# Differential Drive Kinematics

The DifferentialDriveKinematics class is a useful tool that converts between a ChassisSpeeds object and a DifferentialDriveWheelSpeeds object, which contains velocities for the left and right sides of a differential drive robot.

## Constructing the Kinematics Object

The DifferentialDriveKinematics object accepts one constructor argument, which is the track width of the robot. This represents the distance between the two sets of wheels on a differential drive.

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In Java and Python, the track width must be in meters. In C++, the units library can be used to pass in the track width using any length unit.

## Converting Chassis Speeds to Wheel Speeds

The toWheelSpeeds(ChassisSpeeds speeds) (Java / Python) / ToWheelSpeeds(ChassisSpeeds speeds) (C++) method should be used to convert a ChassisSpeeds object to a DifferentialDriveWheelSpeeds object. This is useful in situations where you have to convert a linear velocity (vx) and an angular velocity (omega) to left and right wheel velocities.

// Creating my kinematics object: track width of 27 inches
DifferentialDriveKinematics kinematics =
new DifferentialDriveKinematics(Units.inchesToMeters(27.0));

// Example chassis speeds: 2 meters per second linear velocity,
// 1 radian per second angular velocity.
var chassisSpeeds = new ChassisSpeeds(2.0, 0, 1.0);

// Convert to wheel speeds
DifferentialDriveWheelSpeeds wheelSpeeds = kinematics.toWheelSpeeds(chassisSpeeds);

// Left velocity
double leftVelocity = wheelSpeeds.leftMetersPerSecond;

// Right velocity
double rightVelocity = wheelSpeeds.rightMetersPerSecond;
// Creating my kinematics object: track width of 27 inches
frc::DifferentialDriveKinematics kinematics{27_in};

// Example chassis speeds: 2 meters per second linear velocity,
// 1 radian per second angular velocity.
frc::ChassisSpeeds chassisSpeeds{2_mps, 0_mps, 1_rad_per_s};

// Convert to wheel speeds. Here, we can use C++17's structured bindings
// feature to automatically split the DifferentialDriveWheelSpeeds
// struct into left and right velocities.
auto [left, right] = kinematics.ToWheelSpeeds(chassisSpeeds);
from wpimath.kinematics import DifferentialDriveKinematics
from wpimath.kinematics import ChassisSpeeds
from wpimath.units import inchesToMeters

# Creating my kinematics object: track width of 27 inches
kinematics = DifferentialDriveKinematics(Units.inchesToMeters(27.0))

# Example chassis speeds: 2 meters per second linear velocity,
# 1 radian per second angular velocity.
chassisSpeeds = ChassisSpeeds(2.0, 0, 1.0)

# Convert to wheel speeds
wheelSpeeds = kinematics.toWheelSpeeds(chassisSpeeds)

# Left velocity
leftVelocity = wheelSpeeds.left
# Right velocity
rightVelocity = wheelSpeeds.right

## Converting Wheel Speeds to Chassis Speeds

One can also use the kinematics object to convert individual wheel speeds (left and right) to a singular ChassisSpeeds object. The toChassisSpeeds(DifferentialDriveWheelSpeeds speeds) (Java / Python) / ToChassisSpeeds(DifferentialDriveWheelSpeeds speeds) (C++) method should be used to achieve this.

// Creating my kinematics object: track width of 27 inches
DifferentialDriveKinematics kinematics =
new DifferentialDriveKinematics(Units.inchesToMeters(27.0));

// Example differential drive wheel speeds: 2 meters per second
// for the left side, 3 meters per second for the right side.
var wheelSpeeds = new DifferentialDriveWheelSpeeds(2.0, 3.0);

// Convert to chassis speeds.
ChassisSpeeds chassisSpeeds = kinematics.toChassisSpeeds(wheelSpeeds);

// Linear velocity
double linearVelocity = chassisSpeeds.vxMetersPerSecond;

// Angular velocity
double angularVelocity = chassisSpeeds.omegaRadiansPerSecond;
// Creating my kinematics object: track width of 27 inches
frc::DifferentialDriveKinematics kinematics{27_in};

// Example differential drive wheel speeds: 2 meters per second
// for the left side, 3 meters per second for the right side.
frc::DifferentialDriveWheelSpeeds wheelSpeeds{2_mps, 3_mps};

// Convert to chassis speeds. Here we can use C++17's structured bindings
// feature to automatically split the ChassisSpeeds struct into its 3 components.
// Note that because a differential drive is non-holonomic, the vy variable
// will be equal to zero.
auto [linearVelocity, vy, angularVelocity] = kinematics.ToChassisSpeeds(wheelSpeeds);
from wpimath.kinematics import DifferentialDriveKinematics
from wpimath.kinematics import DifferentialDriveWheelSpeeds
from wpimath.units import inchesToMeters

# Creating my kinematics object: track width of 27 inches
kinematics = DifferentialDriveKinematics(inchesToMeters(27.0))

# Example differential drive wheel speeds: 2 meters per second
# for the left side, 3 meters per second for the right side.
wheelSpeeds = DifferentialDriveWheelSpeeds(2.0, 3.0)

# Convert to chassis speeds.
chassisSpeeds = kinematics.toChassisSpeeds(wheelSpeeds)

# Linear velocity
linearVelocity = chassisSpeeds.vx

# Angular velocity
angularVelocity = chassisSpeeds.omega