Trajectory Generation

This article goes over how to generate a trajectory. The next few articles in this series will go over how to actually follow the generated trajectory. There are a few things that your robot must have before you dive into the world of trajectories:

  • A way to measure the position and velocity of each side of the robot. An encoder is the best way to do this; however, other options may include optical flow sensors, etc.

  • A way to measure the angle or angular rate of the robot chassis. A gyroscope is the best way to do this. Although the angular rate can be calculated using encoder velocities, this method is NOT recommended because of wheel scrubbing.


A spline refers to a set of curves that interpolate between points. Think of it as connecting dots, except with curves. FTCLib supports two types of splines: hermite clamped cubic and hermite quintic.

  • Hermite clamped cubic: This is the recommended option for most users. Generation of trajectories using these splines involves specifying the (x, y) coordinates of all points, and the headings at the start and end waypoints. The headings at the interior waypoints are automatically determined to ensure continuous curvature (rate of change of the heading) throughout.

  • Hermite quintic: This is a more advanced option which requires the user to specify (x, y) coordinates and headings for all waypoints. This should be used if you are unhappy with the trajectories that are being generated by the clamped cubic splines or if you want finer control of headings at the interior points.

Splines are used as a tool to generate trajectories; however, the spline itself does not have any information about velocities and accelerations. Therefore, it is not recommended that you use the spline classes directly. In order to generate a smooth path with velocities and accelerations, a trajectory must be generated.

Creating the Trajectory Configuration

A configuration must be created in order to generate a trajectory. The config contains information about special constraints, the max velocity, the max acceleration in addition to the start velocity and end velocity. The config also contains information about whether the trajectory should be reversed (robot travels backward along the waypoints). The TrajectoryConfig class should be used to construct a config. The constructor for this class takes two arguments, the max velocity and max acceleration. The other fields (startVelocity, endVelocity, reversed, constraints) are defaulted to reasonable values (0, 0, false, {}) when the object is created. If you wish to modify the values of any of these fields, you can call the following methods:

  • setStartVelocity(double startVelocityMetersPerSecond)

  • setEndVelocity(double endVelocityMetersPerSecond)

  • setReversed(boolean reversed)

  • addConstraint(TrajectoryConstraint constraint)


The reversed property simply represents whether the robot is traveling backward. If you specify four waypoints, a, b, c, and d, the robot will still travel in the same order through the waypoints when the reversed flag is set to true. This also means that you must account for the direction of the robot when providing the waypoints. For example, if your robot is facing your alliance station wall and travels backwards to some field element, the starting waypoint should have a rotation of 180 degrees.

Generating the Trajectory

The method used to generate a trajectory is generateTrajectory(...). There are four overloads for this method. Two that use clamped cubic splines and the two others that use quintic splines. For each type of spline, there are two ways to construct a trajectory. The easiest methods are the overloads that accept Pose2d objects.

For clamped cubic splines, this method accepts two Pose2d objects, one for the starting waypoint and one for the ending waypoint. The method takes in a vector of Translation2d objects which represent the interior waypoints. The headings at these interior waypoints are determined automatically to ensure continuous curvature. For quintic splines, the method simply takes in a list of Pose2d objects, with each Pose2d representing a point and heading on the field.

The more complex overload accepts “control vectors” for splines. The ControlVector class consists of two double arrays. Each array represents one dimension (x or y), and its elements represent the derivatives at that point. For example, the value at element 0 of the x array represents the x coordinate (0th derivative), the value at element 1 represents the 1st derivative in the x dimension and so on.

When using clamped cubic splines, the length of the array must be 2 (0th and 1st derivatives), whereas when using quintic splines, the length of the array should be 3 (0th, 1st, and 2nd derivative). Unless you know exactly what you are doing, the first and simpler method is HIGHLY recommended for manually generating trajectories.

Here is an example of generating a trajectory using clamped cubic splines for the 2018 game, FIRST Power Up:

class ExampleTrajectory {
  public void generateTrajectory() {

    // 2018 cross scale auto waypoints.
    var sideStart = new Pose2d(Units.feetToMeters(1.54), Units.feetToMeters(23.23),
    var crossScale = new Pose2d(Units.feetToMeters(23.7), Units.feetToMeters(6.8),

    var interiorWaypoints = new ArrayList<Translation2d>();
    interiorWaypoints.add(new Translation2d(Units.feetToMeters(14.54), Units.feetToMeters(23.23)));
    interiorWaypoints.add(new Translation2d(Units.feetToMeters(21.04), Units.feetToMeters(18.23)));

    TrajectoryConfig config = new TrajectoryConfig(Units.feetToMeters(12), Units.feetToMeters(12));

    var trajectory = TrajectoryGenerator.generateTrajectory(

Note that this is not code from FTCLib and is instead a sample from WPILib docs. The keyword var is used here, but that is a feature from Java 10 which is not supported for Android development. The keyword has the compiler interpret the variable type and assign accordingly. Instead of this, use the actual variable type definition. The Units class is also not available in FTCLib and is instead a WPILib utility.

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