*Article* **Precise Trajectory Tracking Control of Ship Towing Systems via a Dynamical Tracking Target**

**Ouxue Li and Yusheng Zhou \***

School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China; gs.oxli19@gzu.edu.cn **\*** Correspondence: yszhou@gzu.edu.cn

**Abstract:** This paper proposes a novel control strategy to address the precise trajectory tracking control problem of a ship towing system. At first, the kinematics and dynamics models of a ship towing system are established by introducing a passive steering angle and using its structure relationship. Then, by using the motion law derived from its nonholonomic constraints, the relative curvature of the target trajectory curve is applied to design a dynamical tracking target. By applying the sliding mode control and inverse dynamic adaptive control methods, two appropriate robust torque controllers are designed via the dynamical tracking target, so that both the tugboat and the towed ship are able to track the desired path precisely. As we show, the proposed strategy has excellent agreement with the numerical simulation results.

**Keywords:** dynamical tracking target; ship towing system; relative curvature; adaptive control
