stateSpaceDubins

State space for Dubins vehicles

Description

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.

Creation

Syntax

space = stateSpaceDubins

space = stateSpaceDubins(bounds)

Description

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.

Properties

Name — Name of state space

'SE2 Dubins' (default) | string

Name of state space, specified as a string.

NumStateVariables — Dimension of the state space

Read-only: 3 (default) | positive integer

This property is read-only.

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

StateBounds — Bounds of state variables

[-100 100; -100 100; -3.1416 3.1416] (default) | 3-by-2 real-valued matrix

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

MinTurningRadius — Minimum turning radius

1 (default) | positive scalar

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

copy	Create deep copy of state space object
distance	Distance between two states
enforceStateBounds	Reduce state to state bounds
interpolate	Interpolate between states
sampleGaussian	Sample state using Gaussian distribution
sampleUniform	Sample state using uniform distribution

Examples

Plan Path Between Two States in Dubins State Space

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.

show(map);
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