Amjad Yaghi

Wayless ·

Vehicle kinematics on the drive to Kelowna

Six-hour commute to Kelowna. Worked out the kinematic model: bicycle model, no-slip assumption, back axle as reference. PR #4 is up.

What I’m trying to achieve

Use the commute to design and implement the vehicle kinematics system.

Research

Model

Using the back axle (the line connecting the two rear wheels) as the reference point for position and heading. The rear wheels don’t steer, which keeps the math clean among other advantages.

No-slip assumption for now: wheels roll without skidding, velocity always aligned with wheel heading. Fine for now, but slipping is fundamental to car physics. We will have to revisit this later.

Bicycle model

Treat the vehicle as two wheels: rear axle (reference) and front (steered). Turn radius:

R = wheelbase / tan(steeringAngle) + trackWidth / 2

Angular velocity: w = speed / R

Position update: pos += (speed * cos(heading), speed * sin(heading)) * dt

Straight-line case (steeringAngle == 0) handled separately to avoid division by zero.

Builder pattern

VehicleBuilder requires pos, heading, wheelbase, and trackWidth before construction. Throws on missing fields. (First time using the builder pattern, super neat.)

Driving questions

  • No-slip is a simplification. How soon will it break down enough to matter?
  • What pixel-to-metres scale makes the simulation feel right?

Next

  • Wire update() into the render loop with a clock.
  • Add pixel-to-metres conversion.
  • Merge PR #4.