Safe multi-agent motion planning in presence of FDIAs via Kalman filter and filtered reinforcement learning

This paper studies safe motion planning for multi-agent systems in complex environments under Gaussian noise and false data injection attacks (FDIAs). Such attacks corrupt sensor measurements, degrade state estimation, and impair collision avoidance. To address this problem, we propose a unified framework for secure estimation and safe control. A secure Kalman filter with online adaptive gain tuning, implemented via simultaneous perturbation stochastic approximation, is developed to mitigate the impact of FDIAs and provide reliable state estimates. Based on these estimates, each agent computes a desired action through a reinforcement-learning-based planning module. These actions are then refined by a centralised quadratic-programming safety filter that enforces workspace constraints, inter-agent collision avoidance, and obstacle avoidance while minimally modifying the learned commands. Simulations show that the proposed method achieves low estimation error and collision-free trajectories under FDIAs, providing a scalable and formally safe solution for multi-agent motion planning in adversarial environments.