plannerRRT

Create an RRT planner for geometric planning

Description

The plannerRRT object creates a rapidly-exploring random tree (RRT) planner for solving geometric planning problems. RRT is a tree-based motion planner that builds a search tree incrementally from samples randomly drawn from a given state space. The tree eventually spans the search space and connects the start state to the goal state. The general tree growing process is as follows:

1. The planner samples a random state x_rand in the state space.

2. The planner finds a state x_near that is already in the search tree and is closest (based on the distance definition in the state space) to x_rand.

3. The planner expands from x_near towards x_rand, until a state x_new is reached.

4. Then new state x_new is added to the search tree.

For geometric RRT, the expansion and connection between two states can be found analytically without violating the constraints specified in the state space of the planner object.

Creation

Syntax

planner = plannerRRT(stateSpace,stateVal)

planner = plannerRRT(___,Name=Value)

Description

planner = plannerRRT(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.

planner = plannerRRT(___,Name=Value) sets properties using one or more name-value arguments in addition to the input arguments in the previous syntax. You can specify the StateSampler, MaxNumTreeNodes, MaxIterations, MaxConnectionDistance, GoalReachedFcn, and GoalBias properties as name-value arguments.

Properties

StateSpace — State space for 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, stateSpaceReedsShepp, and stateSpaceSE3. You can also customize a state space object using the nav.StateSpace object.

StateValidator — State validator for planner

state validator object

State validator for the planner, specified as a state validator object. You can use state validator objects such as validatorOccupancyMap, validatorVehicleCostmap, and validatorOccupancyMap3D.

StateSampler — State space sampler for sampling input space

stateSamplerUniform object (default) | stateSamplerGaussian object | stateSamplerMPNET object | nav.StateSampler object

Since R2023b

State space sampler used for finding state samples in the input space, specified as a stateSamplerUniform object, stateSamplerGaussian object, stateSamplerMPNET object, or nav.StateSampler object. By default, the plannerRRT uses uniform state sampling.

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.

Example: MaxNumTreeNodes=2500

Data Types: single | double

MaxIterations — Maximum number of iterations

1e4 (default) | positive integer

Maximum number of iterations, specified as a positive integer.

Example: MaxIterations=2500

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.

Example: MaxConnectionDistance=0.3

Data Types: single | double

GoalReachedFcn — Callback function to evaluate whether goal is reached

@nav.algs.checkIfGoalIsReached | function handle

Callback function to evaluate 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 plannerRRT 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 range [0,1]

Probability of choosing the goal state during state sampling, specified as a real scalar in range [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.

Example: GoalBias=0.1

Data Types: single | double

Object Functions

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

Examples

Plan Path Between Two States

Create a state space.

ss = stateSpaceSE2;

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

sv = validatorOccupancyMap(ss);

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

load exampleMaps
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 the path planner and increase the maximum connection distance.

planner = plannerRRT(ss,sv,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'); % for repeatable result
[pthObj,solnInfo] = plan(planner,start,goal);

Visualize the results.

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

Plan Path Through 3-D Occupancy Map Using RRT Planner

Load a 3-D occupancy map of a city block into the workspace. Specify the threshold to consider cells as obstacle-free.

mapData = load("dMapCityBlock.mat");
omap = mapData.omap;
omap.FreeThreshold = 0.5;

Inflate the occupancy map to add a buffer zone for safe operation around the obstacles.

inflate(omap,1)

Create an SE(3) state space object with bounds for state variables.

ss = stateSpaceSE3([0 220;0 220;0 100;inf inf;inf inf;inf inf;inf inf]);

Create a 3-D occupancy map state validator using the created state space. Assign the occupancy map to the state validator object. Specify the sampling distance interval.

sv = validatorOccupancyMap3D(ss, ...
     Map = omap, ...
     ValidationDistance = 0.1);

Create a RRT path planner with increased maximum connection distance and reduced maximum number of iterations. Specify a custom goal function that determines that a path reaches the goal if the Euclidean distance to the target is below a threshold of 1 meter.

planner = plannerRRT(ss,sv, ...
          MaxConnectionDistance = 50, ...
          MaxIterations = 1000, ...
          GoalReachedFcn = @(~,s,g)(norm(s(1:3)-g(1:3))<1), ...
          GoalBias = 0.1);

Specify start and goal poses.

start = [40 180 25 0.7 0.2 0 0.1];
goal = [150 33 35 0.3 0 0.1 0.6];

Configure the random number generator for repeatable result.

rng(1,"twister");

Plan the path.

[pthObj,solnInfo] = plan(planner,start,goal);

Visualize the planned path.

show(omap)
axis equal
view([-10 55])
hold on
% Start state
scatter3(start(1,1),start(1,2),start(1,3),"g","filled")
% Goal state
scatter3(goal(1,1),goal(1,2),goal(1,3),"r","filled")
% Path
plot3(pthObj.States(:,1),pthObj.States(:,2),pthObj.States(:,3), ...
      "r-",LineWidth=2)

References

[1] S.M. Lavalle and J.J. Kuffner. "Randomized Kinodynamic Planning." The International Journal of Robotics Research. Vol. 20, Number 5, 2001, pp. 378 – 400.

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.

Version History

Introduced in R2019b

R2023b: Specify sampling approach for path planning

You can now specify uniform sampling, Gaussian sampling, MPNet sampling, or a custom sampling approach to generate samples for path planning. Use the name, value argument StateSampler to specify the sampling approach.