Distributed model predictive trajectory control for collision-free formation of heterogeneous unmanned under-actuated surface vehicles

• Distributed NMPC Formation Control: A leader-follower DNMPC strategy is developed for precise and safe trajectory tracking of heterogeneous under-actuated USV formations. • Time-Parameterized Collision Avoidance: A dual-constraint mechanism with both hard and soft constraints models predicted trajectories as time-parameterized state constraints, enhancing intra-formation collision avoidance and external obstacle avoidance. • Validated Effectiveness: A PIC-SINDy method identifies USV dynamics, and the proposed strategy is verified through simulations and full-scale experiments, demonstrating robust collision-free formation control. This paper proposes a distributed model predictive trajectory control strategy for heterogeneous under-actuated unmanned surface vehicle (USV) formations, enabling collision-free coordinated navigation. Under a leader-follower framework, follower reference trajectories are generated from the leader’s path and formation parameters. A distributed nonlinear model predictive control (DNMPC)-based trajectory-tracking controller is designed to achieve accurate formation keeping. A dual-constraint mechanism with both hard and soft constraints is introduced to incorporate intra-formation and external collision-avoidance requirements, where the predicted trajectories of formation members are modeled as time-parameterized nonlinear state constraints, rather than relying solely on their current positions. In addition, a physics-informed constrained sparse identification of nonlinear dynamics (PIC-SINDy) method is developed to identify USV dynamic models, meeting the practical need for accurate models in MPC design. The proposed strategy is validated through both numerical simulations and full-scale experiments, demonstrating its effectiveness and robustness in ensuring safe and reliable formation control.