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 through TrapezoidProfileSubsystems and TrapezoidProfileCommands.
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++).
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++):
// 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);
// 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};
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);
// 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};
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.
// 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));
// 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}};
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:
// Profile will end stationary at 5 meters
// Profile will start stationary at zero position
// Returns the motion profile state after 5 seconds of motion
profile.calculate(5, new TrapezoidProfile.State(5, 0), new TrapezoidProfile.State(0, 0));
// Profile will end stationary at 5 meters
// Profile will start stationary at zero position
// Returns the motion profile state after 5 seconds of motion
profile.Calculate(5_s,
frc::TrapezoidProfile<units::meters>::State{5_m, 0_mps},
frc::TrapezoidProfile<units::meters>::State{0_m, 0_mps});
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):
var setpoint = profile.calculate(elapsedTime, goalState, initialState);
controller.calculate(encoder.getDistance(), setpoint.position);
auto setpoint = profile.Calculate(elapsedTime, goalState, initialState);
controller.Calculate(encoder.GetDistance(), setpoint.position.value());
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++):
5package edu.wpi.first.wpilibj.examples.elevatortrapezoidprofile;
6
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;
11
12public class Robot extends TimedRobot {
13 private static double kDt = 0.02;
14
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);
19
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();
24
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 }
30
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 }
38
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);
43
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);
47
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 }
54}
5#include <numbers>
6
7#include <frc/Joystick.h>
8#include <frc/TimedRobot.h>
9#include <frc/controller/SimpleMotorFeedforward.h>
10#include <frc/trajectory/TrapezoidProfile.h>
11#include <units/acceleration.h>
12#include <units/length.h>
13#include <units/time.h>
14#include <units/velocity.h>
15#include <units/voltage.h>
16
17#include "ExampleSmartMotorController.h"
18
19class Robot : public frc::TimedRobot {
20 public:
21 static constexpr units::second_t kDt = 20_ms;
22
23 Robot() {
24 // Note: These gains are fake, and will have to be tuned for your robot.
25 m_motor.SetPID(1.3, 0.0, 0.7);
26 }
27
28 void TeleopPeriodic() override {
29 if (m_joystick.GetRawButtonPressed(2)) {
30 m_goal = {5_m, 0_mps};
31 } else if (m_joystick.GetRawButtonPressed(3)) {
32 m_goal = {0_m, 0_mps};
33 }
34
35 // Create a motion profile with the given maximum velocity and maximum
36 // acceleration constraints for the next setpoint, the desired goal, and the
37 // current setpoint.
38 frc::TrapezoidProfile<units::meters> profile{m_constraints, m_goal,
39 m_setpoint};
40
41 // Retrieve the profiled setpoint for the next timestep. This setpoint moves
42 // toward the goal while obeying the constraints.
43 m_setpoint = profile.Calculate(kDt);
44
45 // Send setpoint to offboard controller PID
46 m_motor.SetSetpoint(ExampleSmartMotorController::PIDMode::kPosition,
47 m_setpoint.position.value(),
48 m_feedforward.Calculate(m_setpoint.velocity) / 12_V);
49 }
50
51 private:
52 frc::Joystick m_joystick{1};
53 ExampleSmartMotorController m_motor{1};
54 frc::SimpleMotorFeedforward<units::meters> m_feedforward{
55 // Note: These gains are fake, and will have to be tuned for your robot.
56 1_V, 1.5_V * 1_s / 1_m};
57
58 frc::TrapezoidProfile<units::meters>::Constraints m_constraints{1.75_mps,
59 0.75_mps_sq};
60 frc::TrapezoidProfile<units::meters>::State m_goal;
61 frc::TrapezoidProfile<units::meters>::State m_setpoint;
62};
63
64#ifndef RUNNING_FRC_TESTS
65int main() {
66 return frc::StartRobot<Robot>();
67}
68#endif