Discrete-time distributed model predictive control-based collision-avoidance formation tracking control for multiple...

Simultaneous trajectory tracking and obstacle avoidance are critical capabilities for unmanned underwater vehicles (UUVs). However, implementing these tasks on digital processors inevitably introduces discretization errors and time delays. Most existing continuous-time methods suffer from significant performance degradation when directly applied to discrete-time systems. Therefore, achieving high-precision control in the discrete-time domain remains a considerable challenge. To address this issue, a robust discrete-time dual-loop control architecture is proposed in this paper. First, a discrete-time distributed model predictive control (DMPC) scheme serves as the outer-loop kinematic controller, solving an online optimization problem to generate collision-free velocity commands. To guarantee closed-loop stability, discrete LQR-based terminal constraints are strictly incorporated. Furthermore, slack variables are introduced to dynamically relax these constraints during obstacle evasion maneuvers. This strategy effectively resolves the inherent conflict between theoretical stability and recursive feasibility in cluttered environments. Second, a discrete-time sliding mode controller (DSMC) is developed for the inner dynamic loop, where a specialized reaching law is designed to strictly confine state fluctuations within a minimal quasi-sliding mode band. In addition, a discrete disturbance observer (DDOB) is introduced to estimate and compensate for the effects of time-varying ocean current disturbances. Extensive simulation results demonstrate that the proposed framework achieves superior tracking accuracy, high computational efficiency, and reliable obstacle avoidance. Furthermore, rigorous theoretical analysis ensures global system stability under discrete-time implementation constraints.