Module kinematics 

Kinematics: maps between actuator motion and body motion, and pose integration.

• DifferentialDrive — wheel ↔ body motion for a differential-drive base.
• Unicycle — the unicycle (body-twist) model.
• integrate — exact-arc SE(2) odometry from a body twist.

Generic over Numeric (so f32/f64/autodiff — an odometry step through Dual gives exact Jacobians). SI units, radians, twists linear-first [v; ω] (matching SE2), poses advance by X · exp(ξ). The velocity model and arc integration follow Thrun/Burgard/Fox, Probabilistic Robotics, ch. 5, and Siegwart/Nourbakhsh, Introduction to Autonomous Mobile Robots, ch. 3.

Structs

BodyArc

The arc a body traces over one tick: arc length [m] and heading change [rad].

BodyTwist

The body twist a differential drive can realise: forward speed [m/s] and yaw rate [rad/s].

DifferentialDrive

Differential-drive geometry.

OdometryStep

The odometry process model, [x, y, θ, Δs, Δθ] → [x', y', θ'].

Unicycle

The unicycle plant at a held body twist: f(t, [x, y, θ]) = [v cosθ, v sinθ, ω].

WheelRotations

Wheel angular displacements over one tick [rad] — what an encoder reports.

WheelVelocities

Wheel angular velocities [rad/s]. Positive drives the body forward.

Functions

integrate

Advances pose by one odometry increment along the exact constant-twist arc, pose · exp([Δs, 0, Δθ]).