Competitor-aware Race Management for Electric Endurance Racing

Abstract

Electric endurance racing is characterized by severe energy constraints and strong aerodynamic interactions. Determining race-winning policies therefore becomes a fundamentally multi-agent, game-theoretic problem. These policies must jointly govern low-level driver inputs as well as high-level strategic decisions, including energy management and charging. This paper proposes a bi-level framework for competitor-aware race management that combines game-theoretic optimal control with reinforcement learning. At the lower level, a multi-agent game-theoretic optimal control problem is solved to capture aerodynamic effects and asymmetric collision-avoidance constraints inspired by motorsport rules. Using this single-lap problem as the environment, reinforcement learning agents are trained to allocate battery energy and schedule pit stops over an entire race. The framework is demonstrated in a two-agent, 45-lap simulated race. The results show that effective exploitation of aerodynamic interactions is decisive for race outcome, with strategies that prioritize finishing position differing fundamentally from single-agent, minimum-time approaches.

Figures (6)

• Figure 1: InMotion's fully electric endurance race car at the Zandvoort circuit.
• Figure 2: Free-body diagrams of the race car illustrating the longitudinal, lateral, and vertical force components shown in blue. Aerodynamic drag $F_{\mathrm{drag}}$ and downforce $F_{\mathrm{down}}$ act at the center of pressure (CoP), while gravitational force $m g$ acts at the center of gravity (CoG). Longitudinal and lateral tire forces at the front and rear axles are denoted by $F_{\mathrm{long},F}$, $F_{\mathrm{long},R}$, $F_{\mathrm{lat},F}$, and $F_{\mathrm{lat},R}$. Vehicle orientation (shown in orange) is described by the orientation $\psi$, and lateral displacement $y$ measured relative to the circuit center line. The slope and banking angles of the track are denoted by $\theta$ and $\phi$, respectively.
• Figure 3: Map of the Zandvoort circuit showing the mini-sectors and the locations at which vehicle positions are evaluated for the upcoming mini-sectors. The lap starts and ends at the sector divider of the last corner before the pitlane, allowing us to model the pit dynamics at the start of the lap. The pit lane is indicated by the blue shaded area. Upon entering the pits, a speed limit of $60\,\mathrm{km\,h^{-1}}$ is enforced in this region.
• Figure 4: Electric motor power, front braking power, velocity, time gap, and battery energy usage for a Nash equilibrium on the Zandvoort circuit. The initial time gap is $0.2\,\mathrm{s}$ in favor of agent B. The maximum battery energy usage per lap is $4.8\%$ and $5.3\%$ for agents A and B, respectively. Owing to drag reduction, agent A achieves higher speeds and lower energy consumption in the first part of the lap. This energy advantage is subsequently exploited in the sequence of Turns 9 and 10, where agent A overtakes its opponent.
• Figure 5: Driven racing lines, electric motor power, and front braking power during the overtaking maneuver through the combination of Turns 9 and 10. Agent A brakes more aggressively into Turn 9 (2), resulting in a reduced entry velocity that enables earlier acceleration (3) and a tighter exit line (5). By spending additional energy, agent A moves ahead of its opponent at the next sector divider (7), thereby gaining the right to select the preferred racing line and complete the overtake (8). The cars and track are shown at their true proportions.