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α-RACER: Real-Time Algorithm for Game-Theoretic Motion Planning and Control in Autonomous Racing using Near-Potential Function

Dvij Kalaria, Chinmay Maheshwari, Shankar Sastry

TL;DR

This work tackles real-time, opponent-aware motion planning for multi-car autonomous racing by formulating the problem as an infinite-horizon dynamic game and introducing α-RACER, a two-phase method that learns a dynamic $\alpha$-potential function offline and uses it online to compute approximate Nash equilibria. The policy parameterization combines MPC-based controllers with a five-parameter reference trajectory that encodes competitive maneuvers such as overtaking and blocking, while incorporating nonlinear tire dynamics via a dynamic bicycle model. The key contributions are (i) a novel policy parametrization and per-step utility that capture competitive behaviors, (ii) a dynamic $\alpha$-potential framework that enables tractable NE approximation, and (iii) a two-phase offline/online procedure that yields real-time decisions validated in 3-car racing against multiple baselines, including IBR and self-play RL, with favorable approximation gaps and Nash-regret. The approach offers a principled, interpretable path to long-horizon, competitive planning in multi-agent racing with potential applicability to other domains requiring real-time game-theoretic control. Overall, α-RACER demonstrates superior performance and provides a scalable, near-equilibrium planning tool for high-speed autonomous racing.

Abstract

Autonomous racing extends beyond the challenge of controlling a racecar at its physical limits. Professional racers employ strategic maneuvers to outwit other competing opponents to secure victory. While modern control algorithms can achieve human-level performance by computing offline racing lines for single-car scenarios, research on real-time algorithms for multi-car autonomous racing is limited. To bridge this gap, we develop game-theoretic modeling framework that incorporates the competitive aspect of autonomous racing like overtaking and blocking through a novel policy parametrization, while operating the car at its limit. Furthermore, we propose an algorithmic approach to compute the (approximate) Nash equilibrium strategy, which represents the optimal approach in the presence of competing agents. Specifically, we introduce an algorithm inspired by recently introduced framework of dynamic near-potential function, enabling real-time computation of the Nash equilibrium. Our approach comprises two phases: offline and online. During the offline phase, we use simulated racing data to learn a near-potential function that approximates utility changes for agents. This function facilitates the online computation of approximate Nash equilibria by maximizing its value. We evaluate our method in a head-to-head 3-car racing scenario, demonstrating superior performance compared to several existing baselines.

α-RACER: Real-Time Algorithm for Game-Theoretic Motion Planning and Control in Autonomous Racing using Near-Potential Function

TL;DR

This work tackles real-time, opponent-aware motion planning for multi-car autonomous racing by formulating the problem as an infinite-horizon dynamic game and introducing α-RACER, a two-phase method that learns a dynamic -potential function offline and uses it online to compute approximate Nash equilibria. The policy parameterization combines MPC-based controllers with a five-parameter reference trajectory that encodes competitive maneuvers such as overtaking and blocking, while incorporating nonlinear tire dynamics via a dynamic bicycle model. The key contributions are (i) a novel policy parametrization and per-step utility that capture competitive behaviors, (ii) a dynamic -potential framework that enables tractable NE approximation, and (iii) a two-phase offline/online procedure that yields real-time decisions validated in 3-car racing against multiple baselines, including IBR and self-play RL, with favorable approximation gaps and Nash-regret. The approach offers a principled, interpretable path to long-horizon, competitive planning in multi-agent racing with potential applicability to other domains requiring real-time game-theoretic control. Overall, α-RACER demonstrates superior performance and provides a scalable, near-equilibrium planning tool for high-speed autonomous racing.

Abstract

Autonomous racing extends beyond the challenge of controlling a racecar at its physical limits. Professional racers employ strategic maneuvers to outwit other competing opponents to secure victory. While modern control algorithms can achieve human-level performance by computing offline racing lines for single-car scenarios, research on real-time algorithms for multi-car autonomous racing is limited. To bridge this gap, we develop game-theoretic modeling framework that incorporates the competitive aspect of autonomous racing like overtaking and blocking through a novel policy parametrization, while operating the car at its limit. Furthermore, we propose an algorithmic approach to compute the (approximate) Nash equilibrium strategy, which represents the optimal approach in the presence of competing agents. Specifically, we introduce an algorithm inspired by recently introduced framework of dynamic near-potential function, enabling real-time computation of the Nash equilibrium. Our approach comprises two phases: offline and online. During the offline phase, we use simulated racing data to learn a near-potential function that approximates utility changes for agents. This function facilitates the online computation of approximate Nash equilibria by maximizing its value. We evaluate our method in a head-to-head 3-car racing scenario, demonstrating superior performance compared to several existing baselines.

Paper Structure

This paper contains 22 sections, 1 theorem, 10 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Other Related Works.
  3. Organization.
  4. Modeling Multi-car Autonomous Racing
  5. Preliminaries on Dynamic Game Theory
  6. Multi-car Racing as a Dynamic Game
  7. Approximating Multi-agent Interaction
  8. $\alpha$-Potential Function
  9. Computational Approach
  10. Numerical Evaluation
  11. Competitive Behavior by Approximating Nash Equilibrium
  12. Performance Comparison
  13. Conclusion
  14. Proof of Proposition \ref{['prop: NE_def_PotMax']}
  15. Description of Single-agent Racing Line
  16. ...and 7 more sections

Key Result

proposition 1

Given an $\alpha$-potential function $\Phi$, for any $\mathbf{x} \in \mathcal{X}$, $\lambda > 0$, and any policy $\theta^\ast$ satisfying $\Phi(\mathbf{x}, \theta^\ast) \geq \max_{\theta \in \Theta} \Phi(\mathbf{x}, \theta) - \lambda,$ the policy $\theta^\ast$ constitutes a $(\lambda + \alpha)$-appr

Figures (4)

  • Figure 1: Histogram of (a) Relative approximation gap of potential function (b) Nash regret
  • Figure 2: Potential values and the trajectories at a given joint state for different (a) $q$ (b) $\zeta$ (c) $s_1$ (d) $s_2$ (e) $s_3$ of only the ego agent. We only denote 2 players here (only 1 player for (a) and (b)) and the 3rd player is far away from this position to not affect any players. Additionally, for ease of readability, we only show the impact of variation in trajectory of other player in response to ego in (e) as such deviations are not significant in (c) and (d).
  • Figure 3: Example overtake in a race MPC vs IBR. Opponent (IBR) overtakes from $t_4$ to $t_5$ but later suffers at the turn from $t_5$ to $t_9$ when the Ego agent (Ours) overtakes back to re-claim it's position
  • Figure 4: Track and the starting position regions

Theorems & Definitions (3)

  • definition 1
  • definition 2
  • proposition 1