Trapezoidal Motion Profiles in WPILib


This article covers the in-code generation of trapezoidal motion profiles. Documentation describing the involved concepts in more detail is forthcoming.


For a guide on implementing the TrapezoidProfile class in the command-based framework framework, see Motion Profiling through TrapezoidProfileSubsystems and TrapezoidProfileCommands.


The TrapezoidProfile class, used on its own, is most useful when composed with a custom controller (such as a «smart» motor controller with a built-in PID functionality). To integrate it with a WPILib PIDController, see Combining Motion Profiling and PID Control with ProfiledPIDController.

While feedforward and feedback control offer convenient ways to achieve a given setpoint, we are often still faced with the problem of generating setpoints for our mechanisms. While the naive approach of immediately commanding a mechanism to its desired state may work, it is often suboptimal. To improve the handling of our mechanisms, we often wish to command mechanisms to a sequence of setpoints that smoothly interpolate between its current state, and its desired goal state.

To help users do this, WPILib provides a TrapezoidProfile class (Java, C++).

Creating a TrapezoidProfile


In C++, the TrapezoidProfile class is templated on the unit type used for distance measurements, which may be angular or linear. The passed-in values must have units consistent with the distance units, or a compile-time error will be thrown. For more information on C++ units, see The C++ Units Library.



The various feedforward helper classes provide methods for calculating the maximum simultaneously-achievable velocity and acceleration of a mechanism. These can be very useful for calculating appropriate motion constraints for your TrapezoidProfile.

In order to create a trapezoidal motion profile, we must first impose some constraints on the desired motion. Namely, we must specify a maximum velocity and acceleration that the mechanism will be expected to achieve during the motion. To do this, we create an instance of the TrapezoidProfile.Constraints class (Java, C++):

// Creates a new set of trapezoidal motion profile constraints
// Max velocity of 10 meters per second
// Max acceleration of 20 meters per second squared
new TrapezoidProfile.Constraints(10, 20);

Start and End States

Next, we must specify the desired starting and ending states for our mechanisms using the TrapezoidProfile.State class (Java, C++). Each state has a position and a velocity:

// Creates a new state with a position of 5 meters
// and a velocity of 0 meters per second
new TrapezoidProfile.State(5, 0);

Putting It All Together


C++ is often able to infer the type of the inner classes, and thus a simple initializer list (without the class name) can be sent as a parameter. The full class names are included in the example below for clarity.

Now that we know how to create a set of constraints and the desired start/end states, we are ready to create our motion profile. The TrapezoidProfile constructor takes 3 parameters, in order: the constraints, the goal state, and the initial state.

// Creates a new TrapezoidProfile
// Profile will have a max vel of 5 meters per second
// Profile will have a max acceleration of 10 meters per second squared
// Profile will end stationary at 5 meters
// Profile will start stationary at zero position
TrapezoidProfile profile = new TrapezoidProfile(new TrapezoidProfile.Constraints(5, 10),
                                                new TrapezoidProfile.State(5, 0),
                                                new TrapezoidProfile.State(0, 0));

Using a TrapezoidProfile

Sampling the Profile

Once we’ve created a TrapezoidProfile, using it is very simple: to get the profile state at the given time after the profile has started, call the calculate() method:

// Returns the motion profile state after 5 seconds of motion

Using the State

The calculate method returns a TrapezoidProfile.State class (the same one that was used to specify the initial/end states when constructing the profile). To use this for actual control, simply pass the contained position and velocity values to whatever controller you wish (for example, a PIDController):

var setpoint = profile.calculate(elapsedTime);
controller.calculate(encoder.getDistance(), setpoint.position);

Complete Usage Example


In this example, the profile is re-computed every timestep. This is a somewhat different usage technique than is detailed above, but works according to the same principles - the profile is sampled at at a time corresponding to the loop period to get the setpoint for the next loop iteration.

A more complete example of TrapezoidProfile usage is provided in the ElevatorTrapezoidProfile example project (Java, C++):

 5package edu.wpi.first.wpilibj.examples.elevatortrapezoidprofile;
 7import edu.wpi.first.math.controller.SimpleMotorFeedforward;
 8import edu.wpi.first.math.trajectory.TrapezoidProfile;
 9import edu.wpi.first.wpilibj.Joystick;
10import edu.wpi.first.wpilibj.TimedRobot;
12public class Robot extends TimedRobot {
13  private static double kDt = 0.02;
15  private final Joystick m_joystick = new Joystick(1);
16  private final ExampleSmartMotorController m_motor = new ExampleSmartMotorController(1);
17  // Note: These gains are fake, and will have to be tuned for your robot.
18  private final SimpleMotorFeedforward m_feedforward = new SimpleMotorFeedforward(1, 1.5);
20  private final TrapezoidProfile.Constraints m_constraints =
21      new TrapezoidProfile.Constraints(1.75, 0.75);
22  private TrapezoidProfile.State m_goal = new TrapezoidProfile.State();
23  private TrapezoidProfile.State m_setpoint = new TrapezoidProfile.State();
25  @Override
26  public void robotInit() {
27    // Note: These gains are fake, and will have to be tuned for your robot.
28    m_motor.setPID(1.3, 0.0, 0.7);
29  }
31  @Override
32  public void teleopPeriodic() {
33    if (m_joystick.getRawButtonPressed(2)) {
34      m_goal = new TrapezoidProfile.State(5, 0);
35    } else if (m_joystick.getRawButtonPressed(3)) {
36      m_goal = new TrapezoidProfile.State(0, 0);
37    }
39    // Create a motion profile with the given maximum velocity and maximum
40    // acceleration constraints for the next setpoint, the desired goal, and the
41    // current setpoint.
42    var profile = new TrapezoidProfile(m_constraints, m_goal, m_setpoint);
44    // Retrieve the profiled setpoint for the next timestep. This setpoint moves
45    // toward the goal while obeying the constraints.
46    m_setpoint = profile.calculate(kDt);
48    // Send setpoint to offboard controller PID
49    m_motor.setSetpoint(
50        ExampleSmartMotorController.PIDMode.kPosition,
51        m_setpoint.position,
52        m_feedforward.calculate(m_setpoint.velocity) / 12.0);
53  }