Robust Game-theoretic Motion Planning over Extended Time Horizons

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.

Solving multi-agent optimal control problems in aerospace such as pursuit-evasion and contested space operations can be modeled as non-convex differential games for which, there are limited algorithms. In this work, a relaxation of generalized Nash Equilibrium problems (GNEPs) to exclude inter-agent control coupling in dynamics, which is representative of many multi-agent systems is introduced. The main contribution is an algorithm for solving a broad class of differential games named FALCON: Fast Augmented Lagrangian Convexification for Open-loop Nash equilibria is presented. Methodologically, sequential convex programming (SCP) is utilized to create tractable convex sub-games which can then be solved via standard convex programming methods involving a potential game reformulation. FALCON is demonstrated to have global convergence guarantees to an open-loop Nash equilibrium for non-convex differential games under mild assumptions. This is numerically shown through both cooperative and competitive differential games.

Robust motion planning in dense traffic requires autonomous vehicles to interact in rare and safety-critical scenarios that are underrepresented in naturalistic driving data. Although adversarial training offers a feasible solution, existing methods often rely on external scenario generators, heuristic perturbations, or simulator-heavy rollouts, which makes them difficult to integrate with modern autoregressive planners. Here, we cast adversarially robust planner learning as a constrained min-max game and propose Adversarial World Modeling (AWM), a theoretically grounded multi-agent self-play fine-tuning framework. Since solving the exact game is intractable, AWM introduces a principled decoupled solver. In the inner minimization, the planner's predictive world model is converted into a role-conditioned adversary that learns sparse, scene-adaptive attack coalitions via counterfactual credit assignment. In the outer maximization, the ego planner optimizes a regret-aware robust best response against the frozen AWM, utilizing tail-risk weighting and reference-anchored trust regions to improve hard-case recovery while preserving nominal driving behavior. Experiments on the nuPlan and InterPlan benchmarks demonstrate that our method generates transferable adversarial interactions and yields a robust planner that achieves competitive closed-loop performance in both nominal and highly interactive long-tail scenarios. Theoretical analysis justifies the decoupled solver and the main optimization components.