On Disturbance-Aware Minimum-Time Trajectory Planning: Evidence from Tests on a Dynamic Driving Simulator

TL;DR

This work investigates disturbance-aware, robustness-embedded reference trajectories for minimum-time lap planning and tests NOM, TLC, and FLC against NO-REF on a high-performance driving simulator with professional drivers. By propagating mean and covariance over a finite horizon and applying probabilistic back-offs, the approach produces tractable, safety-aware references that trade lap time against steering effort. The experiments show FLC provides substantial steering-effort reductions with modest lap-time penalties and can even outperform the nominal planner for skilled drivers, while TLC offers the lowest effort at the cost of longer lap times. Overall, disturbance-aware planning, particularly FLC, demonstrates promise for training and fast yet stable trajectories in motorsport-like driving and challenging circuits.

Abstract

This work investigates how disturbance-aware, robustness-embedded reference trajectories translate into driving performance when executed by professional drivers in a dynamic simulator. Three planned reference trajectories are compared against a free-driving baseline (NOREF) to assess trade-offs between lap time (LT) and steering effort (SE): NOM, the nominal time-optimal trajectory; TLC, a track-limit-robust trajectory obtained by tightening margins to the track edges; and FLC, a friction-limit-robust trajectory obtained by tightening against axle and tire saturation. All trajectories share the same minimum lap-time objective with a small steering-smoothness regularizer and are evaluated by two professional drivers using a high-performance car on a virtual track. The trajectories derive from a disturbance-aware minimum-lap-time framework recently proposed by the authors, where worst-case disturbance growth is propagated over a finite horizon and used to tighten tire-friction and track-limit constraints, preserving performance while providing probabilistic safety margins. LT and SE are used as performance indicators, while RMS lateral deviation, speed error, and drift angle characterize driving style. Results show a Pareto-like LT-SE trade-off: NOM yields the shortest LT but highest SE; TLC minimizes SE at the cost of longer LT; FLC lies near the efficient frontier, substantially reducing SE relative to NOM with only a small LT increase. Removing trajectory guidance (NOREF) increases both LT and SE, confirming that reference trajectories improve pace and control efficiency. Overall, the findings highlight reference-based and disturbance-aware planning, especially FLC, as effective tools for training and for achieving fast yet stable trajectories.

Figures (11)

• Figure 1: Single-track model used as a basis for our stochastic vehicle dynamics model.
• Figure 2: Comparison between axle lateral forces obtained from the simulator telemetry (red) and from the calibrated Magic Formula tire model (black) for the front and rear axles.
• Figure 3: Comparison between longitudinal, lateral, and vertical axle forces obtained from the simulator (Sim data, red) and from the single-track minimum-lap-time optimization (ST data, black) while attempting to follow the optimized trajectory, plotted against the normalized distances along the track.
• Figure 4: Comparison between steering-wheel angle recorded at the driving simulator (Sim data, red) and steering input from the single-track minimum-lap-time optimization (ST data, black), plotted against the normalized distance along the track while attempting to follow the optimized trajectory.
• Figure 5: Dynamic Simulator view from the driver's perspective with the racing ribbon overlaid on the scene, indicating the desired trajectory to follow.