Strategically Robust Game-Theoretic Multi-Agent Trajectory Optimization

2026-09-28

AI Summary

This study addresses the sensitivity of multi-agent trajectory planning in air traffic to execution uncertainty and its reliance on centralized coordination by proposing a strategy-robust game-theoretic model. By introducing an adversarial perturbation budget to safeguard trajectories, the approach enables decentralized autonomous planning. We theoretically prove that this robust game remains an exact dynamic potential game and derive a quasi-closed-form solution for the inner adversarial problem under linear dynamics, significantly reducing computational overhead. Experimental results demonstrate that the proposed method generates more robust trajectories in high-risk scenarios while exerting negligible performance impact in low-risk settings, with only a moderate increase in runtime.

Abstract

Aviation authorities worldwide expect Advanced Air Mobility (AAM) traffic management to be decentralized among service providers, requiring AAM flights to autonomously plan trajectories by predicting other flights'control inputs rather than relying on centralized coordination. Game-theoretic approaches that formulate multi-agent collision avoidance as an exact dynamic potential game can efficiently find open-loop equilibria, but they assume that agents exactly follow their equilibrium trajectories---an unrealistic assumption given uncertainties in actuation, perception, and computation. We propose a strategically robust formulation where each agent protects against a fictitious adversary that, for each timestep, perturbs other agents'control inputs within a bounded budget to minimize distance at that timestep. We show that, under reasonable assumptions on agents'distance cost and robustness levels, the strategically robust game remains an exact dynamic potential game and admits a quasi-closed-form solution to the inner adversarial problem for linear dynamics, which limits computational overhead. Experiments with up to eight agents using logarithmic distance costs show that strategic robustness selects more robust trajectories in high-collision-risk configurations while leaving low-risk trajectories nearly unchanged, with only a modest increase in runtime.

Problem

• Multi-Agent Trajectory Optimization
• Game Theory
• Strategic Robustness
• Advanced Air Mobility
• Collision Avoidance

Innovation

• Strategic Robustness
• Dynamic Potential Game
• Multi-Agent Trajectory Optimization
• Adversarial Perturbation
• Advanced Air Mobility