plannerRRTStar

Create an optimal RRT path planner (RRT*)

Description

The plannerRRTStar object creates an asymptotically-optimal RRT planner, RRT*. The RRT* algorithm converges to an optimal solution in terms of the state space distance. Also, its runtime is a constant factor of the runtime of the RRT algorithm. RRT* is used to solve geometric planning problems. A geometric planning problem requires that any two random states drawn from the state space can be connected.

Creation

Syntax

planner = plannerRRTStar(stateSpace,stateVal)

Description

planner = plannerRRTStar(stateSpace,stateVal) creates an RRT* planner from a state space object, stateSpace, and a state validator object, stateVal. The state space of stateVal must be the same as stateSpace. stateSpace and stateVal also sets the StateSpace and StateValidator properties of the planner object.

Properties

BallRadiusConstant — Constant used to estimate the near neighbors search radius

100 (default) | positive scalar

Constant used to estimate the near neighbors search radius, specified as a positive scalar. With a larger ball radius, the searching radius reduces slower as the number of nodes in the tree increases. The radius is estimated as following:

$$r=\min \left({\left\{\frac{\gamma \ln (n)}{n{V}_d}\right\}}^{1/d},\eta \right)$$

where:

• d — Dimension of the state space

• n — Number of nodes in the search tree

• η — The value of the MaxConnectionDistance property

• V_d — Volume of the unit ball in the dth dimension

Data Types: single | double

ContinueAfterGoalReached — Continue to optimize after goal is reached

false (default) | true

Decide if the planner continues to optimize after the goal is reached, specified as false or true. The planner also terminates regardless of the value of this property if the maximum number of iterations or maximum number of tree nodes is reached.

Data Types: logical

StateSpace — State space for the planner

state space object

State space for the planner, specified as a state space object. You can use state space objects such as stateSpaceSE2, stateSpaceDubins, and stateSpaceReedsShepp. You can also customize a state space object using the nav.StateSpace object.

StateValidator — State validator for the planner

state validator object

State validator for the planner, specified as a state validator object. You can use state validator objects such as validatorOccupancyMap and validatorVehicleCostmap.

MaxNumTreeNodes — Maximum number of nodes in the search tree

1e4 (default) | positive integer

Maximum number of nodes in the search tree (excluding the root node), specified as a positive integer.

Data Types: single | double

MaxIterations — Maximum number of iterations

1e4 (default) | positive integer

Maximum number of iterations, specified as a positive integer.

Data Types: single | double

MaxConnectionDistance — Maximum length of motion

0.1 (default) | positive scalar

Maximum length of a motion allowed in the tree, specified as a scalar.

Data Types: single | double

GoalReachedFcn — Callback function to determine whether goal is reached

@nav.algs.checkIfGoalIsReached | function handle

Callback function to determine whether the goal is reached, specified as a function handle. You can create your own goal reached function. The function must follow this syntax:

 function isReached = myGoalReachedFcn(planner,currentState,goalState)

where:

• planner — The created planner object, specified as plannerRRTStar object.

• currentState — The current state, specified as a three element real vector.

• goalState — The goal state, specified as a three element real vector.

• isReached — A boolean variable to indicate whether the current state has reached the goal state, returned as true or false.

To use custom GoalReachedFcn in code generation workflow, this property must be set to a custom function handle before calling the plan function and it cannot be changed after initialization.

Data Types: function handle

GoalBias — Probability of choosing goal state during state sampling

0.05 (default) | real scalar in [0,1]

Probability of choosing the goal state during state sampling, specified as a real scalar in [0,1]. The property defines the probability of choosing the actual goal state during the process of randomly selecting states from the state space. You can start by setting the probability to a small value such as 0.05.

Data Types: single | double

Object Functions

plan	Plan path between two states
copy	Create copy of planner object

Examples

Plan Optimal Path Between Two States

Create a state space.

ss = stateSpaceSE2;

Create a occupancyMap-based state validator using the created state space.

sv = validatorOccupancyMap(ss);

Create an occupany map from an example map and set map resolution as 10 cells/meter.

load exampleMaps.mat
map = occupancyMap(simpleMap, 10);
sv.Map = map;

Set validation distance for the validator.

sv.ValidationDistance = 0.01;

Update state space bounds to be the same as map limits.

ss.StateBounds = [map.XWorldLimits; map.YWorldLimits; [-pi pi]];

Create RRT* path planner and allow further optimization after goal is reached.

planner = plannerRRTStar(ss,sv);
planner.ContinueAfterGoalReached = true;

Reduce max iterations and increase max connection distance.

planner.MaxIterations = 2500;
planner.MaxConnectionDistance = 0.3;

Set the start and goal states.

start = [0.5, 0.5 0];
goal = [2.5, 0.2, 0];

Plan a path with default settings.

rng(100, 'twister') % repeatable result
[pthObj, solnInfo] = plan(planner,start,goal);

Visualize the results.

map.show;
hold on;
plot(solnInfo.TreeData(:,1),solnInfo.TreeData(:,2), '.-'); % tree expansion
plot(pthObj.States(:,1),pthObj.States(:,2),'r-','LineWidth',2); % draw path

References

[1] Karaman, S. and E. Frazzoli. "Sampling-Based Algorithms for Optimal Motion Planning." The International Journal of Robotics Research. Vol. 30, Number 7, 2011, pp 846 – 894.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• To use custom GoalReachedFcn in code generation workflow, this property must be set to a custom function handle before calling the plan function and it cannot be changed after initialization.