Trapezoidal Motion Profiles in WPILib

Note

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

Note

For a guide on implementing the TrapezoidProfile class in the command-based framework framework, see Motion Profiling in Command-based.

Note

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++, Python).

Creating a TrapezoidProfile

Note

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.

Constraints

Note

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++, Python):

JAVA

// 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);

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
frc::TrapezoidProfile<units::meters>::Constraints{10_mps, 20_mps_sq};

PYTHON

from wpimath.trajectory import TrapezoidProfile
# Creates a new set of trapezoidal motion profile constraints
# Max velocity of 10 meters per second
# Max acceleration of 20 meters per second squared
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++, Python). Each state has a position and a velocity:

JAVA

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

C++

// Creates a new state with a position of 5 meters
// and a velocity of 0 meters per second
frc::TrapezoidProfile<units::meters>::State{5_m, 0_mps};

PYTHON

from wpimath.trajectory import TrapezoidProfile
# Creates a new state with a position of 5 meters
# and a velocity of 0 meters per second
TrapezoidProfile.State(5, 0)

Putting It All Together

Note

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 1 parameter: the constraints.

JAVA

// 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
TrapezoidProfile profile = new TrapezoidProfile(new TrapezoidProfile.Constraints(5, 10));

C++

// 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
frc::TrapezoidProfile<units::meters> profile{
  frc::TrapezoidProfile<units::meters>::Constraints{5_mps, 10_mps_sq}};

PYTHON

from wpimath.trajectory import TrapezoidProfile
# 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 = TrapezoidProfile(TrapezoidProfile.Constraints(5, 10))

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 with the goal state and initial state:

JAVA

// Profile will start stationary at zero position
// Profile will end stationary at 5 meters
// Returns the motion profile state after 5 seconds of motion
profile.calculate(5, new TrapezoidProfile.State(0, 0), new TrapezoidProfile.State(5, 0));

C++

// Profile will start stationary at zero position
// Profile will end stationary at 5 meters
// Returns the motion profile state after 5 seconds of motion
profile.Calculate(5_s,
frc::TrapezoidProfile<units::meters>::State{0_m, 0_mps},
frc::TrapezoidProfile<units::meters>::State{5_m, 0_mps});

PYTHON

# Profile will start stationary at zero position
# Profile will end stationary at 5 meters
# Returns the motion profile state after 5 seconds of motion
profile.calculate(5, TrapezoidProfile.State(0, 0), TrapezoidProfile.State(5, 0))

Using the State

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

JAVA

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

C++

auto setpoint = profile.Calculate(elapsedTime, initialState, goalState);
controller.Calculate(encoder.GetDistance(), setpoint.position.value());

PYTHON

setpoint = profile.calculate(elapsedTime, initialState, goalState)
controller.calculate(encoder.getDistance(), setpoint.position)

Complete Usage Example

Note

In this example, the initial state 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 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++, Python):

JAVA

package edu.wpi.first.wpilibj.examples.elevatortrapezoidprofile;

import edu.wpi.first.math.controller.SimpleMotorFeedforward;
import edu.wpi.first.math.trajectory.TrapezoidProfile;
import edu.wpi.first.wpilibj.Joystick;
import edu.wpi.first.wpilibj.TimedRobot;

public class Robot extends TimedRobot {
  private static double kDt = 0.02;

  private final Joystick m_joystick = new Joystick(1);
  private final ExampleSmartMotorController m_motor = new ExampleSmartMotorController(1);
  // Note: These gains are fake, and will have to be tuned for your robot.
  private final SimpleMotorFeedforward m_feedforward = new SimpleMotorFeedforward(1, 1.5);

  // Create a motion profile with the given maximum velocity and maximum
  // acceleration constraints for the next setpoint.
  private final TrapezoidProfile m_profile =
      new TrapezoidProfile(new TrapezoidProfile.Constraints(1.75, 0.75));
  private TrapezoidProfile.State m_goal = new TrapezoidProfile.State();
  private TrapezoidProfile.State m_setpoint = new TrapezoidProfile.State();

  public Robot() {
    // Note: These gains are fake, and will have to be tuned for your robot.
    m_motor.setPID(1.3, 0.0, 0.7);
  }

  @Override
  public void teleopPeriodic() {
    if (m_joystick.getRawButtonPressed(2)) {
      m_goal = new TrapezoidProfile.State(5, 0);
    } else if (m_joystick.getRawButtonPressed(3)) {
      m_goal = new TrapezoidProfile.State();
    }

    // Retrieve the profiled setpoint for the next timestep. This setpoint moves
    // toward the goal while obeying the constraints.
    m_setpoint = m_profile.calculate(kDt, m_setpoint, m_goal);

    // Send setpoint to offboard controller PID
    m_motor.setSetpoint(
        ExampleSmartMotorController.PIDMode.kPosition,
        m_setpoint.position,
        m_feedforward.calculate(m_setpoint.velocity) / 12.0);
  }
}

C++

#include <numbers>

#include <frc/Joystick.h>
#include <frc/TimedRobot.h>
#include <frc/controller/SimpleMotorFeedforward.h>
#include <frc/trajectory/TrapezoidProfile.h>
#include <units/acceleration.h>
#include <units/length.h>
#include <units/time.h>
#include <units/velocity.h>
#include <units/voltage.h>

#include "ExampleSmartMotorController.h"

class Robot : public frc::TimedRobot {
 public:
  static constexpr units::second_t kDt = 20_ms;

  Robot() {
    // Note: These gains are fake, and will have to be tuned for your robot.
    m_motor.SetPID(1.3, 0.0, 0.7);
  }

  void TeleopPeriodic() override {
    if (m_joystick.GetRawButtonPressed(2)) {
      m_goal = {5_m, 0_mps};
    } else if (m_joystick.GetRawButtonPressed(3)) {
      m_goal = {0_m, 0_mps};
    }

    // Retrieve the profiled setpoint for the next timestep. This setpoint moves
    // toward the goal while obeying the constraints.
    m_setpoint = m_profile.Calculate(kDt, m_setpoint, m_goal);

    // Send setpoint to offboard controller PID
    m_motor.SetSetpoint(ExampleSmartMotorController::PIDMode::kPosition,
                        m_setpoint.position.value(),
                        m_feedforward.Calculate(m_setpoint.velocity) / 12_V);
  }

 private:
  frc::Joystick m_joystick{1};
  ExampleSmartMotorController m_motor{1};
  frc::SimpleMotorFeedforward<units::meters> m_feedforward{
      // Note: These gains are fake, and will have to be tuned for your robot.
      1_V, 1.5_V * 1_s / 1_m};

  // Create a motion profile with the given maximum velocity and maximum
  // acceleration constraints for the next setpoint.
  frc::TrapezoidProfile<units::meters> m_profile{{1.75_mps, 0.75_mps_sq}};
  frc::TrapezoidProfile<units::meters>::State m_goal;
  frc::TrapezoidProfile<units::meters>::State m_setpoint;
};

#ifndef RUNNING_FRC_TESTS
int main() {
  return frc::StartRobot<Robot>();
}
#endif

PYTHON

import wpilib
import wpimath.controller
from wpimath.trajectory import TrapezoidProfile

import examplesmartmotorcontroller


class MyRobot(wpilib.TimedRobot):
    kDt = 0.02

    def robotInit(self):
        self.joystick = wpilib.Joystick(1)
        self.motor = examplesmartmotorcontroller.ExampleSmartMotorController(1)
        # Note: These gains are fake, and will have to be tuned for your robot.
        self.feedforward = wpimath.controller.SimpleMotorFeedforwardMeters(1, 1.5)

        # Create a motion profile with the given maximum velocity and maximum
        # acceleration constraints for the next setpoint.
        self.profile = TrapezoidProfile(TrapezoidProfile.Constraints(1.75, 0.75))

        self.goal = TrapezoidProfile.State()
        self.setpoint = TrapezoidProfile.State()

        # Note: These gains are fake, and will have to be tuned for your robot.
        self.motor.setPID(1.3, 0.0, 0.7)

    def teleopPeriodic(self):
        if self.joystick.getRawButtonPressed(2):
            self.goal = TrapezoidProfile.State(5, 0)
        elif self.joystick.getRawButtonPressed(3):
            self.goal = TrapezoidProfile.State(0, 0)

        # Retrieve the profiled setpoint for the next timestep. This setpoint moves
        # toward the goal while obeying the constraints.
        self.setpoint = self.profile.calculate(self.kDt, self.setpoint, self.goal)

        # Send setpoint to offboard controller PID
        self.motor.setSetPoint(
            examplesmartmotorcontroller.ExampleSmartMotorController.PIDMode.kPosition,
            self.setpoint.position,
            self.feedforward.calculate(self.setpoint.velocity) / 12,
        )