A Forward-Inverse Dynamic Game Framework for Enhanced Multi-Agent Trajectory Planning
2026-08-03 • Robotics
Robotics
AI summaryⓘ
The authors study how multiple agents can plan their paths together when each has unknown goals and their behaviors affect each other depending on their positions. They create a new method that balances following optimal plans and sticking to typical behaviors by adjusting how much each matters based on the situation. To learn the unknown goals from watching agent behavior, they use a special learning approach that respects the physics of the system. They prove their method is mathematically sound and test it successfully with simulations and real robots navigating and merging in groups.
Feedback Nash EquilibriumDynamic Game TheoryInverse Reinforcement LearningKL-regularizationBounded RationalityMulti-agent SystemsTrajectory PlanningState-dependent CouplingMaximum EntropyLipschitz Continuity
Authors
Tianle Liu, Youcheng Niu, Jing Zeng, Shuo Li, Jinming Xu
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.