Nonlinear receding-horizon differential game for drone racing along a three-dimensional path
Drone racing requires high-speed navigation through three-dimensional paths, posing significant challenges in control engineering. Existing control methods lack a feedback control framework that simultaneously addresses nonlinear drone dynamics and multi-agent competitive interactions, such as overtaking or obstructing opponents. To overcome this limitation, this study proposes a game-theoretic control framework, the nonlinear receding-horizon differential game (NRHDG), for competitive drone racing. NRHDG accounts explicitly for adversarial behavior by predicting and countering an opponent's worst-case behavior in real time. It extends standard nonlinear model predictive control (NMPC), which typically assumes a fixed opponent model. First, we develop a novel path-following formulation based on projection-point dynamics, eliminating the need for computationally expensive distance minimization during online control. Second, we propose a potential function that enables each drone to dynamically switch between overtaking and obstructing maneuvers, depending on the race situation. Third, we establish new performance metrics to evaluate NRHDG against NMPC across racing scenarios. Simulation results demonstrate that NRHDG outperforms NMPC in both overtaking and obstructing performance. Specifically, for randomly generated initial conditions and different levels of speed advantage for the rear-start drone, the 95\% confidence intervals for the arc-length-based mean performance differences excluded zero, indicating statistically significant advantages of NRHDG over NMPC in both overtaking and obstructing.