Main Content


Create an optimal RRT path planner (RRT*)


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.




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.


expand all

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:



  • d — Dimension of the state space

  • n — Number of nodes in the search tree

  • η — The value of the MaxConnectionDistance property

Data Types: single | double

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.

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

Maximum number of nodes in the search tree (excluding the root node), 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)


  • 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

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

planPlan path between two states
copyCreate copy of planner object


collapse all

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

Figure contains an axes object. The axes object with title Occupancy Grid contains 3 objects of type image, line.


[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

Introduced in R2019b