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Piyush Verma
DEFIANZ / ENGINEERING NOTES / 02

Vehicle control. Models & comparisons.

Switch the controller, change the conditions, then watch its steering decisions unfold. Every trace comes from the simulation you run.

READY / PAUSED
THE TEST CIRCUIT166 M / KINEMATIC BICYCLE
MPPI0% OF LAP
Driven pathPrediction / targetCandidate rollouts
Measured lateral error / metres
StartLatest
Controller
Target speed6 m/s
Lookahead / initial guess4 m
Prediction horizon16 steps
Grip ceiling μ1
Initial lateral offset2 m

Changing a setting resets the lap. Steering is limited to ±31.5° and 0.9 rad/s. The visible road is ±3 m; a run stops beyond ±6 m or 200 s.

Actual speed4.0 m/s
RMS lateral error0.00 m
Steering0.0°
Simulated time0.0 s
MPPI

Sample many futures.

wk ∝ exp(−(Sk − min S) / λ)

72 noisy steering sequences are rolled forward. Exponentially weighted perturbations update the nominal sequence, with the control/noise correction included. The orange line is the updated prediction.

Same circuit. Same starting point.

Compare the current settings and seed 16. A stopped run’s error covers only the distance it completed; it should not be ranked as a successful lap.

UNDER THE HOOD

What you’re seeing.

My work: MPC and MPPI vehicle control, comparison of navigation approaches, steering actuation and emergency braking. The portfolio experiments implement these ideas afresh.

The model: ẋ = v cos ψ, ẏ = v sin ψ, ψ̇ = v tan δ / L. L = 2.06 m is an illustrative wheelbase. The timestep is 80 ms, with acceleration, steering and yaw-rate limits. Pure Pursuit and PID use no optimization horizon. MPC uses a small coordinate search rather than a production nonlinear solver; MPCC and hierarchical MPC are reduced educational formulations.

Interpretation: this is a low-speed kinematic comparison, without actuator delay, perception uncertainty or dynamic tire slip. It cannot establish the best controller for the real E16. Try high speed and low grip to expose these limits.

Explore the RL / IL comparison with trainable policies ↗

Educational reconstructions of ideas from my work. Demo results are computed here; they are not team test results.