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trajectoryGeneratorFrenet

Find optimal trajectory along reference path

Since R2020b

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Description

The trajectoryGeneratorFrenet object generates alternate trajectories using fourth or fifth-order polynomials relative to a given reference path. Each trajectory defines a motion between Frenet states over a specified time span.

Frenet states describe their position, velocity and acceleration relative to a static reference path, specified as a referencePathFrenet object.

The object expresses Frenet states as a vector of form [S dS ddS L dL ddL], where S is the arc length and L is the perpendicular deviation from the direction of the reference path. Derivatives of S are relative to time. Derivatives of L are relative to the arc length, S.

Depiction of Frenet states relative to a reference path

To generate alternative trajectories, specify the initial and terminal Frenet states with a given time span to the connect object function.

Creation

Syntax

connectorFrenet = trajectoryGeneratorFrenet(refPath)
connectorFrenet = trajectoryGeneratorFrenet(refPath,'TimeResolution',timeValue)

Description

connectorFrenet = trajectoryGeneratorFrenet(refPath) generates trajectories between initial and terminal states relative to a reference path refPath specified as a referencePathFrenet object. The refPath input argument sets the ReferencePath property.

example

connectorFrenet = trajectoryGeneratorFrenet(refPath,'TimeResolution',timeValue) specifies the time interval for discretization. The timeValue argument sets the TimeResolution property.

Properties

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Discretization time interval between sampled Frenet states, specified as a positive scalar in seconds. When using the connect object function, this property determines the resolution of the Times field of the generated trajectory structures, frenetTrajectory and globalTrajectory.

Data Types: double

Reference path in Frenet coordinates, specified as a referencePathFrenet object.

Object Functions

connectConnect initial and terminal Frenet states
createParallelStateCreate states using Frenet and global parameters

Examples

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Open Live Script

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 object. The axes object contains 3 objects of type line. One or more of the lines displays its values using only markers 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,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

Figure contains an axes object. The axes object contains 9 objects of type line. One or more of the lines displays its values using only markers 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 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

Figure contains an axes object. The axes object contains 3 objects of type line. One or more of the lines displays its values using only markers 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 object. The axes object contains 3 objects of type line. One or more of the lines displays its values using only markers

References

[1] Werling, Moritz, Julius Ziegler, Sören Kammel, and Sebastian Thrun. "Optimal Trajectory Generation for Dynamic Street Scenarios in a Frenet Frame." 2010 IEEE International Conference on Robotics and Automation. 2010, pp. 987–993.

Extended Capabilities

Version History

Introduced in R2020b

See Also

Objects

Functions

Topics