# 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

### Description

example

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

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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:

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

where:

• d — Dimension of the state space

• n — Number of nodes in the search tree

• η — The value of the MaxConnectionDistance property

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

Data Types: object

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

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.

Data Types: object

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

Data Types: object

Maximum number of nodes in the search tree, specified as a positive integer.

Data Types: single | double

Maximum number of iterations, specified as a positive integer.

Data Types: single | double

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

Data Types: single | double

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.

Data Types: function handle

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

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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 and set map resolution as 10 cells/meter.

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.

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." International Journal of Robotics Research . Vol. 30, Number 7, 2011, pp 846 – 894.