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sampleGaussian

Sample state using Gaussian distribution

Description

example

states = sampleGaussian(manipSS,meanState,stdDev) samples a state in the state space manipSS from a Gaussian (normal) distribution centered on the mean meanState with the standard deviation, stdDev.

states = sampleGaussian(manipSS,meanState,stdDev,numSamples) samples the number of multiple states specified by numSamples.

Examples

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Generate states to form a path, validate motion between states, and check for self-collisions and environmental collisions with objects in your world. The manipulatorStateSpace object represents the joint configuration space of your rigid body tree robot model, and can sample states, calculate distances, and enforce state bounds. The manipulatorCollisionBodyValidator object validates the state and motion based on the collision bodies in your robot model and any obstacles in your environment.

Load Robot Model

Use the loadrobot function to access predefined robot models. This example uses the Quanser QArm™ robot and joint configurations are specified as row vectors.

robot = loadrobot("quanserQArm",DataFormat="row");
figure(Visible="on")
show(robot);
xlim([-0.5 0.5])
ylim([-0.5 0.5])
zlim([-0.25 0.75])
hold on

Figure contains an axes object. The axes object contains 16 objects of type patch, line. These objects represent world, base_link, YAW, BICEP, FOREARM, END-EFFECTOR, base_link_mesh, YAW_mesh, BICEP_mesh, FOREARM_mesh, END-EFFECTOR_mesh.

Configure State Space and State Validation

Create the state space and state validator from the robot model.

ss = manipulatorStateSpace(robot);
sv = manipulatorCollisionBodyValidator(ss);

Set the validation distance to 0.05, which is based on the distance normal between two states. You can configure the validator to ignore self collisions to improve the speed of validation, but must consider whether your robot model has the proper joint limit settings set to ensure it does not collide with itself.

sv.ValidationDistance = 0.05;
sv.IgnoreSelfCollision = true;

Place collision objects in the robot environment. Set the Environment property of the collision validator object using a cell array of objects.

box = collisionBox(0.1,0.1,0.5); % XYZ Lengths
box.Pose = trvec2tform([0.2 0.2 0.5]); % XYZ Position
sphere = collisionSphere(0.25); % Radius
sphere.Pose = trvec2tform([-0.2 -0.2 0.5]); % XYZ Position
env = {box sphere};
sv.Environment = env;

Visualize the environment.

for i = 1:length(env)
    show(env{i})
end
view(60,10)

Figure contains an axes object. The axes object contains 18 objects of type patch, line. These objects represent world, base_link, YAW, BICEP, FOREARM, END-EFFECTOR, base_link_mesh, YAW_mesh, BICEP_mesh, FOREARM_mesh, END-EFFECTOR_mesh.

Plan Path

Start with the home configuration as the first point on the path.

rng(0); % Repeatable results
start = homeConfiguration(robot);
path = start;
idx = 1;

Plan a path using these steps, in a loop:

  • Sample a nearby goal configuration, using the Gaussian distribution, by specifying the standard deviation for each joint angle.

  • Check if the sampled goal state is valid.

  • If the sampled goal state is valid, check if the motion between states is valid and, if so, add it to the path.

for i = 2:25
    goal = sampleGaussian(ss,start,0.25*ones(4,1));
    validState = isStateValid(sv,goal);
    
    if validState % If state is valid, check motion between states.
        [validMotion,~] = isMotionValid(sv,path(idx,:),goal);

        if validMotion % If motion is valid, add to path.
            path = [path; goal];
            idx = idx + 1;
        end
    end
end

Visualize Path

After generating the path of valid motions, visualize the robot motion. Because you sampled random states near the home configuration, you should see the arm move around that initial configuration.

To visualize the path of the end effector in 3-D, get the transformation, relative to the base world frame at each point. Store the points as an xyz translation vector. Plot the path of the end effector.

eePose = nan(3,size(path,1));

for i = 1:size(path,1)
    show(robot,path(i,:),PreservePlot=false);
    eePos(i,:) = tform2trvec(getTransform(robot,path(i,:),"END-EFFECTOR")); % XYZ translation vector
    plot3(eePos(:,1),eePos(:,2),eePos(:,3),"-b",LineWidth=2)
    drawnow
end

Figure contains an axes object. The axes object contains 28 objects of type patch, line. These objects represent world, base_link, YAW, BICEP, FOREARM, END-EFFECTOR, base_link_mesh, YAW_mesh, BICEP_mesh, FOREARM_mesh, END-EFFECTOR_mesh.

Input Arguments

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Manipulator state space, specified as a manipulatorStateSpace object, which is a subclass of nav.StateSpace (Navigation Toolbox).

Mean state position, specified as an n-element row vector, where n is the dimension of the state space specified in the NumStateVariables property of manipSS.

Standard deviation around the mean state, specified as an n-element row vector. Each element corresponds to an element in meanState.

Number of samples, specified as a positive integer.

Output Arguments

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Sampled states from the state space, returned as an n-element row vector or m-by-n matrix. n is the dimension of the state space specified in the NumStateVariables property of manipSS. m is the number of samples specified in numSamples. All states are sampled within the bounds specified by the StateBounds property of manipSS.

Introduced in R2021b