trajectoryGeneratorFrenet

Find optimal trajectory along reference path

Since R2020b

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`.

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

example

````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. ```
````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

 `connect` Connect initial and terminal Frenet states `createParallelState` Create states using Frenet and global parameters

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```

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.

Version History

Introduced in R2020b