Out of memory when using ode45(@t,x)

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mohammed tifr on 9 Dec 2022

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https://se.mathworks.com/matlabcentral/answers/1875022-out-of-memory-when-using-ode45-t-x

Answered: Sam Chak on 11 Dec 2022

function xdot=r2dof(t,x,ths,spec,Kpid)
xdot=zeros(8,1);
%% set-points
th1s=ths(1);
th2s=ths(2);
%% Robot Specifications
M1=spec(3);
M2=spec(4);
L1=spec(1);
L2=spec(2);
g=9.8;
%% Inertia Matrix
b11=(M1+M2)*L1^2+M2*L2^2+2*M2*L1*L2*cos(x(4));
b12=M2*L2^2+M2*L1*L2*cos(x(4));
b21=M2*L2^2+M2*L1*L2*cos(x(4));
b22=M2*L2^2;
Bq=[b11 b12;b21 b22];
%% C Matrix
c1=-M2*L1*L2*sin(x(4))*(2*x(5)*x(6)+x(6)^2);
c2=-M2*L1*L2*sin(x(4))*x(5)*x(6);
Cq=[c1;c2];
%% Gravity Matrix
g1=-(M1+M2)*g*L1*sin(x(3))-M2*g*L2*sin(x(3)+x(4));
g2=-M2*g*L2*sin(x(3)+x(4));
Gq=[g1;g2];
%% PID Control
% PID parameters for theta 1
Kp1=Kpid(1);
Kd1=Kpid(2);
Ki1=Kpid(3);
% PID parameters for theta 2
Kp2=Kpid(4);
Kd2=Kpid(5);
Ki2=Kpid(6);
%decoupled control input
f1=Kp1*(th1s-x(3))-Kd1*x(5)+Ki1*(x(1));
f2=Kp2*(th2s-x(4))-Kd2*x(6)+Ki2*(x(2));
Fhat=[f1;f2];
F=Bq*Fhat; % actual input to the system
%% System states
xdot(1)=(th1s-x(3)); %dummy state of theta1 integration
xdot(2)=(th2s-x(4)); %dummy state of theta2 integration
xdot(3)=x(5); %theta1-dot
xdot(4)=x(6); %theta2-dot
q2dot=inv(Bq)*(-Cq-Gq+F);
xdot(5)=q2dot(1); %theta1-2dot
xdot(6)=q2dot(2); %theta1-2dot
%control input function output to outside computer program
xdot(7)=F(1);
xdot(8)=F(2);

2) System Solution and Simulation (“r2dof_cntrl.m”)

close all
clear all
clc
%% Initilization
th_int=[-pi/2 pi/2]; %initial positions
ths=[pi/2 -pi/2]; %set-points
x0=[0 0 th_int 0 0 0 0]; %states initial values
Ts=[0 20]; %time span
%% Robot Specifications
L1=1; %link 1
L2=1; %link 2
M1=1; %mass 1
M2=1; %mass 2
spec=[L1 L2 M1 M2];
%% PID Parameters
% PID parameters for theta 1
Kp1=15;
Kd1=7;
Ki1=10;
% PID parameters for theta 2
Kp2=15;
Kd2=10;
Ki2=10;
Kpid=[Kp1 Kd1 Ki1 Kp2 Kd2 Ki2];
%% ODE solving
% opt1=odeset('RelTol',1e-10,'AbsTol',1e-20,'NormControl','off');
[T,X] = ode45(@(t,x) r2dof(t,x,ths,spec,Kpid),Ts,x0);

//////////////////////////////////////////////////////

ERROR

Out of memory. The likely cause is an infinite recursion within the program.

Error in r2dof (line 75)

[T,X] = ode45(@(t,x) r2dof(1, [0 0 th_int 0 0 0 0], [pi/2 -pi/2], [1 1 1 1],[1 1 1 1 1 1]),[0 20],1);

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mohammed tifr on 10 Dec 2022

Capture d’écran 2022-12-10 190235.jpg

first thank you for your answer then

the modified code

[T,X] = ode45(@(t,x) r2dof(t,x, [pi/2 -pi/2], [1 1 1 1],[1 1 1 1 1 1]),[0 20],1);

Errors(see the capture)

Torsten on 10 Dec 2022

Edited: Torsten on 10 Dec 2022

Open in MATLAB Online

Works for me.

But your call to ode45 is wrong.

[T,X] = ode45(@(t,x)r2dof(t,x,[pi/2 -pi/2],[1 1 1 1],[1 1 1 1 1 1 ]),tspan,x0)

would be correct.

r2dof(1,[0 0 [-pi/2 pi/2] 0 0 0 0 ],[pi/2 -pi/2],[1 1 1 1],[1 1 1 1 1 1 ])
ans = 8×1
    3.1416
   -3.1416
         0
         0
   -6.6584
    6.6584
    6.2832
         0
function xdot=r2dof(t,x,ths,spec,Kpid)
xdot=zeros(8,1);
%% set-points
th1s=ths(1);
th2s=ths(2);
%% Robot Specifications
M1=spec(3);
M2=spec(4);
L1=spec(1);
L2=spec(2);
g=9.8;
%% Inertia Matrix
b11=(M1+M2)*L1^2+M2*L2^2+2*M2*L1*L2*cos(x(4));
b12=M2*L2^2+M2*L1*L2*cos(x(4));
b21=M2*L2^2+M2*L1*L2*cos(x(4));
b22=M2*L2^2;
Bq=[b11 b12;b21 b22];
%% C Matrix
c1=-M2*L1*L2*sin(x(4))*(2*x(5)*x(6)+x(6)^2);
c2=-M2*L1*L2*sin(x(4))*x(5)*x(6);
Cq=[c1;c2];
%% Gravity Matrix
g1=-(M1+M2)*g*L1*sin(x(3))-M2*g*L2*sin(x(3)+x(4));
g2=-M2*g*L2*sin(x(3)+x(4));
Gq=[g1;g2];
%% PID Control
% PID parameters for theta 1
Kp1=Kpid(1);
Kd1=Kpid(2);
Ki1=Kpid(3);
% PID parameters for theta 2
Kp2=Kpid(4);
Kd2=Kpid(5);
Ki2=Kpid(6);
%decoupled control input
f1=Kp1*(th1s-x(3))-Kd1*x(5)+Ki1*(x(1));
f2=Kp2*(th2s-x(4))-Kd2*x(6)+Ki2*(x(2));
Fhat=[f1;f2];
F=Bq*Fhat; % actual input to the system
%% System states
xdot(1)=(th1s-x(3)); %dummy state of theta1 integration
xdot(2)=(th2s-x(4)); %dummy state of theta2 integration
xdot(3)=x(5); %theta1-dot
xdot(4)=x(6); %theta2-dot
q2dot=inv(Bq)*(-Cq-Gq+F);
xdot(5)=q2dot(1); %theta1-2dot
xdot(6)=q2dot(2); %theta1-2dot
%control input function output to outside computer program
xdot(7)=F(1);
xdot(8)=F(2);
end

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Answer 1

Jan on 10 Dec 2022

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https://se.mathworks.com/matlabcentral/answers/1875022-out-of-memory-when-using-ode45-t-x#answer_1125027

Edited: Jan on 10 Dec 2022

Open in MATLAB Online

I've copied your code without any changes (but adding en end at the bottom) and it is working:

%% Initilization

th_int=[-pi/2 pi/2]; %initial positions

ths=[pi/2 -pi/2]; %set-points

x0=[0 0 th_int 0 0 0 0]; %states initial values

Ts=[0 20]; %time span

%% Robot Specifications

L1=1; %link 1

L2=1; %link 2

M1=1; %mass 1

M2=1; %mass 2

spec=[L1 L2 M1 M2];

%% PID Parameters

% PID parameters for theta 1

Kp1=15;

Kd1=7;

Ki1=10;

% PID parameters for theta 2

Kp2=15;

Kd2=10;

Ki2=10;

Kpid=[Kp1 Kd1 Ki1 Kp2 Kd2 Ki2];

%% ODE solving

% opt1=odeset('RelTol',1e-10,'AbsTol',1e-20,'NormControl','off');

[T,X] = ode45(@(t,x) r2dof(t,x,ths,spec,Kpid),Ts,x0);

plot(T, X)

function xdot=r2dof(t,x,ths,spec,Kpid)

xdot=zeros(8,1);

%% set-points

th1s=ths(1);

th2s=ths(2);

%% Robot Specifications

M1=spec(3);

M2=spec(4);

L1=spec(1);

L2=spec(2);

g=9.8;

%% Inertia Matrix

b11=(M1+M2)*L1^2+M2*L2^2+2*M2*L1*L2*cos(x(4));

b12=M2*L2^2+M2*L1*L2*cos(x(4));

b21=M2*L2^2+M2*L1*L2*cos(x(4));

b22=M2*L2^2;

Bq=[b11 b12;b21 b22];

%% C Matrix

c1=-M2*L1*L2*sin(x(4))*(2*x(5)*x(6)+x(6)^2);

c2=-M2*L1*L2*sin(x(4))*x(5)*x(6);

Cq=[c1;c2];

%% Gravity Matrix

g1=-(M1+M2)*g*L1*sin(x(3))-M2*g*L2*sin(x(3)+x(4));

g2=-M2*g*L2*sin(x(3)+x(4));

Gq=[g1;g2];

%% PID Control

% PID parameters for theta 1

Kp1=Kpid(1);

Kd1=Kpid(2);

Ki1=Kpid(3);

% PID parameters for theta 2

Kp2=Kpid(4);

Kd2=Kpid(5);

Ki2=Kpid(6);

%decoupled control input

f1=Kp1*(th1s-x(3))-Kd1*x(5)+Ki1*(x(1));

f2=Kp2*(th2s-x(4))-Kd2*x(6)+Ki2*(x(2));

Fhat=[f1;f2];

F=Bq*Fhat; % actual input to the system

%% System states

xdot(1)=(th1s-x(3)); %dummy state of theta1 integration

xdot(2)=(th2s-x(4)); %dummy state of theta2 integration

xdot(3)=x(5); %theta1-dot

xdot(4)=x(6); %theta2-dot

q2dot=inv(Bq)*(-Cq-Gq+F);

xdot(5)=q2dot(1); %theta1-2dot

xdot(6)=q2dot(2); %theta1-2dot

%control input function output to outside computer program

xdot(7)=F(1);

xdot(8)=F(2);

end

So if you get errors, you do not run the posted code.

If you still have problem, post the code you run.

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Answer 2

Sam Chak on 11 Dec 2022

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https://se.mathworks.com/matlabcentral/answers/1875022-out-of-memory-when-using-ode45-t-x#answer_1125377

Open in MATLAB Online

Hi @mohammed tifr

The desired control torques cannot be integrated directly in

and

, because the actual torques are delivered by the motors. This, some minor modifications are made to assume and include the motor dynamics in

and

, as well as joint dynamics

and

.

However, I didn't check if the kinematics

and

are true for large angles. Swinging

° to

° are relatively large motion. Logically, there should be some constraints (or maybe singularity), like the elbow and shoulder.

%% Initilization

th_int = [-pi/2 pi/2]; % initial positions

ths = [ pi/2 -pi/2]; % setpoints

x0 = [0 0 th_int 0 0 0 0]; % states initial values

Ts = linspace(0, 10, 1001); % time span

%% Robot Specifications

L1 = 1; % link 1

L2 = 1; % link 2

M1 = 1; % mass 1

M2 = 1; % mass 2

spec = [L1 L2 M1 M2];

%% PID Parameters

% PID parameters for theta 1

Kp1 = 15;

Kd1 = 7;

Ki1 = 10;

% PID parameters for theta 2

Kp2 = 15;

Kd2 = 10;

Ki2 = 10;

Kpid = [Kp1 Kd1 Ki1 Kp2 Kd2 Ki2];

%% ODE solving

% opt1=odeset('RelTol',1e-10,'AbsTol',1e-20,'NormControl','off');

[t, x] = ode45(@(t,x) r2dof(t, x, ths, spec, Kpid), Ts, x0);

plot(t, x(:,3:4)*180/pi), grid on, ylabel('Angle, [\circ]')

legend('\theta_1', '\theta_2', 'fontsize', 16)

yticks(-150:60:150)

plot(t, x(:,7:8)), grid on, ylabel('Torque, [Nm]')

legend('\tau_1', '\tau_2', 'fontsize', 16)

function xdot = r2dof(t, x, ths, spec, Kpid)

xdot = zeros(8, 1);

%% set-points

th1s = ths(1);

th2s = ths(2);

%% Robot Specifications

M1 = spec(3);

M2 = spec(4);

L1 = spec(1);

L2 = spec(2);

g = 9.8;

%% Inertia Matrix

b11 = (M1 + M2)*L1^2 + M2*L2^2 + 2*M2*L1*L2*cos(x(4));

b12 = M2*L2^2 + M2*L1*L2*cos(x(4));

b21 = M2*L2^2 + M2*L1*L2*cos(x(4));

b22 = M2*L2^2;

Bq = [b11 b12; b21 b22];

%% C Matrix

c1 = - M2*L1*L2*sin(x(4))*(2*x(5)*x(6) + x(6)^2);

c2 = - M2*L1*L2*sin(x(4))*x(5)*x(6);

Cq = [c1; c2];

%% Gravity Matrix

g1 = - (M1 + M2)*g*L1*sin(x(3)) - M2*g*L2*sin(x(3) + x(4));

g2 = - M2*g*L2*sin(x(3) + x(4));

Gq = [g1; g2];

%% PID Control

% PID parameters for theta 1

Kp1 = Kpid(1);

Kd1 = Kpid(2);

Ki1 = Kpid(3);

% PID parameters for theta 2

Kp2 = Kpid(4);

Kd2 = Kpid(5);

Ki2 = Kpid(6);

% decoupled control input

f1 = - Kp1*(x(3) - th1s) - Kd1*x(5) - Ki1*(x(1));

f2 = - Kp2*(x(4) - th2s) - Kd2*x(6) - Ki2*(x(2));

Fhat = [f1; f2];

F = Bq*Fhat; % desired torques computed by formulas to the system, x7 & x8 are the actual torques delivered by the motors to the joints

%% System states

xdot(1) = x(3) - th1s; % dummy state of theta1 integration

xdot(2) = x(4) - th2s; % dummy state of theta2 integration

xdot(3) = x(5); % theta1-dot

xdot(4) = x(6); % theta2-dot

q2dot = inv(Bq)*(- Cq - Gq + [x(7); x(8)]); % actuated torques are delivered by the motors

xdot(5) = q2dot(1); % theta1-2dot

xdot(6) = q2dot(2); % theta1-2dot

% control input function output to outside computer program

% (assume the motor is fast enough to be approximated by a 1st-order function)

xdot(7) = - 1e2*(x(7) - F(1)); % can modify the motor constant

xdot(8) = - 1e2*(x(8) - F(2));

end

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Out of memory when using ode45(@t,x)

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