Time-optimal trajectory planning for a race car considering variable tyre-road friction coefficients

Abstract

This paper shows the planning of time-optimal trajectories, which allows an autonomous race car to drive at the handling limits, taking into account locally changing road friction values. For this purpose, the minimum lap time problem is described as an optimal control problem, converted to a nonlinear programme using direct orthogonal Gauss-Legendre collocation and then solved by the interior-point method IPOPT. Reduced computing times are achieved using a curvilinear abscissa approach for track description, algorithmic differentiation using the software framework CasADi, and a smoothing of the track input data by approximate spline regression. The vehicle's behaviour is approximated as a single track and double track model with quasi-steady state tyre load simplification and nonlinear tyre model. The results are used to evaluate which vehicle physics are important for the calculation of the time-optimal trajectory. The novelty of this work is the consideration of wheel-specific tyre-road friction coefficients along the racetrack using a track friction map. It is shown that variable friction coefficients have a significant impact on the trajectory, and therefore significantly improve lap times on inhomogenous racetracks. The proposed trajectory planning has proven its practical suitability in first tests on an autonomous race car and will be used in the coming racing season in the Roborace competition.