368 Current time = 9.376 Current time = 9.384 Current time = 9.392 Current time = 9.4 Current time = 9.408 Current time = 9.416 Current time = 9.424 Current time = 9.432 Current time = 9.44 Current time = 9.448 Current time = 9.456 Current time = 9.464 Current time = 9.472 Current time = 9.48 Current time = 9.488 Current time = 9.496 Current time = 9.504 Current time = 9.512 Current time = 9.52 Current time = 9.528 Current time = 9.536 Current time = 9.544 Current time = 9.552 Current time = 9.56 Current time = 9.568 Current time = 9.576 Current time = 9.584 Current time = 9.592 Current time = 9.6 Current time = 9.608 Current time = 9.616 Current time = 9.624 Current time = 9.632 Current time = 9.64 Current time = 9.648 Current time = 9.656 Current time = 9.664 Current time = 9.672 Current time = 9.68 Current time = 9.688 Current time = 9.696 Current time = 9.704 Current time = 9.712 Current time = 9.72 Current time = 9.728 Current time = 9.736 Current time = 9.744 Current time = 9.752 Current time = 9.76 Current time = 9.768 Current time = 9.776 Current time = 9.784 Current time = 9.792 Current time = 9.8 Current time = 9.808 Current time = 9.816 Current time = 9.824 Current time = 9.832 Current time = 9.84 Current time = 9.848 Current time = 9.856 Current time = 9.864 Current time = 9.872 Current time = 9.88 Current time = 9.888 Current time = 9.896 Current time = 9.904 Current time = 9.912 Current time = 9.92 Current time = 9.928 Current time = 9.936 Current time = 9.944 Current time = 9.952 Current time = 9.96 Current time = 9.968 Current time = 9.976 Current time = 9.984 Current time = 9.992 Current time = 10 Current time = 10.008 Current time = 10.016 Current time = 10.024 Current time = 10.032 Current time = 10.04 Current time = 10.048 Current time = 10.056 Current time = 10.064 Current time = 10.072 Current time = 10.08 Current time = 10.088 Current time = 10.096 Current time = 10.104 Current time = 10.112 Current time = 10.12 Current time = 10.128 Current time = 10.136 Current time = 10.144 Current time = 10.152 Current time = 10.16 Current time = 10.168 Current time = 10.176 Current time = 10.184 Current time = 10.192 Current time = 10.2 Current time = 10.208 Current time = 10.216 Current time = 10.224 Current time = 10.232 Current time = 10.24 Current time = 10.248 Current time = 10.256 Current time = 10.264 Current time = 10.272 Current time = 10.28 Current time = 10.288 Current time = 10.296 Current time = 10.304 Current time = 10.312 Current time = 10.32 Current time = 10.328 Current time = 10.336 Current time = 10.344 Current time = 10.352 Current time = 10.36 Current time = 10.368 Current time = 10.376 Current time = 10.384 Current time = 10.392 Current time = 10.4 Current time = 10.408 Current time = 10.416 Current time = 10.424 Current time = 10.432 Current time = 10.44 Current time = 10.448 Current time = 10.456 Current time = 10.464 Current time = 10.472 Current time = 10.48 Current time = 10.488 Current time = 10.496 Current time = 10.504 Current time = 10.512 Current time = 10.52 Current time = 10.528 Current time = 10.536 Current time = 10.544 Current time = 10.552 Current time = 10.56 Current time = 10.568 Current time = 10.576 Current time = 10.584 Current time = 10.592 Current time = 10.6 Current time = 10.608 Current time = 10.616 Current time = 10.624 Current time = 10.632 Current time = 10.64 Current time = 10.648 Current time = 10.656 Current time = 10.664 Current time = 10.672 Current time = 10.68 Current time = 10.688 Current time = 10.696 Current time = 10.704 Current time = 10.712 Current time = 10.72 Current time = 10.728 Current time = 10.736 Current time = 10.744 Current time = 10.752 Current time = 10.76 Current time = 10.768 Current time = 10.776 Current time = 10.784 Current time = 10.792 Current time = 10.8 Current time = 10.808 Current time = 10.816 Current time = 10.824 Current time = 10.832 Current time = 10.84 Current time = 10.848 Current time = 10.856 Current time = 10.864 Current time = 10.872 Current time = 10.88 Current time = 10.888 Current time = 10.896 Current time = 10.904 Current time = 10.912 Current time = 10.92 Current time = 10.928 Current time = 10.936 Current time = 10.944 Current time = 10.952 Current time = 10.96 Current time = 10.968 Current time = 10.976 Current time = 10.984 Current time = 10.992 Current time = 11 Current time = 11.008 Current time = 11.016 Current time = 11.024 Current time = 11.032 Current time = 11.04 Current time = 11.048 Current time = 11.056 Current time = 11.064 Current time = 11.072 Current time = 11.08 Current time = 11.088 Current time = 11.096 Current time = 11.104 Current time = 11.112 Current time = 11.12 Current time = 11.128 Current time = 11.136 Current time = 11.144 Current time = 11.152 Current time = 11.16 Current time = 11.168 Current time = 11.176 Current time = 11.184 Current time = 11.192 Current time = 11.2 Current time = 11.208 Current time = 11.216 Current time = 11.224 Current time = 11.232 Current time = 11.24 Current time = 11.248 Current time = 11.256 Current time = 11.264 Current time = 11.272 Current time = 11.28 Current time = 11.288 Current time = 11.296 Current time = 11.304 Current time = 11.312 Current time = 11.32 Current time = 11.328 Current time = 11.336 Current time = 11.344 Current time = 11.352 Current time = 11.36 Current time = 11.368 Current time = 11.376 Current time = 11.384 Current time = 11.392 Current time = 11.4 Current time = 11.408 Current time = 11.416 Current time = 11.424 Current time = 11.432 Current time = 11.44 Current time = 11.448 Current time = 11.456 Current time = 11.464 Current time = 11.472 Current time = 11.48 Current time = 11.488 Current time = 11.496 Current time = 11.504 Current time = 11.512 Current time = 11.52 Current time = 11.528 Current time = 11.536 Current time = 11.544 Current time = 11.552 Current time = 11.56 Current time = 11.568 Current time = 11.576 Current time = 11.584 Current time = 11.592 Current time = 11.6 Current time = 11.608 Current time = 11.616 Current time = 11.624 Current time = 11.632 Current time = 11.64 Current time = 11.648 Current time = 11.656 Current time = 11.664 Current time = 11.672 Current time = 11.68 Current time = 11.688 Current time = 11.696 Current time = 11.704 Current time = 11.712 Current time = 11.72 Current time = 11.728 Current time = 11.736 Current time = 11.744 Current time = 11.752 Current time = 11.76 Current time = 11.768 Current time = 11.776 Current time = 11.784 Current time = 11.792 Current time = 11.8 Current time = 11.808 Current time = 11.816 Current time = 11.824 Current time = 11.832 Current time = 11.84 Current time = 11.848 Current time = 11.856 Current time = 11.864 Current time = 11.872 Current time = 11.88 Current time = 11.888 Current time = 11.896 Current time = 11.904 Current time = 11.912 Current time = 11.92 Current time = 11.928 Current time = 11.936 Current time = 11.944 Current time = 11.952 Current time = 11.96 Current time = 11.968 Current time = 11.976 Current time = 11.984 Current time = 11.992 Current time = 12 Current time = 12.008 Current time = 12.016 Current time = 12.024 Current time = 12.032 Current time = 12.04 Current time = 12.048 Current time = 12.056 Current time = 12.064 Current time = 12.072 Current time = 12.08 Current time = 12.088 Current time = 12.096 Current time = 12.104 Current time = 12.112 Current time = 12.12 Current time = 12.128 Current time = 12.136 Current time = 12.144 Current time = 12.152 Current time = 12.16 Current time = 12.168 Current time = 12.176 Current time = 12.184 Current time = 12.192 Current time = 12.2 Current time = 12.208 Current time = 12.216 Current time = 12.224 Current time = 12.232 Current time = 12.24 Current time = 12.248 Current time = 12.256 Current time = 12.264 Current time = 12.272 Current time = 12.28 Current time = 12.288 Current time = 12.296 Current time = 12.304 Current time = 12.312 Current time = 12.32 Current time = 12.328 Current time = 12.336 Current time = 12.344 Current time = 12.352 Current time = 12.36 Current time = 12.368 Current time = 12.376 Current time = 12.384 Current time = 12.392 Current time = 12.4 Current time = 12.408 Current time = 12.416 Current time = 12.424 Current time = 12.432 Current time = 12.44 Current time = 12.448 Current time = 12.456 Current time = 12.464 Current time = 12.472 Current time = 12.48 Current time = 12.488 Current time = 12.496 Current time = 12.504 Current time = 12.512 Current time = 12.52 Current time = 12.528 Current time = 12.536 Current time = 12.544 Current time = 12.552 Current time = 12.56 Current time = 12.568 Current time = 12.576 Current time = 12.584 Current time = 12.592 Current time = 12.6 Current time = 12.608 Current time = 12.616 Current time = 12.624 Current time = 12.632 Current time = 12.64 Current time = 12.648 Current time = 12.656 Current time = 12.664 Current time = 12.672 Current time = 12.68 Current time = 12.688 Current time = 12.696 Current time = 12.704 Current time = 12.712 Current time = 12.72 Current time = 12.728 Current time = 12.736 Current time = 12.744 Current time = 12.752 Current time = 12.76 Current time = 12.768 Current time = 12.776 Current time = 12.784 Current time = 12.792 Current time = 12.8 Current time = 12.808 Current time = 12.816 Current time = 12.824 Current time = 12.832 Current time = 12.84 Current time = 12.848 Current time = 12.856 Current time = 12.864 Current time = 12.872 Current time = 12.88 Current time = 12.888 Current time = 12.896 Current time = 12.904 Current time = 12.912 Current time = 12.92 Current time = 12.928 Current time = 12.936 Current time = 12.944 Current time = 12.952 Current time = 12.96 Current time = 12.968 Current time = 12.976 Current time = 12.984 Current time = 12.992 Current time = 13 Current time = 13.008 Current time = 13.016 Current time = 13.024 Current time = 13.032 Current time = 13.04 Current time = 13.048 Current time = 13.056 Current time = 13.064 Current time = 13.072 Current time = 13.08 Current time = 13.088 Current time = 13.096 Current time = 13.104 Current time = 13.112 Current time = 13.12 Current time = 13.128 Current time = 13.136 Current time = 13.144 Current time = 13.152 Current time = 13.16 Current time = 13.168 Current time = 13.176 Current time = 13.184 Current time = 13.192 Current time = 13.2 Current time = 13.208 Current time = 13.216 Current time = 13.224 Current time = 13.232 Current time = 13.24 Current time = 13.248 Current time = 13.256 Current time = 13.264 Current time = 13.272 Current time = 13.28 Current time = 13.288 Current time = 13.296 Current time = 13.304 Current time = 13.312 Current time = 13.32 Current time = 13.328 Current time = 13.336 Current time = 13.344 Current time = 13.352 Current time = 13.36 Current time = 13.368 Current time = 13.376 Current time = 13.384 Current time = 13.392 Current time = 13.4 Current time = 13.408 Current time = 13.416 Current time = 13.424 Current time = 13.432 Current time = 13.44 Current time = 13.448 Current time = 13.456 Current time = 13.464 Current time = 13.472 Current time = 13.48 Current time = 13.488 Current time = 13.496 Current time = 13.504 Current time = 13.512 Current time = 13.52 Current time = 13.528 Current time = 13.536 Current time = 13.544 Current time = 13.552 Current time = 13.56 Current time = 13.568 Current time = 13.576 Current time = 13.584 Current time = 13.592 Current time = 13.6 Current time = 13.608 Current time = 13.616 Current time = 13.624 Current time = 13.632 Current time = 13.64 Current time = 13.648 Current time = 13.656 Current time = 13.664 Current time = 13.672 Current time = 13.68 Current time = 13.688 Current time = 13.696 Current time = 13.704 Current time = 13.712 Current time = 13.72 Current time = 13.728 Current time = 13.736 Current time = 13.744 Current time = 13.752 Current time = 13.76 Current time = 13.768 Current time = 13.776 Current time = 13.784 Current time = 13.792 Current time = 13.8 Current time = 13.808 Current time = 13.816 Current time = 13.824 Current time = 13.832 Current time = 13.84 Current time = 13.848 Current time = 13.856 Current time = 13.864 Current time = 13.872 Current time = 13.88 Current time = 13.888 Current time = 13.896 Current time = 13.904 Current time = 13.912 Current time = 13.92 Current time = 13.928 Current time = 13.936 Current time = 13.944 Current time = 13.952 Current time = 13.96 Current time = 13.968 Current time = 13.976 Current time = 13.984 Current time = 13.992 Current time = 14 Current time = 14.008 Current time = 14.016 Current time = 14.024 Current time = 14.032 Current time = 14.04 Current time = 14.048 Current time = 14.056 Current time = 14.064 Current time = 14.072 Current time = 14.08 Current time = 14.088 Current time = 14.096 Current time = 14.104 Current time = 14.112 Current time = 14.12 Current time = 14.128 Current time = 14.136 Current time = 14.144 Current time = 14.152 Current time = 14.16 Current time = 14.168 Current time = 14.176 Current time = 14.184 Current time = 14.192 Current time = 14.2 Current time = 14.208 Current time = 14.216 Current time = 14.224 Current time = 14.232 Current time = 14.24 Current time = 14.248 Current time = 14.256 Current time = 14.264 Current time = 14.272 Current time = 14.28 Current time = 14.288 Current time = 14.296 Current time = 14.304 Current time = 14.312 Current time = 14.32 Current time = 14.328 Current time = 14.336 Current time = 14.344 Current time = 14.352 Current time = 14.36 Current time = 14.368 Current time = 14.376 Current time = 14.384 Current time = 14.392 Current time = 14.4 Current time = 14.408 Current time = 14.416 Current time = 14.424 Current time = 14.432 Current time = 14.44 Current time = 14.448 Current time = 14.456 Current time = 14.464 Current time = 14.472 Current time = 14.48 Current time = 14.488 Current time = 14.496 Current time = 14.504 Current time = 14.512 Current time = 14.52 Current time = 14.528 Current time = 14.536 Current time = 14.544 Current time = 14.552 Current time = 14.56 Current time = 14.568 Current time = 14.576 Current time = 14.584 Current time = 14.592 Current time = 14.6 Current time = 14.608 Current time = 14.616 Current time = 14.624 Current time = 14.632 Current time = 14.64 Current time = 14.648 Current time = 14.656 Current time = 14.664 Current time = 14.672 Current time = 14.68 Current time = 14.688 Current time = 14.696 Current time = 14.704 Current time = 14.712 Current time = 14.72 Current time = 14.728 Current time = 14.736 Current time = 14.744 Current time = 14.752 Current time = 14.76 Current time = 14.768 Current time = 14.776 Current time = 14.784 Current time = 14.792 Current time = 14.8 Current time = 14.808 Current time = 14.816 Current time = 14.824 Current time = 14.832 Current time = 14.84 Current time = 14.848 Current time = 14.856 Current time = 14.864 Current time = 14.872 Current time = 14.88 Current time = 14.888 Current time = 14.896 Current time = 14.904 Current time = 14.912 Current time = 14.92 Current time = 14.928 Current time = 14.936 Current time = 14.944 Current time = 14.952 Current time = 14.96 Current time = 14.968 Current time = 14.976 Current time = 14.984 Current time = 14.992 Current time = 15 Current time = 15.008 Current time = 15.016 Current time = 15.024 Current time = 15.032 Current time = 15.04 Current time = 15.048 Current time = 15.056 Current time = 15.064 Current time = 15.072 Current time = 15.08 Current time = 15.088 Current time = 15.096 Current time = 15.104 Current time = 15.112 Current time = 15.12 Current time = 15.128 Current time = 15.136 Current time = 15.144 Current time = 15.152 Current time = 15.16 Current time = 15.168 Current time = 15.176 Current time = 15.184 Current time = 15.192 Current time = 15.2 Current time = 15.208 Current time = 15.216 Current time = 15.224 Current time = 15.232 Current time = 15.24 Current time = 15.248 Current time = 15.256 Current time = 15.264 Current time = 15.272 Current time = 15.28 Current time = 15.288 Current time = 15.296 Current time = 15.304 Current time = 15.312 Current time = 15.32 Current time = 15.328 Current time = 15.336 Current time = 15.344 Current time = 15.352 Current time = 15.36 Current time = 15.368 Current time = 15.376 Current time = 15.384 Current time = 15.392 Current time = 15.4 Current time = 15.408 Current time = 15.416 Current time = 15.424 Current time = 15.432 Current time = 15.44 Current time = 15.448 Current time = 15.456 Current time = 15.464 Current time = 15.472 Current time = 15.48 Current time = 15.488 Current time = 15.496 Current time = 15.504 Current time = 15.512 Current time = 15.52 Current time = 15.528 Current time = 15.536 Current time = 15.544 Current time = 15.552 Current time = 15.56 Current time = 15.568 Current time = 15.576 Current time = 15.584 Current time = 15.592 Current time = 15.6 Current time = 15.608 Current time = 15.616 Current time = 15.624 Current time = 15.632 Current time = 15.64 Current time = 15.648 Current time = 15.656 Current time = 15.664 Current time = 15.672 Current time = 15.68 Current time = 15.688 Current time = 15.696 Current time = 15.704 Current time = 15.712 Current time = 15.72 Current time = 15.728 Current time = 15.736 Current time = 15.744 Current time = 15.752 Current time = 15.76 Current time = 15.768 Current time = 15.776 Current time = 15.784 Current time = 15.792 Current time = 15.8 Current time = 15.808 Current time = 15.816 Current time = 15.824 Current time = 15.832 Current time = 15.84 Current time = 15.848 Current time = 15.856 Current time = 15.864 Current time = 15.872 Current time = 15.88 Current time = 15.888 Current time = 15.896 Current time = 15.904 Current time = 15.912 Current time = 15.92 Current time = 15.928 Current time = 15.936 Current time = 15.944 Current time = 15.952 Current time = 15.96 Current time = 15.968 Current time = 15.976 Current time = 15.984 Current time = 15.992 Current time = 16 Current time = 16.008 Current time = 16.016 Current time = 16.024 Current time = 16.032 Current time = 16.04 Current time = 16.048 Current time = 16.056 Current time = 16.064 Current time = 16.072 Current time = 16.08 Current time = 16.088 Current time = 16.096 Current time = 16.104 Current time = 16.112 Current time = 16.12 Current time = 16.128 Current time = 16.136 Current time = 16.144 Current time = 16.152 Current time = 16.16 Current time = 16.168 Current time = 16.176 Current time = 16.184 Current time = 16.192 Current time = 16.2 Current time = 16.208 Current time = 16.216 Current time = 16.224 Current time = 16.232 Current time = 16.24 Current time = 16.248 Current time = 16.256 Current time = 16.264 Current time = 16.272 Current time = 16.28 Current time = 16.288 Current time = 16.296 Current time = 16.304 Current time = 16.312 Current time = 16.32 Current time = 16.328 Current time = 16.336 Current time = 16.344 Current time = 16.352 Current time = 16.36 Current time = 16.368 Current time = 16.376 Current time = 16.384 Current time = 16.392 Current time = 16.4 Current time = 16.408 Current time = 16.416 Current time = 16.424 Current time = 16.432 Current time = 16.44 Current time = 16.448 Current time = 16.456 Current time = 16.464 Current time = 16.472 Current time = 16.48 Current time = 16.488 Current time = 16.496 Current time = 16.504 Current time = 16.512 Current time = 16.52 Current time = 16.528 Current time = 16.536 Current time = 16.544 Current time = 16.552 Current time = 16.56 Current time = 16.568 Current time = 16.576 Current time = 16.584 Current time = 16.592 Current time = 16.6 Current time = 16.608 Current time = 16.616 Current time = 16.624 Current time = 16.632 Current time = 16.64 Current time = 16.648 Current time = 16.656 Current time = 16.664 Current time = 16.672 Current time = 16.68 Current time = 16.688 Current time = 16.696 Current time = 16.704 Current time = 16.712 Current time = 16.72 Current time = 16.728 Current time = 16.736 Current time = 16.744 Current time = 16.752 Current time = 16.76 Current time = 16.768 Current time = 16.776 Current time = 16.784 Current time = 16.792 Current time = 16.8 Current time = 16.808 Current time = 16.816 Current time = 16.824 Current time = 16.832 Current time = 16.84 Current time = 16.848 Current time = 16.856 Current time = 16.864 Current time = 16.872 Current time = 16.88 Current time = 16.888 Current time = 16.896 Current time = 16.904 Current time = 16.912 Current time = 16.92 Current time = 16.928 Current time = 16.936 Current time = 16.944 Current time = 16.952 Current time = 16.96 Current time = 16.968 Current time = 16.976 Current time = 16.984 Current time = 16.992 Current time = 17 Current time = 17.008 Current time = 17.016 Current time = 17.024 Current time = 17.032 Current time = 17.04 Current time = 17.048 Current time = 17.056 Current time = 17.064 Current time = 17.072 Current time = 17.08 Current time = 17.088 Current time = 17.096 Current time = 17.104 Current time = 17.112 Current time = 17.12 Current time = 17.128 Current time = 17.136 Current time = 17.144 Current time = 17.152 Current time = 17.16 Current time = 17.168 Current time = 17.176 Current time = 17.184 Current time = 17.192 Current time = 17.2 Current time = 17.208 Current time = 17.216 Current time = 17.224 Current time = 17.232 Current time = 17.24 Current time = 17.248 Current time = 17.256 Current time = 17.264 Current time = 17.272 Current time = 17.28 Current time = 17.288 Current time = 17.296 Current time = 17.304 Current time = 17.312 Current time = 17.32 Current time = 17.328 Current time = 17.336 Current time = 17.344 Current time = 17.352 Current time = 17.36 Current time = 17.368 Current time = 17.376 Current time = 17.384 Current time = 17.392 Current time = 17.4 Current time = 17.408 Current time = 17.416 Current time = 17.424 Current time = 17.432 Current time = 17.44 Current time = 17.448 Current time = 17.456 Current time = 17.464 Current time = 17.472 Current time = 17.48 Current time = 17.488 Current time = 17.496 Current time = 17.504 Current time = 17.512 Current time = 17.52 Current time = 17.528 Current time = 17.536 Current time = 17.544 Current time = 17.552 Current time = 17.56 Current time = 17.568 Current time = 17.576 Current time = 17.584 Current time = 17.592 Current time = 17.6 Current time = 17.608 Current time = 17.616 Current time = 17.624 Current time = 17.632 Current time = 17.64 Current time = 17.648 Current time = 17.656 Current time = 17.664 Current time = 17.672 Current time = 17.68 Current time = 17.688 Current time = 17.696 Current time = 17.704 Current time = 17.712 Current time = 17.72 Current time = 17.728 Current time = 17.736 Current time = 17.744 Current time = 17.752 Current time = 17.76 Current time = 17.768 Current time = 17.776 Current time = 17.784 Current time = 17.792 Current time = 17.8 Current time = 17.808 Current time = 17.816 Current time = 17.824 Current time = 17.832 Current time = 17.84 Current time = 17.848 Current time = 17.856 Current time = 17.864 Current time = 17.872 Current time = 17.88 Current time = 17.888 Current time = 17.896 Current time = 17.904 Current time = 17.912 Current time = 17.92 Current time = 17.928 Current time = 17.936 Current time = 17.944 Current time = 17.952 Current time = 17.96 Current time = 17.968 Current time = 17.976 Current time = 17.984 Current time = 17.992 Current time = 18 Current time = 18.008 Current time = 18.016 Current time = 18.024 Current time = 18.032 Current time = 18.04 Current time = 18.048 Current time = 18.056 Current time = 18.064 Current time = 18.072 Current time = 18.08 Current time = 18.088 Current time = 18.096 Current time = 18.104 Current time = 18.112 Current time = 18.12 Current time = 18.128 Current time = 18.136 Current time = 18.144 Current time = 18.152 Current time = 18.16 Current time = 18.168 Current time = 18.176 Current time = 18.184 Current time = 18.192 Current time = 18.2 Current time = 18.208 Current time = 18.216 Current time = 18.224 Current time = 18.232 Current time = 18.24 Current time = 18.248 Current time = 18.256 Current time = 18.264 Current time = 18.272 Current time = 18.28 Current time = 18.288 Current time = 18.296 Current time = 18.304 Current time = 18.312 Current time = 18.32 Current time = 18.328 Current time = 18.336 Current time = 18.344 Current time = 18.352 Current time = 18.36 Current time = 18.368 Current time = 18.376 Current time = 18.384 Current time = 18.392 Current time = 18.4 Current time = 18.408 Current time = 18.416 Current time = 18.424 Current time = 18.432 Current time = 18.44 Current time = 18.448 Current time = 18.456 Current time = 18.464 Current time = 18.472 Current time = 18.48 Current time = 18.488 Current time = 18.496 Current time = 18.504 Current time = 18.512 Current time = 18.52 Current time = 18.528 Current time = 18.536 Current time = 18.544 Current time = 18.552 Current time = 18.56 Current time = 18.568 Current time = 18.576 Current time = 18.584 Current time = 18.592 Current time = 18.6 Current time = 18.608 Current time = 18.616 Current time = 18.624 Current time = 18.632 Current time = 18.64 Current time = 18.648 Current time = 18.656 Current time = 18.664 Current time = 18.672 Current time = 18.68 Current time = 18.688 Current time = 18.696 Current time = 18.704 Current time = 18.712 Current time = 18.72 Current time = 18.728 Current time = 18.736 Current time = 18.744 Current time = 18.752 Current time = 18.76 Current time = 18.768 Current time = 18.776 Current time = 18.784 Current time = 18.792 Current time = 18.8 Current time = 18.808 Current time = 18.816 Current time = 18.824 Current time = 18.832 Current time = 18.84 Current time = 18.848 Current time = 18.856 Current time = 18.864 Current time = 18.872 Current time = 18.88 Current time = 18.888 Current time = 18.896 Current time = 18.904 Current time = 18.912 Current time = 18.92 Current time = 18.928 Current time = 18.936 Current time = 18.944 Current time = 18.952 Current time = 18.96 Current time = 18.968 Current time = 18.976 Current time = 18.984 Current time = 18.992 Current time = 19 Current time = 19.008 Current time = 19.016 Current time = 19.024 Current time = 19.032 Current time = 19.04 Current time = 19.048 Current time = 19.056 Current time = 19.064 Current time = 19.072 Current time = 19.08 Current time = 19.088 Current time = 19.096 Current time = 19.104 Current time = 19.112 Current time = 19.12 Current time = 19.128 Current time = 19.136 Current time = 19.144 Current time = 19.152 Current time = 19.16 Current time = 19.168 Current time = 19.176 Current time = 19.184 Current time = 19.192 Current time = 19.2 Current time = 19.208 Current time = 19.216 Current time = 19.224 Current time = 19.232 Current time = 19.24 Current time = 19.248 Current time = 19.256 Current time = 19.264 Current time = 19.272 Current time = 19.28 Current time = 19.288 Current time = 19.296 Current time = 19.304 Current time = 19.312 Current time = 19.32 Current time = 19.328 Current time = 19.336 Current time = 19.344 Current time = 19.352 Current time = 19.36 Current time = 19.368 Current time = 19.376 Current time = 19.384 Current time = 19.392 Current time = 19.4 Current time = 19.408 Current time = 19.416 Current time = 19.424 Current time = 19.432 Current time = 19.44 Current time = 19.448 Current time = 19.456 Current time = 19.464 Current time = 19.472 Current time = 19.48 Current time = 19.488 Current time = 19.496 Current time = 19.504 Current time = 19.512 Current time = 19.52 Current time = 19.528 Current time = 19.536 Current time = 19.544 Current time = 19.552 Current time = 19.56 Current time = 19.568 Current time = 19.576 Current time = 19.584 Current time = 19.592 Current time = 19.6 Current time = 19.608 Current time = 19.616 Current time = 19.624 Current time = 19.632 Current time = 19.64 Current time = 19.648 Current time = 19.656 Current time = 19.664 Current time = 19.672 Current time = 19.68 Current time = 19.688 Current time = 19.696 Current time = 19.704 Current time = 19.712 Current time = 19.72 Current time = 19.728 Current time = 19.736 Current time = 19.744 Current time = 19.752 Current time = 19.76 Current time = 19.768 Current time = 19.776 Current time = 19.784 Current time = 19.792 Current time = 19.8 Current time = 19.808 Current time = 19.816 Current time = 19.824 Current time = 19.832 Current time = 19.84 Current time = 19.848 Current time = 19.856 Current time = 19.864 Current time = 19.872 Current time = 19.88 Current time = 19.888 Current time = 19.896 Current time = 19.904 Current time = 19.912 Current time = 19.92 Current time = 19.928 Current time = 19.936 Current time = 19.944 Current time = 19.952 Current time = 19.96 Current time = 19.968 Current time = 19.976 Current time = 19.984 Current time = 19.992 Current time = 20 Current time = 20.008 Current time = 20.016 Current time = 20.024 Current time = 20.032 Current time = 20.04 Current time = 20.048 Current time = 20.056 Current time = 20.064 Current time = 20.072 Current time = 20.08 Current time = 20.088 Current time = 20.096 Current time = 20.104 Current time = 20.112 Current time = 20.12 Current time = 20.128 Current time = 20.136 Current time = 20.144 Current time = 20.152 Current time = 20.16 Current time = 20.168 Current time = 20.176 Current time = 20.184 Current time = 20.192 Current time = 20.2 Current time = 20.208 Current time = 20.216 Current time = 20.224 Current time = 20.232 Current time = 20.24 Current time = 20.248 Current time = 20.256 Current time = 20.264 Current time = 20.272 Current time = 20.28 Current time = 20.288 Current time = 20.296 Current time = 20.304 Current time = 20.312 Current time = 20.32 Current time = 20.328 Current time = 20.336 Current time = 20.344 Current time = 20.352 Current time = 20.36 Current time = 20.368 Current time = 20.376 Current time = 20.384 Current time = 20.392 Current time = 20.4 Current time = 20.408 Current time = 20.416 Current time = 20.424 Current time = 20.432 Current time = 20.44 Current time = 20.448 Current time = 20.456 Current time = 20.464 Current time = 20.472 Current time = 20.48 Current time = 20.488 Current time = 20.496 Current time = 20.504 Current time = 20.512 Current time = 20.52 Current time = 20.528 Current time = 20.536 Current time = 20.544 Current time = 20.552 Current time = 20.56 Current time = 20.568 Current time = 20.576 Current time = 20.584 Current time = 20.592 Current time = 20.6 Current time = 20.608 Current time = 20.616 Current time = 20.624 Current time = 20.632 Current time = 20.64 Current time = 20.648 Current time = 20.656 Current time = 20.664 Current time = 20.672 Current time = 20.68 Current time = 20.688 Current time = 20.696 Current time = 20.704 Current time = 20.712 Current time = 20.72 Current time = 20.728 Current time = 20.736 Current time = 20.744 Current time = 20.752 Current time = 20.76 Current time = 20.768 Current time = 20.776 Current time = 20.784 Current time = 20.792 Current time = 20.8 Current time = 20.808 Current time = 20.816 Current time = 20.824 Current time = 20.832 Current time = 20.84 Current time = 20.848 Current time = 20.856 Current time = 20.864 Current time = 20.872 Current time = 20.88 Current time = 20.888 Current time = 20.896 Current time = 20.904 Current time = 20.912 Current time = 20.92 Current time = 20.928 Current time = 20.936 Current time = 20.944 Current time = 20.952 Current time = 20.96 Current time = 20.968 Current time = 20.976 Current time = 20.984 Current time = 20.992 Current time = 21 Current time = 21.008 Current time = 21.016 Current time = 21.024 Current time = 21.032 Current time = 21.04 Current time = 21.048 Current time = 21.056 Current time = 21.064 Current time = 21.072 Current time = 21.08 Current time = 21.088 Current time = 21.096 Current time = 21.104 Current time = 21.112 Current time = 21.12 Current time = 21.128 Current time = 21.136 Current time = 21.144 Current time = 21.152 Current time = 21.16 Current time = 21.168 Current time = 21.176 Current time = 21.184 Current time = 21.192 Current time = 21.2 Current time = 21.208 Current time = 21.216 Current time = 21.224 Current time = 21.232 Current time = 21.24 Current time = 21.248 Current time = 21.256 Current time = 21.264 Current time = 21.272 Current time = 21.28 Current time = 21.288 Current time = 21.296 Current time = 21.304 Current time = 21.312 Current time = 21.32 Current time = 21.328 Current time = 21.336 Current time = 21.344 Current time = 21.352 Current time = 21.36 Current time = 21.368 Current time = 21.376 Current time = 21.384 Current time = 21.392 Current time = 21.4 Current time = 21.408 Current time = 21.416 Current time = 21.424 Current time = 21.432 Current time = 21.44 Current time = 21.448 Current time = 21.456 Current time = 21.464 Current time = 21.472 Current time = 21.48 Current time = 21.488 Current time = 21.496 Current time = 21.504 Current time = 21.512 Current time = 21.52 Current time = 21.528 Current time = 21.536 Current time = 21.544 Current time = 21.552 Current time = 21.56 Current time = 21.568 Current time = 21.576 Current time = 21.584 Current time = 21.592 Current time = 21.6 Current time = 21.608 Current time = 21.616 Current time = 21.624 Current time = 21.632 Current time = 21.64 Current time = 21.648 Current time = 21.656 Current time = 21.664 Current time = 21.672 Current time = 21.68 Current time = 21.688 Current time = 21.696 Current time = 21.704 Current time = 21.712 Current time = 21.72 Current time = 21.728 Current time = 21.736 Current time = 21.744 Current time = 21.752 Current time = 21.76 Current time = 21.768 Current time = 21.776 Current time = 21.784 Current time = 21.792 Current time = 21.8 Current time = 21.808 Current time = 21.816 Current time = 21.824 Current time = 21.832 Current time = 21.84 Current time = 21.848 Current time = 21.856 Current time = 21.864 Current time = 21.872 Current time = 21.88 Current time = 21.888 Current time = 21.896 Current time = 21.904 Current time = 21.912 Current time = 21.92 Current time = 21.928 Current time = 21.936 Current time = 21.944 Current time = 21.952 Current time = 21.96 Current time = 21.968 Current time = 21.976 Current time = 21.984 Current time = 21.992 Current time = 22 Current time = 22.008 Current time = 22.016 Current time = 22.024 Current time = 22.032 Current time = 22.04 Current time = 22.048 Current time = 22.056 Current time = 22.064 Current time = 22.072 Current time = 22.08 Current time = 22.088 Current time = 22.096 Current time = 22.104 Current time = 22.112 Current time = 22.12 Current time = 22.128 Current time = 22.136 Current time = 22.144 Current time = 22.152 Current time = 22.16 Current time = 22.168 Current time = 22.176 Current time = 22.184 Current time = 22.192 Current time = 22.2 Current time = 22.208 Current time = 22.216 Current time = 22.224 Current time = 22.232 Current time = 22.24 Current time = 22.248 Current time = 22.256 Current time = 22.264 Current time = 22.272 Current time = 22.28 Current time = 22.288 Current time = 22.296 Current time = 22.304 Current time = 22.312 Current time = 22.32 Current time = 22.328 Current time = 22.336 Current time = 22.344 Current time = 22.352 Current time = 22.36 Current time = 22.368 Current time = 22.376 Current time = 22.384 Current time = 22.392 Current time = 22.4 Current time = 22.408 Current time = 22.416 Current time = 22.424 Current time = 22.432 Current time = 22.44 Current time = 22.448 Current time = 22.456 Current time = 22.464 Current time = 22.472 Current time = 22.48 Current time = 22.488 Current time = 22.496 Current time = 22.504 Current time = 22.512 Current time = 22.52 Current time = 22.528 Current time = 2...

figure(1)

plot(xd, yd, 'linewidth', 1.5, 'color', '#528AFA');

hold on

plot(x, y, 'color', '#FA477A'), grid on, axis square, axis equal

xlabel({'$x$-coordinate'}, 'interpreter', 'latex')

ylabel({'$y$-coordinate'}, 'interpreter', 'latex')

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Pallov Anand on 24 Apr 2023

Ya, that I observed, but I dont think it should happen, because if we take xd and yd as just points, then changing alpha values wont matter. I wanted to know, why, in case of circular trajectory, with change in alpha trajectories varies.

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Track a circular trajectory by solving a QP and using quadprog solver (using CLF approach)

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Track a circular trajectory by solving a QP and using quadprog solver (using CLF approach)

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