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

arXiv: https://arxiv.org/abs/2402.01918 · HTML: https://mlsanity.com/paper/2402.01918/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning-based Dynamic Adaptation for Sampling-Based Motion Planning in Agile Autonomous Driving](https://mlsanity.com/paper/2510.10567/) (2025)

## Abstract (arXiv)

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.