A Novel Continuous Nonsingular Finite–Time Control for Underwater Robot Manipulators

Zengcheng Zhou,Guoyuan Tang,Ruikun Xu,Lijun Han,Maolin Cheng

doi:10.3390/jmse9030269

Abstract

In this paper, the tracking control problem of underwater robot manipulators is investigated under the influence of the lumped disturbances, including unknown ocean current disturbances and parameter uncertainties. The proposed novel continuous nonsingular finite–time (CNFT) control method is twofold. Firstly, the modified adaptive super–twisting algorithm (ASTA) is proposed with a nonsingular fast terminal sliding mode (NFTSM) manifold to guarantee the finite–time convergence both in the sliding mode phase and the reaching phase. Secondly, a higher–order super–twisting disturbance observer (HOSTDO) is exploited to attenuate the effects of the lumped disturbances. Considering the time–varying gain matrix of the closed–loop control system, the bounded stability is strictly proved via the Lyapunov theory. Hence, the superiority of the proposed controller is singularity–free, fast convergence, chattering–free, high steady–state tracking performance, and good robustness by resorting to the methods of CNFT control and ASTA in combination with a disturbance observer. Finally, numerical simulations are conducted on a two degree–of–freedom (DOF) underwater robot manipulator to demonstrate the effectiveness and high tracking performance of the designed controller.

Highlights

The last few decades have seen giant undersea technological improvements on underwater robot manipulators in many scientific fields, such as oceanographic observation, sub–sea detection, and some military applications [1]
Sliding mode control was designed for the underwater manipulator but the hydrodynamic effect was only regarded as the external disturbances [8]
A novel higher–order super–twisting disturbance observer (HOSTDO)–based continuous nonsingular finite–time (CNFT) control with the adaptive super–twisting algorithm (ASTA) method was proposed for underwater robot manipulators under time–varying lumped disturbances

Summary

Introduction

The last few decades have seen giant undersea technological improvements on underwater robot manipulators in many scientific fields, such as oceanographic observation, sub–sea detection, and some military applications [1]. Considering the roughly modeled hydrodynamics, some robust control strategies have been proposed for underwater manipulators in the last few decades to achieve satisfactory tracking performance. In 2020, an adaptive sliding mode control was proposed for the underwater manipulator to achieve finite time tracking with the asymmetric saturation [9]. In the SM control community, the super–twisting algorithm (STA) is one of the most effective HOSM techniques to achieve a high control accuracy [22,23] These control methods require the prior information of the lumped disturbances, which is not accessible for the underwater robot manipulator system in a submarine environment. The contributions of our paper are concluded as follows: (1) A novel HOSTDO–based NFTSM control with the modified ASTA scheme is firstly proposed for the underwater robot manipulators considering the unknown lumped disturbances. Considering the fact that the acceleration of the underwater manipulator body is always slow, the added mass torque and the vortex influence are small enough to be neglected in practical underwater robotic applications

Fundamental Facts

The Design of CNFT Control Based on HOSTDO and ASTA

The Design of HOSTDO

Simulation Results

Conclusions