Swerve Drive Kinematics

The SwerveDriveKinematics class is a useful tool that converts between a ChassisSpeeds object and several SwerveModuleState objects, which contains velocities and angles for each swerve module of a swerve drive robot.

Nota

Swerve drive kinematics uses a common coordinate system. You may wish to reference the Coordinate System section for details.

The swerve module state class

The SwerveModuleState class contains information about the velocity and angle of a singular module of a swerve drive. The constructor for a SwerveModuleState takes in two arguments, the velocity of the wheel on the module, and the angle of the module.

Nota

In Java / Python, the velocity of the wheel must be in meters per second. In C++, the units library can be used to provide the velocity using any linear velocity unit.

Nota

An angle of 0 corresponds to the modules facing forward.

Constructing the kinematics object

The SwerveDriveKinematics class accepts a variable number of constructor arguments, with each argument being the location of a swerve module relative to the robot center (as a Translation2d. The number of constructor arguments corresponds to the number of swerve modules.

Nota

A swerve drive must have 2 or more modules.

Nota

In C++, the class is templated on the number of modules. Therefore, when constructing a SwerveDriveKinematics object as a member variable of a class, the number of modules must be passed in as a template argument. For example, for a typical swerve drive with four modules, the kinematics object must be constructed as follows: frc::SwerveDriveKinematics<4> m_kinematics{...}.

The locations for the modules must be relative to the center of the robot. Positive x values represent moving toward the front of the robot whereas positive y values represent moving toward the left of the robot.

// Locations for the swerve drive modules relative to the robot center.
Translation2d m_frontLeftLocation = new Translation2d(0.381, 0.381);
Translation2d m_frontRightLocation = new Translation2d(0.381, -0.381);
Translation2d m_backLeftLocation = new Translation2d(-0.381, 0.381);
Translation2d m_backRightLocation = new Translation2d(-0.381, -0.381);

// Creating my kinematics object using the module locations
SwerveDriveKinematics m_kinematics = new SwerveDriveKinematics(
  m_frontLeftLocation, m_frontRightLocation, m_backLeftLocation, m_backRightLocation
);
// Locations for the swerve drive modules relative to the robot center.
frc::Translation2d m_frontLeftLocation{0.381_m, 0.381_m};
frc::Translation2d m_frontRightLocation{0.381_m, -0.381_m};
frc::Translation2d m_backLeftLocation{-0.381_m, 0.381_m};
frc::Translation2d m_backRightLocation{-0.381_m, -0.381_m};

// Creating my kinematics object using the module locations.
frc::SwerveDriveKinematics<4> m_kinematics{
  m_frontLeftLocation, m_frontRightLocation, m_backLeftLocation,
  m_backRightLocation};
# Python requires using the right class for the number of modules you have

from wpimath.geometry import Translation2d
from wpimath.kinematics import SwerveDrive4Kinematics

# Locations for the swerve drive modules relative to the robot center.
frontLeftLocation = Translation2d(0.381, 0.381)
frontRightLocation = Translation2d(0.381, -0.381)
backLeftLocation = Translation2d(-0.381, 0.381)
backRightLocation = Translation2d(-0.381, -0.381)

# Creating my kinematics object using the module locations
self.kinematics = SwerveDrive4Kinematics(
  frontLeftLocation, frontRightLocation, backLeftLocation, backRightLocation
)

Converting chassis speeds to module states

The toSwerveModuleStates(ChassisSpeeds speeds) (Java / Python) / ToSwerveModuleStates(ChassisSpeeds speeds) (C++) method should be used to convert a ChassisSpeeds object to a an array of SwerveModuleState objects. This is useful in situations where you have to convert a forward velocity, sideways velocity, and an angular velocity into individual module states.

The elements in the array that is returned by this method are the same order in which the kinematics object was constructed. For example, if the kinematics object was constructed with the front left module location, front right module location, back left module location, and the back right module location in that order, the elements in the array would be the front left module state, front right module state, back left module state, and back right module state in that order.

// Example chassis speeds: 1 meter per second forward, 3 meters
// per second to the left, and rotation at 1.5 radians per second
// counterclockwise.
ChassisSpeeds speeds = new ChassisSpeeds(1.0, 3.0, 1.5);

// Convert to module states
SwerveModuleState[] moduleStates = kinematics.toSwerveModuleStates(speeds);

// Front left module state
SwerveModuleState frontLeft = moduleStates[0];

// Front right module state
SwerveModuleState frontRight = moduleStates[1];

// Back left module state
SwerveModuleState backLeft = moduleStates[2];

// Back right module state
SwerveModuleState backRight = moduleStates[3];
// Example chassis speeds: 1 meter per second forward, 3 meters
// per second to the left, and rotation at 1.5 radians per second
// counterclockwise.
frc::ChassisSpeeds speeds{1_mps, 3_mps, 1.5_rad_per_s};

// Convert to module states. Here, we can use C++17's structured
// bindings feature to automatically split up the array into its
// individual SwerveModuleState components.
auto [fl, fr, bl, br] = kinematics.ToSwerveModuleStates(speeds);
from wpimath.kinematics import ChassisSpeeds

# Example chassis speeds: 1 meter per second forward, 3 meters
# per second to the left, and rotation at 1.5 radians per second
# counterclockwise.
speeds = ChassisSpeeds(1.0, 3.0, 1.5)

# Convert to module states
frontLeft, frontRight, backLeft, backRight = self.kinematics.toSwerveModuleStates(speeds)

Module angle optimization

The SwerveModuleState class contains a static optimize() (Java) / Optimize() (C++) method that is used to «optimize» the speed and angle setpoint of a given SwerveModuleState to minimize the change in heading. For example, if the angular setpoint of a certain module from inverse kinematics is 90 degrees, but your current angle is -89 degrees, this method will automatically negate the speed of the module setpoint and make the angular setpoint -90 degrees to reduce the distance the module has to travel.

This method takes two parameters: the desired state (usually from the toSwerveModuleStates method) and the current angle. It will return the new optimized state which you can use as the setpoint in your feedback control loop.

var frontLeftOptimized = SwerveModuleState.optimize(frontLeft,
   new Rotation2d(m_turningEncoder.getDistance()));
auto flOptimized = frc::SwerveModuleState::Optimize(fl,
   units::radian_t(m_turningEncoder.GetDistance()));
from wpimath.kinematics import SwerveModuleState
from wpimath.geometry import Rotation2d

frontLeftOptimized = SwerveModuleState.optimize(frontLeft,
   Rotation2d(self.m_turningEncoder.getDistance()))

Cosine compensation

Cosine compensation is a technique that reduces the speed of a module when it is not pointing in the desired direction. This is done by multiplying the desired speed of the module by the cosine of the angle error.

  • If the wheel is pointing straight in the desired direction, then the speed remains unchanged as \(\cos(0^\circ) = 1\).

  • If the wheel is perpendicular to the desired direction of motion, then the speed is reduced to 0 as \(\cos(90^\circ) = 0\).

  • Everything in between follows the cosine curve.

Cosine compensation has been shown to reduce the amount of «skew» a swerve drive experiences when changing direction.

var currentAngle = new Rotation2d.fromRadians(m_turningEncoder.getDistance());

var frontLeftOptimized = SwerveModuleState.optimize(frontLeft, currentAngle);
frontLeftOptimized.speedMetersPerSecond *= frontLeftOptimized.angle.minus(currentAngle).getCos();
Rotation2d currentAngle(m_turningEncoder.GetDistance());

auto flOptimized = frc::SwerveModuleState::Optimize(fl, currentAngle);
flOptimized.speed *= (flOptimized.angle - currentAngle).Cos();
from wpimath.kinematics import SwerveModuleState
from wpimath.geometry import Rotation2d

currentAngle = Rotation2d(self.m_turningEncoder.getDistance())

frontLeftOptimized = SwerveModuleState.optimize(frontLeft, currentAngle)
frontLeftOptimized.speed *= (frontLeftOptimized.angle - currentAngle).cos()

Field-oriented drive

Recall that a ChassisSpeeds object can be created from a set of desired field-oriented speeds. This feature can be used to get module states from a set of desired field-oriented speeds.

// The desired field relative speed here is 2 meters per second
// toward the opponent's alliance station wall, and 2 meters per
// second toward the left field boundary. The desired rotation
// is a quarter of a rotation per second counterclockwise. The current
// robot angle is 45 degrees.
ChassisSpeeds speeds = ChassisSpeeds.fromFieldRelativeSpeeds(
  2.0, 2.0, Math.PI / 2.0, Rotation2d.fromDegrees(45.0));

// Now use this in our kinematics
SwerveModuleState[] moduleStates = kinematics.toSwerveModuleStates(speeds);
// The desired field relative speed here is 2 meters per second
// toward the opponent's alliance station wall, and 2 meters per
// second toward the left field boundary. The desired rotation
// is a quarter of a rotation per second counterclockwise. The current
// robot angle is 45 degrees.
frc::ChassisSpeeds speeds = frc::ChassisSpeeds::FromFieldRelativeSpeeds(
  2_mps, 2_mps, units::radians_per_second_t(std::numbers::pi / 2.0), Rotation2d(45_deg));

// Now use this in our kinematics
auto [fl, fr, bl, br] = kinematics.ToSwerveModuleStates(speeds);
from wpimath.kinematics import ChassisSpeeds
import math
from wpimath.geometry import Rotation2d

# The desired field relative speed here is 2 meters per second
# toward the opponent's alliance station wall, and 2 meters per
# second toward the left field boundary. The desired rotation
# is a quarter of a rotation per second counterclockwise. The current
# robot angle is 45 degrees.
speeds = ChassisSpeeds.fromFieldRelativeSpeeds(
  2.0, 2.0, math.pi / 2.0, Rotation2d.fromDegrees(45.0))

# Now use this in our kinematics
self.moduleStates = self.kinematics.toSwerveModuleStates(speeds)

Using custom centers of rotation

Sometimes, rotating around one specific corner might be desirable for certain evasive maneuvers. This type of behavior is also supported by the WPILib classes. The same ToSwerveModuleStates() method accepts a second parameter for the center of rotation (as a Translation2d). Just like the wheel locations, the Translation2d representing the center of rotation should be relative to the robot center.

Nota

Because all robots are a rigid frame, the provided vx and vy velocities from the ChassisSpeeds object will still apply for the entirety of the robot. However, the omega from the ChassisSpeeds object will be measured from the center of rotation.

For example, one can set the center of rotation on a certain module and if the provided ChassisSpeeds object has a vx and vy of zero and a non-zero omega, the robot will appear to rotate around that particular swerve module.

Converting module states to chassis speeds

One can also use the kinematics object to convert an array of SwerveModuleState objects to a singular ChassisSpeeds object. The toChassisSpeeds(SwerveModuleState... states) (Java / Python) / ToChassisSpeeds(SwerveModuleState... states) (C++) method can be used to achieve this.

// Example module states
var frontLeftState = new SwerveModuleState(23.43, Rotation2d.fromDegrees(-140.19));
var frontRightState = new SwerveModuleState(23.43, Rotation2d.fromDegrees(-39.81));
var backLeftState = new SwerveModuleState(54.08, Rotation2d.fromDegrees(-109.44));
var backRightState = new SwerveModuleState(54.08, Rotation2d.fromDegrees(-70.56));

// Convert to chassis speeds
ChassisSpeeds chassisSpeeds = kinematics.toChassisSpeeds(
  frontLeftState, frontRightState, backLeftState, backRightState);

// Getting individual speeds
double forward = chassisSpeeds.vxMetersPerSecond;
double sideways = chassisSpeeds.vyMetersPerSecond;
double angular = chassisSpeeds.omegaRadiansPerSecond;
// Example module States
frc::SwerveModuleState frontLeftState{23.43_mps, Rotation2d(-140.19_deg)};
frc::SwerveModuleState frontRightState{23.43_mps, Rotation2d(-39.81_deg)};
frc::SwerveModuleState backLeftState{54.08_mps, Rotation2d(-109.44_deg)};
frc::SwerveModuleState backRightState{54.08_mps, Rotation2d(-70.56_deg)};

// Convert to chassis speeds. Here, we can use C++17's structured bindings
// feature to automatically break up the ChassisSpeeds struct into its
// three components.
auto [forward, sideways, angular] = kinematics.ToChassisSpeeds(
  frontLeftState, frontRightState, backLeftState, backRightState);
from wpimath.kinematics import SwerveModuleState
from wpimath.geometry import Rotation2d

# Example module states
frontLeftState = SwerveModuleState(23.43, Rotation2d.fromDegrees(-140.19))
frontRightState = SwerveModuleState(23.43, Rotation2d.fromDegrees(-39.81))
backLeftState = SwerveModuleState(54.08, Rotation2d.fromDegrees(-109.44))
backRightState = SwerveModuleState(54.08, Rotation2d.fromDegrees(-70.56))

# Convert to chassis speeds
chassisSpeeds = self.kinematics.toChassisSpeeds(
  frontLeftState, frontRightState, backLeftState, backRightState)

# Getting individual speeds
forward = chassisSpeeds.vx
sideways = chassisSpeeds.vy
angular = chassisSpeeds.omega

Module state visualization with AdvantageScope

By recording a set of swerve module states using NetworkTables or WPILib data logs, AdvantageScope can be used to visualize the state of a swerve drive. The code below shows how a set of SwerveModuleState objects can be published to NetworkTables.

public class Example {
  private final StructArrayPublisher<SwerveModuleState> publisher;

  public Example() {
    // Start publishing an array of module states with the "/SwerveStates" key
    publisher = NetworkTableInstance.getDefault()
      .getStructArrayTopic("/SwerveStates", SwerveModuleState.struct).publish();
  }

  public void periodic() {
    // Periodically send a set of module states
    publisher.set(new SwerveModuleState[] {
      frontLeftState,
      frontRightState,
      backLeftState,
      backRightState
    });
  }
}
class Example {
  nt::StructArrayPublisher<frc::SwerveModuleState> publisher

 public:
  Example() {
    // Start publishing an array of module states with the "/SwerveStates" key
    publisher = nt::NetworkTableInstance::GetDefault()
      .GetStructArrayTopic<frc::SwerveModuleState>("/SwerveStates").Publish();
  }

  void Periodic() {
    // Periodically send a set of module states
    swervePublisher.Set(
      std::vector{
        frontLeftState,
        frontRightState,
        backLeftState,
        backRightState
      }
    );
  }
};
import ntcore
from wpimath.kinematics import SwerveModuleState

# get the default instance of NetworkTables
nt = ntcore.NetworkTableInstance.getDefault()

# Start publishing an array of module states with the "/SwerveStates" key
topic = nt.getStructArrayTopic("/SwerveStates", SwerveModuleState)
self.pub = topic.publish()

def periodic(self):
  # Periodically send a set of module states
  self.pub.set([frontLeftState,frontRightState,backLeftState,backRightState])

See the documentation for the swerve tab for more details on visualizing this data using AdvantageScope.

Screenshot of an AdvantageScope window displaying a swerve visualization.