Disturbance-aware minimum-time planning strategies for motorsport vehicles with probabilistic safety certificates

This paper presents a disturbance-aware framework that embeds robustness into minimum-lap-time trajectory optimization for motorsport. Two formulations are introduced. (i) Open-loop, horizon-based covariance propagation uses worst-case uncertainty growth over a finite window to tighten tire-friction and track-limit constraints. (ii) Closed-loop, covariance-aware planning incorporates a time-varying LQR feedback law in the optimizer, providing a feedback-consistent estimate of disturbance attenuation and enabling sharper yet reliable constraint tightening. Both methods yield reference trajectories for human or artificial drivers: in autonomous applications the modelled controller can replicate the on-board implementation, while for human driving accuracy increases with the extent to which the driver can be approximated by the assumed time-varying LQR policy. Computational tests on a representative Barcelona-Catalunya sector show that both schemes meet the prescribed safety probability, yet the closed-loop variant incurs smaller lap-time penalties than the more conservative open-loop solution, while the nominal (non-robust) trajectory remains infeasible under the same uncertainties. By accounting for uncertainty growth and feedback action during planning, the proposed framework delivers trajectories that are both performance-optimal and probabilistically safe, advancing minimum-time optimization toward real-world deployment in high-performance motorsport and autonomous racing.

A Lie Group-Based Race Car Model for Systematic Trajectory Optimization on 3D Tracks

In this paper we derive the dynamic equations of a race-car model via Lie-group methods. Lie-group methods are nowadays quite familiar to computational dynamicists and roboticists, but their diffusion within the vehicle dynamics community is still limited. We try to bridge this gap by showing that this framework merges gracefully with the Articulated Body Algorithm (ABA) and enables a fresh and systematic formulation of the vehicle dynamics. A significant contribution is represented by a rigorous reconciliation of the ABA steps with the salient features of vehicle dynamics, such as road-tire interactions, aerodynamic forces and load transfers. The proposed approach lends itself both to the definition of direct simulation models and to the systematic assembly of vehicle dynamics equations required, in the form of equality constraints, in numerical optimal control problems. We put our approach on a test in the latter context which involves the solution of minimum lap-time problem (MLTP). More specifically, a MLTP for a race car on the N\"urburgring circuit is systematically set up with our approach. The equations are then discretized with the direct collocation method and solved within the CasADi optimization suite. Both the quality of the solution and the computational efficiency demonstrate the validity of the presented approach.