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State space for Reeds-Shepp vehicles

Since R2019b


The stateSpaceReedsShepp object stores parameters and states in the Reeds-Shepp state space, which is composed of state vectors represented by [x, y, θ]. x and y are Cartesian coordinates, and θ is the orientation angle. The Reeds-Shepp state space has a lower limit on the turning radius (specified by the MinTurningRadius property in the object) and forward and reverse costs (specified by the ForwardCost and ReverseCost properties in the object) for navigating between states.




space = stateSpaceReedsShepp creates a Reeds-Shepp state space object with default state bounds for x, y, and θ.

sapce = stateSpaceReedsShepp(bounds) specifies the bounds for x, y, and θ. The state values beyond the bounds are truncated to the bounds. The input, bounds, sets the value of the StateBounds property.


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Name of state space, specified as a string.

This property is read-only.

Dimension of the state space, specified as a positive integer.

Bounds of state variables, specified as a 3-by-2 real-valued matrix.

  • The first row specifies the lower and upper bounds for the x state in meters.

  • The second row specifies the lower and upper bounds for the y state in meters.

  • The third row specifies the lower and upper bounds for the θ state in radians.

Data Types: double

Minimum turning radius in meters, specified as a positive scalar. The minimum turning radius is for the smallest circle the vehicle can make with maximum steer in a single direction.

Cost multiplier for forward motion, specified as a positive scalar. Increase the cost to penalize forward motion.

Cost multiplier for reverse motion, specified as a positive scalar. Increase the cost to penalize reverse motion.

Object Functions

copyCreate deep copy of state space object
distanceDistance between two states
enforceStateBoundsReduce state to state bounds
interpolateInterpolate between states
sampleGaussianSample state using Gaussian distribution
sampleUniformSample state using uniform distribution


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Create a ReedsShepp state space.

ss = stateSpaceReedsShepp;

Create an occupanyMap-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
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 max connection distance.

planner = plannerRRT(ss,sv);
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] = planner.plan(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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2019b