Chance Constraint Game‐Theoretic Differential Dynamic Programming for Safe Trajectory Optimization Under Uncertainties

This paper presents a novel Chance‐Constrained Game‐Theoretic Differential Dynamic Programming (CC‐GT‐DDP) framework for safe trajectory optimization under uncertainty. In many real‐world applications, agents not only optimize their performance but also ensure safety despite the presence of uncertainty and strategic interactions. By embedding the chance‐constrained formulation into the game‐theoretic DDP structure, our method explicitly enforces probabilistic safety guarantees and ensures that critical constraints such as obstacle avoidance are satisfied with high probability throughout the trajectory. The framework systematically approximates the Hamilton‐Jacobi‐Bellman‐Isaacs (HJBI) equations through a second‐order expansion and enables efficient computation of optimal, safe, and robust control strategies. We demonstrate the effectiveness of CC‐GT‐DDP through a quadcopter navigation task, where the vehicle must reach a designated target while safely avoiding multiple obstacles under dynamic uncertainty. The proposed method is also applied to a pursuit‐evasion game. Simulation results demonstrate that the proposed method generates reliable and collision‐free trajectories and significantly improves safety over existing risk‐agnostic or deterministic approaches.