Optimal adaptive race strategy for a Formula-E car

Abstract

Appropriately managing battery state-of-charge and temperature while ensuring minimized lap time represents a crucial issue in Formula-E competitions. An open research question might relate to simultaneously guarantee near-optimality in the race strategy solution, computational light-weighting, and effective adaptability with respect to varying and unpredictable race conditions. In this paper, a novel near-optimal real-time capable Formula-E race controller is introduced that takes inspiration from the adaptive equivalent consumption minimization strategy (A-ECMS) approach. A reduced-order Formula-E car plant model is detailed first. The optimal Formula-E race problem subsequently discussed involves controlling at each lap the depletable battery energy, the thermal management mode, and the race mode in order to minimize the overall race time. Moreover, avoiding excessively depleting the battery energy and overheating the battery are considered as constraints for the race optimization problem. Dynamic programing (DP) is implemented first to obtain the global optimal Formula-E race strategy solution in an off-line control approach. The proposed real-time capable A-ECMS based race controller finds then detailed illustration. The flexibility of the introduced A-ECMS Formula-E race controller is guaranteed by optimally calibrating the related equivalence factors to adapt to the current vehicle states (i.e. battery state-of-charge, battery temperature, and lap number). Simulation results for the Marrakesh e-prix considering different race scenarios in terms of battery initial temperature and Safety car entry demonstrate that the estimated race time achieved by the A-ECMS race controller is always near-optimal being 1.7% higher at most compared with the corresponding global optimal benchmark provided by DP.