Robust Tracking Control and Stabilization of Underactuated Ships

Abstract

This paper addresses the problem of tracking control and stabilization for underactuated ships subjected to parametric modeling uncertainties. By designing a novel error state transformation scheme, some auxiliary variables are provided to be regarded as additional virtual control signals, while these variables can change their structures for different reference trajectories. Then, a robust control scheme is presented to achieve practical convergence of tracking errors and the ship's velocities to bounded neighborhoods of the origin. Simulation results are performed to illustrate the effectiveness of the proposed control scheme.

Robust practical tracking control of an underactuated hovercraft

“…, onlyṽ e has the derivative that contains unknown disturbances, and in addition, f v containsṽ e ; see (18). Let us rewrite .…”

“…Researchers have recently developed novel techniques that can steer the USV system to achieve practical tracking of any smooth reference trajectory, either feasible or non-feasible and either PE or not. [6,[16][17][18][19] The term "practical" is in the sense that the tracking errors are driven converging into small compact balls near the origin rather than to 0. In Xie and Ma, [19] an external oscillator combined with state transformations is used to derive a control strategy that achieves practical tracking for an underactuated planar vehicle.…”

“…In Xie and Ma, [19] an external oscillator combined with state transformations is used to derive a control strategy that achieves practical tracking for an underactuated planar vehicle. The position-only tracking/stabilization control is investigated in Li [18] by the backstepping method, achieving the ultimate convergence of error states for an underactuated ship. The results in literature [6,16,17] follow the theoretical framework of transverse function (TF) approach [20] that allows for practical stabilization of any smooth reference trajectory for nonholonomic systems, including USVs.…”

Adaptive Backstepping Sliding Mode Tracking Control for Underactuated Unmanned Surface Vehicle With Disturbances and Input Saturation

“…In order to further study the tracking control problem subject to parameter uncertainties and external disturbances under input saturation, Zhu et al synthesized the uncertain parameters and unknown external disturbances through the compounded uncertain vector and approximated the input saturation into Gaussian error function in the adaptive vector-backstepping design framework [15]. Considering the condition of input saturation and parameter modeling uncertainty, a saturation robust adaptive controller is designed based on backstepping technique, dynamic surface control method and Lyapunov direct method [16]. In the later research, some auxiliary variables are used as additional virtual control signals to design an error state transition scheme affected by model uncertainty [17].…”

“…Sun et al proposed a robust adaptive trajectory tracking algorithm based on proportional integral sliding mode control and backstepping technology to improve the robustness of control system under model uncertainties and environmental disturbances [23]. It can be seen from above literatures that the current research on ship motion control mainly focuses on solving the model parameters uncertainty [13], [14], [16]- [19], [21]- [23], environmental disturbances [13], [14], [19], [20], [23] and input saturation [13], [14], [16], [18], [20]. In this paper, a novel virtual control law can not only avoid the singularity of error, but also avoid the problem of input saturation when the error is large.…”