Formula-E race strategy development using distributed policy gradient reinforcement learning

Optimal adaptive race strategy for a Formula-E car

“…In this framework, a strategic hint might relate to activating the attack mode in the final phases of the e-prix as performed by A-ECMS in Figure 8(a). This contrasts with the attack mode activation being performed in the first laps of the e-prix as in Liu et al 21 Indeed, an eventual Safety car entry leading the drivers to queue in a slow speed platoon might nullify the time advantage achieved earlier in the race at the expenses of lowering both the battery available energy and the allowed margin in battery temperature increase. 3 for obtained results in terms of ERT for both DP and A-ECMS in these race conditions.…”

“…TM is supposed not to have a direct impact on SOC, while its impact on the lap time can be derived as well from the 2D lookup table f. In this paper, the Marrakesh e-prix track is considered, and the corresponding lookup table f is illustrated in Figure 2. f allows predicting the lap time as a function of BE lap and TM and it has been derived in this case from Liu et al 21 As concerns the attack mode, a value of 0 for AM stands for the normal mode being selected for the current lap. On the other hand, a value of 1 denotes the activation of the attack mode to enter in operation for the following lap, while a value of 2 represents the attack mode being in operation for the current lap, thus having the extra 35 kW of tractive power enabled.…”

“…Considering these input data, a sensitivity analysis is performed in this sub-section to determine the most suitable grid sizes to be retained for control and state variables in DP when solving the optimal race problem under analysis. In particular, the mesh for the control variable BE lap is discretized with [6,11,16,21,26,31] elements, while the corresponding state variable SOC is discretized with 10 times the number of elements compared with BE lap . As concerns T batt , the corresponding state variable is discretized with [11,21,31,41,51,61,71,81,91,101] elements.…”

“…In particular, the mesh for the control variable BE lap is discretized with [6,11,16,21,26,31] elements, while the corresponding state variable SOC is discretized with 10 times the number of elements compared with BE lap . As concerns T batt , the corresponding state variable is discretized with [11,21,31,41,51,61,71,81,91,101] elements. Finally, the discretization of TM is performed considering a number of elements equal to rounding-up the size of T batt divided by 5.…”

“…A dedicated actor model was developed to handle both discrete and continuous action types, and the latter type was found particularly effective in the identification of an optimized race strategy in terms of overall time while accounting for both residual energy and temperature of the battery. 21 Despite the above cited works from Liu et al entail a considerable advancement in the research field of optimal Formula E Ò race strategy, they characterize for few key limitations and assumptions. Namely, the proposed real-time race strategies were not demonstrated identifying the global optimal race solution, for example they were not benchmarked with an optimal off-line controller.…”