A Forward-Inverse Dynamic Game Framework for Enhanced Multi-Agent Trajectory Planning

2026-08-02

AI Summary

This work addresses the challenge of trajectory planning in nonlinear dynamical multi-agent systems characterized by unknown objectives, state coupling, and spatially varying interaction strengths. To this end, we propose a forward–inverse dynamic game framework. The forward module employs a KL-regularized game with state-adaptive weights, balancing optimality and behavioral priors under feedback Nash equilibrium. The inverse module integrates maximum entropy inverse reinforcement learning with physics-informed regularization to recover unknown cost functions from demonstrated trajectories. Our approach effectively models bounded rationality and context-aware interactions, while Lipschitz continuity analysis ensures well-posedness of local games. Extensive simulations and real-world experiments in multi-robot cooperative navigation and merging scenarios demonstrate significant improvements in planning safety and adaptability.

Abstract

This paper studies feedback Nash equilibrium (FBNE) seeking for multi-agent trajectory planning in nonlinear dynamical systems with unknown agents' objectives and state-dependent inter-agent coupling. While dynamic game theory provides a principled framework for such problems, existing approaches typically assume fully rational agents with known objectives or rely on fixed regularization, limiting their ability to capture bounded rationality and spatially varying interaction intensity in safety-critical settings. To this end, we propose a KL-regularized dynamic game with a state-dependent weight that adaptively balances optimality and behavioral priors. To infer unknown cost parameters from demonstrated behaviors, we develop a context-aware inverse game module based on maximum-entropy inverse reinforcement learning with physics-informed regularization, ensuring structural consistency with the forward game. We establish per-iteration well-posedness of the regularized local game and show that the adaptive weighting function remains Lipschitz continuous under bounded nominal-trajectory updates. Numerical simulations and multi-robot experiments on cooperative navigation and merging scenarios validate the effectiveness of the proposed framework.

Problem

• multi-agent trajectory planning
• feedback Nash equilibrium
• unknown objectives
• state-dependent coupling
• bounded rationality

Innovation

• dynamic game
• inverse reinforcement learning
• KL regularization
• multi-agent trajectory planning
• state-dependent coupling