Open-Loop and Feedback Nash Trajectories for Competitive Racing with iLQGames

TL;DR

This work casts autonomous racing as a discrete-time dynamic game and uses iLQGames to compute Nash equilibria that account for reciprocal opponent behavior. By comparing open-loop and feedback solutions within a moving-horizon framework, the study reveals how interaction awareness, enabled by a coupled cost structure including collision and competitive terms, can yield less conservative, more aggressive, yet safer racing behaviors on a straight track. Key contributions include demonstrating the applicability of iLQGame to racing, showing how cost parameterization governs aggressiveness and responsibility, and highlighting the distinct behavioral outcomes produced by open-loop versus feedback equilibria. The findings suggest that game-theoretic planning enhances interaction-aware planning quality over sequential approaches, with practical implications for real-time multi-vehicle racing and future extensions to oval and road courses with more agents.

Abstract

Interaction-aware trajectory planning is crucial for closing the gap between autonomous racing cars and human racing drivers. Prior work has applied game theory as it provides equilibrium concepts for non-cooperative dynamic problems. With this contribution, we formulate racing as a dynamic game and employ a variant of iLQR, called iLQGames, to solve the game. iLQGames finds trajectories for all players that satisfy the equilibrium conditions for a linear-quadratic approximation of the game and has been previously applied in traffic scenarios. We analyze the algorithm's applicability for trajectory planning in racing scenarios and evaluate it based on interaction awareness, competitiveness, and safety. With the ability of iLQGames to solve for open-loop and feedback Nash equilibria, we compare the behavioral outcomes of the two equilibrium concepts in simple scenarios on a straight track section.

Figures (4)

• Figure 1: Example of yielding behavior by sequential planning approaches in racing scenarios.
• Figure 2: Interaction awareness and dependency on the cost parameterization.
• Figure 3: Frequencies of overtaking times when the opponent uses a sequential planning approach for different ego vehicle planning approaches.
• Figure 4: Exemplary comparison of the open-loop and feedback solution. The opponent uses a sequential planning approach with $c_\mathrm{c}^2=10 c_\mathrm{c}^1$.