3D Bicycle-Model Path Tracking

Vehicle model

Sensor range 10 m

Sensor field of view 100°

Max steering angle 32°

Cruise speed 3.2 m/s

Telemetry

Speed

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Steering angle δ

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Turning radius

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Nearest sensed

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Goals reached

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Collisions

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How it works

The vehicle drives on a real kinematic bicycle model — a fixed wheelbase L, a steering angle clamped to ±δ_max, and a steering actuator with a rate limit, so the front wheels ramp toward a commanded angle instead of snapping there, exactly like the simplified vehicle geometry real autonomous-driving stacks plan against.

x' = v·cos(θ)      y' = v·sin(θ)
θ' = (v / L)·tan(δ)
δ  → δ_cmd  at a limited °/s   (actuator lag)

Its only sensor is a forward LIDAR cone — visualised as the translucent wedge and ray fan on the ground plane — with a tunable range and field of view. Obstacles outside the cone are invisible to the planner (shown dim). A potential field blends attraction to the goal beacon with repulsion from every currently-sensed pillar into a local target point; a pure-pursuit controller then converts that target into the one steering angle the bicycle-model geometry needs:

κ = 2·sin(α) / Ld
δ_cmd = atan(L·κ)   clamped to ±δ_max

Speed drops automatically for hard steering or a close sensed obstacle, the same throttle behaviour a real self-driving car uses before a tight bend.

Sensor range / field of view — a narrower or shorter LIDAR cone means less warning before an obstacle must be steered around within the car's real minimum turning radius.
Max steering angle — sets the minimum turning radius R = L / tan(δ_max); tight gaps become physically un-threadable below a certain angle, not just difficult.
Cruise speed — higher speed shortens the time available to react once an obstacle enters sensor range.

Vehicle Goal Sensed obstacle Unsensed (outside cone/range)

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