Authors: Victor L. Qin, Nicolas Lanzetti, Saverio Bolognani, Hamsa Balakrishnan
Organizations: Department of Aeronautics and Astronautics, MIT. · Department of Computing and Mathematical Sciences, Caltech. · Automatic Control Laboratory, ETH Zurich.
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.
Autonomous racing demands planning algorithms that balance vehicle dynamics at the limits of handling with strategic decision-making in competitive multi-agent scenarios. Game theory provides a mathematical framework for modeling these interactions, enabling interactive trajectory planning and strategic behaviors, such as blocking. However, directly solving full dynamic games online is computationally prohibitive and challenging to integrate into robust, high-frequency autonomous software stacks. This paper proposes a hybrid architecture that integrates game-theoretic reasoning into a sampling-based motion planner, combining strategic interactions with robust trajectory generation. Building upon an α-potential game formulation, we utilize an offline-learned potential function to capture multi-agent interactions. During online operation, a gradient-based optimization dynamically refines interaction parameters to generate an \textit{Interaction Reference Path}. This path serves as a dynamic cost bias within a high-frequency sampling planner. We evaluate our approach in a high-fidelity simulation environment on the Yas Marina Circuit. Qualitative and quantitative results demonstrate that our approach successfully induces defensive behaviors like blocking without carrying the computational burden of full dynamic game solvers.
Alexander Langmann, Frederico Pita de Araujo, Mattia Piccinini +1
Professorship of Autonomous Vehicle Systems, TUM School of Engineering and Design, Technical University of Munich, 85748 Garching, Germany; Munich Institute of Robotics and Machine Intelligence (MIRMI)
Advanced Air Mobility (AAM) operations are expected to significantly increase aerial traffic in urban airspace, requiring autonomous traffic management systems to ensure collision-free operations in highly congested environments. In this paper, we propose a multi-agent coordination framework that uses minimum time-to-reach (TTR) as a unifying metric for priority assignment, temporal separation, and safety filtering. We focus on the problem of coordinating multiple aerial vehicles merging into an air corridor while maintaining safe separation between vehicles. Vehicles are assigned arrival-consistent priority based on TTR, and target TTR values are used to enforce temporal spacing that induces spatial separation. A priority-consistent safety filtering layer based on Hamilton-Jacobi reachability value functions ensures collision avoidance while minimally modifying the reference guidance. Simulation results in a highly congested corridor merging scenario show that the proposed method improves safety, fairness, and efficiency compared to time-optimal guidance and priority-agnostic safety filtering.
Matthew Low, Jasmine Jerry Aloor, Victoria Marie Tuck +2
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley · Department of Aeronautics and Astronautics, Massachusetts Institute of Technology · GRASP Laboratory, University of Pennsylvania +1
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.
Tianle Liu, Youcheng Niu, Jing Zeng +2
College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China