Physics-informed neural predictive formation control: A unified framework for safe multi-vehicle coordination

Multi-vehicle formation control in obstacle-rich environments requires simultaneous optimization of competing objectives including formation maintenance, collision avoidance, and energy efficiency. Existing approaches face two critical limitations: 1) high sensitivity to trade-off parameters, requiring scenario-specific manual tuning when balancing formation maintenance against collision avoidance, and 2) the inherent difficulty of simultaneously optimizing competing objectives, specifically the balance between maintaining formation cohesion and ensuring collision avoidance, which often destabilizes learning and degrades performance. This paper presents Physics-Informed Neural Predictive Formation Control (PINPFC), a unified framework integrating physics-informed neural networks, reinforcement learning, and model predictive control to address these challenges. The PINPFC architecture employs a multi-branch neural network embedding vehicle dynamics, safety constraints, and formation requirements as differentiable physics-informed loss functions, significantly mitigating the need for manual hyperparameter tuning by making competing objectives intrinsic to the network structure. A self-attention mechanism adaptively allocates control authority among branches by learning from real-time formation errors, safety violations, and physical consistency, while the MPC layer ensures hard constraint satisfaction and recursive feasibility. Theoretical analysis establishes formation convergence with explicit ultimate bounds, strict collision avoidance through hierarchical MPC-enforced constraints, and bounded suboptimality relative to centralized control. Comprehensive experimental validation across varying obstacle densities demonstrates that PINPFC achieves measurable improvements in strict success rates and near-collision rates compared to baseline methods, with performance advantages becoming increasingly pronounced in high-density scenarios.