Model Predictive Control Strategies for Electric Endurance Race Cars Accounting for Competitors Interactions

Abstract

This paper presents model predictive control strategies for battery electric endurance race cars accounting for interactions with the competitors. In particular, we devise an optimization framework capturing the impact of the actions of the ego vehicle when interacting with competitors in a probabilistic fashion, jointly accounting for the optimal pit stop decision making, the charge times and the driving style in the course of the race. We showcase our method for a simulated 1h endurance race at the Zandvoort circuit, using real-life data of internal combustion engine race cars from a previous event. Our results show that optimizing both the race strategy as well as the decision making during the race is very important, resulting in a significant 21s advantage over an always overtake approach, whilst revealing the competitiveness of e-race cars w.r.t. conventional ones.

Figures (6)

• Figure 1: Overview of the controller architecture. The race strategy optimization uses lap time maps to compute reference trajectories every lap, while the decision making algorithm provides an action and feeds back the actual states.
• Figure 2: Lap time map for the base-lap using $n_\mathrm{fits}=50$ piecewise affine functions. The normalized root-mean-square error (RMSE) of the model is 0.012% w.r.t. the maximum lap time.
• Figure 3: Mini-sector definition for the Zandvoort reference track.
• Figure 4: Evolution of driven distance and position as a function of time for the ego vehicle and competitors, together with a zoom of an overtake. The ego vehicle starts at the first position, but has to charge before the competitors make their pit stop, resulting in a loss of several positions. Thereafter, the ego vehicle starts overtaking the competitors, resulting in the 13 overall finishing position among 32 participants.
• Figure 5: Comparison between the baseline strategy and the optimal solution for the total time gap and the battery State of Charge (SoC) $\xi$, where the baseline strategy represents is always overtake. The optimal strategy saves energy by staying behind competitors and overtaking at more favorable locations on the track, resulting in a total time saving of about 21.4 s .