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connect

Connect initial and terminal Frenet states

Since R2020b

Description

frenetTrajectory = connect(connectorFrenet,initialState,terminalState,timeSpan) connects the specified initial Frenet states to the specified terminal states over a span of time in seconds. This object function supports 1-to-n, n-to-1, or n-to-n pairwise trajectory connections.

example

[___,globalTrajectory] = connect(___) returns the trajectories in global coordinates in addition to all arguments in the previous syntax.

Examples

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Generate alternative trajectories for a reference path using Frenet coordinates. Specify different initial and terminal states for your trajectories. Tune your states based on the generated trajectories.

Generate a reference path from a set of waypoints. Create a trajectoryGeneratorFrenet object from the reference path.

waypoints = [0 0; ...
	50 20; ...
	100 0; ...
	150 10];
refPath = referencePathFrenet(waypoints);
connector = trajectoryGeneratorFrenet(refPath);

Generate a five-second trajectory between the path origin and a point 30 m down the path as Frenet states.

initState = [0 0 0 0 0 0];  % [S ds ddS L dL ddL]
termState = [30 0 0 0 0 0]; % [S ds ddS L dL ddL]
[~,trajGlobal] = connect(connector,initState,termState,5);

Display the trajectory in global coordinates.

show(refPath);
hold on
axis equal
plot(trajGlobal.Trajectory(:,1),trajGlobal.Trajectory(:,2),'b')
legend(["Waypoints","Reference Path","Trajectory to 30m"])

Create a matrix of terminal states with lateral deviations between –3 m and 3 m. Generate trajectories that cover the same arc length in 10 seconds, but deviate laterally from the reference path. Display the new alternative paths.

termStateDeviated = termState + ([-3:3]' * [0 0 0 1 0 0]);
[~,trajGlobal] = connect(connector,initState,termStateDeviated,10);

clf
show(refPath);
hold on
axis equal
for i = 1:length(trajGlobal)
    plot(trajGlobal(i).Trajectory(:,1),trajGlobal(i).Trajectory(:,2),'g')
end
legend(["Waypoints","Reference Path","Alternative Trajectories"])
hold off

Specify a new terminal state to generate a new trajectory. This trajectory is not desirable because it requires reverse motion to achieve a longitudinal velocity of 10 m/s.

newTermState = [5 10 0 5 0 0];
[~,newTrajGlobal] = connect(connector,initState,newTermState,3);

clf
show(refPath);
hold on
axis equal
plot(newTrajGlobal.Trajectory(:,1),newTrajGlobal.Trajectory(:,2),'b');
legend(["Waypoint","Reference Path","New Trajectory"])
hold off

Relax the restriction on the longitudinal state by specifying an arc length of NaN. Generate and display the trajectory again. The new position shows a good alternative trajectory that deviates off the reference path.

relaxedTermState = [NaN 10 0 5 0 0];
[~,trajGlobalRelaxed] = connect(connector,initState,relaxedTermState,3);

clf
show(refPath);
hold on
axis equal
plot(trajGlobalRelaxed.Trajectory(:,1),trajGlobalRelaxed.Trajectory(:,2),'g');
hold off

Input Arguments

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Frenet trajectory generator, specified as a trajectoryGeneratorFrenet object.

Initial Frenet states, specified as an n-by-6 numeric matrix. Each row of the matrix is a set of Frenet coordinates for the initial state of a trajectory in the form [S dS ddS L dL ddL]. The value of n must be equal to the number of rows in the terminalState argument or 1.

Final Frenet states, specified as an n-by-6 numeric matrix. Each row of the matrix is a set of Frenet coordinates for the initial state of a trajectory in the form [S dS ddS L dL ddL]. The value of n must be equal to the number of rows in the initialState argument or 1.

Time horizon for all trajectories, specified as a positive scalar in seconds. The generated trajectories are sampled evenly across this time span based on the TimeResolution property of the trajectoryGeneratorFrenet object specified in the connectorFrenet argument.

Output Arguments

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Frenet trajectories between all initial and final states, returned as a structure array with these fields:

  • Trajectoryn-by-6 numeric matrix. Each row of the matrix is a set of Frenet coordinates for the initial state of a trajectory in the form [S dS ddS L dL ddL].

  • Time — Vector of positive scalars from 0 to timeSpan in seconds.

Depiction of Frenet states relative to a reference path

This function supports 1-to-n, n-to-1, or n-to-n pairwise trajectory connections based on the number of rows of initialState and terminalState.

Global trajectories between all initial and final states, returned as structure or structure array with fields:

  • Trajectoryn-by-6 numeric matrix. Each row of the matrix is a set of global sates of the form [x y theta kappa v a].

  • Time — Vector of positive scalars from 0 to timeSpan in seconds.

Depiction of global Frenet coordinates

This function supports 1-to-n, n-to-1, or n-to-n pairwise trajectory connections based on the number of rows of initialState and terminalState.

Extended Capabilities

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

Version History

Introduced in R2020b