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connect

Connect initial and terminal Frenet states

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"])

Figure contains an axes. The axes contains 3 objects of type line. These objects represent 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,5);

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

Figure contains an axes. The axes contains 9 objects of type line. These objects represent Waypoints, Reference Path, Alternative Trajectories.

Specify a new terminal state to generate a new trajectory. This trajectory is not desirable because it requires reverse motion to achieve a lateral 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

Figure contains an axes. The axes contains 3 objects of type line. These objects represent Waypoint, Reference Path, New Trajectory.

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

Figure contains an axes. The axes contains 3 objects of type line.

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 dkappa s].

  • 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™.

Introduced in R2020b