Direct propeller-speed tube model predictive control for unmanned underwater vehicle trajectory tracking with integrated nonlinear thruster mapping

Conventional UUV trajectory tracking relies on hierarchical motion control, thrust allocation, and thrust-to-speed conversion, which can accumulate mapping errors and complicate direct actuator-constraint enforcement. This paper proposes a tube-based model predictive control (Tube-MPC) method that directly optimizes propeller rotation speeds (PRS) using a nonlinear PRS-level prediction model. A nominal MPC law is combined with an LQR-based ancillary controller containing a bounded smooth nonlinear correction to attenuate model mismatch and disturbances. Because the nonlinear residual depends on the candidate tube radius, a monotone self-consistency map is introduced. Under the stated domain-containment and finite-supersolution conditions, an offline fixed-point iteration yields a robust positively invariant hyperrectangular outer tube. The tube provides PRS-amplitude and state-constraint tightening, while a first-move parameterization reduces the online optimization burden. Under the stated terminal, initialization, reference-matching, and operating-domain conditions, the method ensures nominal recursive feasibility, robust PRS-amplitude and state-constraint satisfaction, and practical tracking. Experiments on a UUV platform cover circular and lemniscate tracking under identical tuning. In both tasks, the proposed method attains lower tracking errors than the tested baselines.