stateSpaceSE2

SE(2) state space

Description

The stateSpaceSE2 object stores parameters and states in the SE(2) 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 object uses Euclidean distance to calculate distance and uses linear interpolation to calculate translation and rotation of the state.

Creation

Syntax

space = stateSpaceSE2

space = stateSpaceSE2(bounds)

Description

space = stateSpaceSE2 creates an SE(2) state space object with default state bounds for x, y, and θ.

space = stateSpaceSE2(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' (default) | string

Name of state space, specified as a string.

NumStateVariables — Dimension of the state space

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 of the x state in meters.

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

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

Data Types: double

WeightXY — Weight applied to x and y distance calculation

1 (default) | nonnegative real scalar

Weight applied to x and y distance calculation, specified as a nonnegative real scalar.

In the object, the distance calculated as:

$$d=\sqrt{\left(w_{xy}(d_x^2+d_y^2)\right)+w_{\theta }{d}_{\theta }^2}$$

w_xy is weight applied to x and y coordinates, and w_θ is the weight applied to the θ coordinate. d_x, d_y, and d_θ are the distances in the x, y, and θ direction, respectively.

Data Types: double

WeightTheta — Weight applied to theta distance calculation

0.1 (default) | nonnegative real scalar

Weight applied to θ distance calculation, specified as a nonnegative real scalar.

In the object, the distance calculated as:

$$d=\sqrt{\left(w_{xy}(d_x^2+d_y^2)\right)+w_{\theta }{d}_{\theta }^2}$$

w_xy is weight applied to x and y coordinates, and w_θ is the weight applied to the θ coordinate. d_x, d_y, and d_θ are the distances in the x, y, and θ direction, respectively.

Data Types: double

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 SE(2) States

Create an SE(2) 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 maximum 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'); % for repeatable result
[pthObj,solnInfo] = planner.plan(start,goal);

Visualize the results.

map.show; 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