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State space for Dubins vehicles


The stateSpaceDubins object stores parameters and states in the Dubins 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 Dubins state space has a lower limit on the turning radius (specified by the MinTurningRadius property in the object) for navigating between states and uses the shortest feasible curve to connect states.




space = stateSpaceDubins creates a Dubins state space object with default state bounds for x, y, and θ.

space = stateSpaceDubins(bounds) specifies the bounds for x, y, and θ. The state values beyond the bounds are truncated to the bounds. The input, bounds, allows you to set 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.

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 Dubins state space and set the minimum turing radius to 0.2.

ss = stateSpaceDubins;
ss.MinTurningRadius = 0.2;

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 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

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

Extended Capabilities

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

Introduced in R2019b