Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation

Abstract

The joint control problem of the underwater manipulator is addressed in this paper, under the influence of uncertainty factors such as model uncertainty, external disturbance, and manipulator joint lag. In general, for the uncertainty factors, it is usually approximated online, but it is difficult to select a reasonable value for the approximation error boundary, too conservative estimated values would cause chattering problem easily. And the influence of joint lag on the manipulator control should be considered in actual work. Unlike most previous control method, in this paper, the function approximation technique (FAT), which uses the Legendre polynomial, is adopted to approximate the uncertainty factors online. Then, based on the proportion integral differential (PID) sliding manifold with the integral and differential of tracking error, a sliding model PID controller is designed to speed up the response and reduce the effects of joint lag. For the error boundary, the adaptive law is proposed, and it will reduce chattering of the control quantity under the steady state of the system. It was proved that the joint error of the control system is uniformly asymptotic convergence through the stability analysis. Finally, the effectiveness of the proposed approach is demonstrated with pool comparison experiments of the underwater manipulator installed in the autonomous underwater vehicles (AUVs).Appl. Sci. 2020, 10, 1728 2 of 15 developed and equipped on multipurpose intervention-AUV [4]. An underwater electric manipulator (MARIS 7080, 7 DOF manipulator) was equipped on semi-autonomous underwater vehicle for the intervention mission (SAUVIM) [5].In UVMS, the underwater manipulator is a key component, and its joint control accuracy directly determines the operating accuracy of the UVMS. At present, underwater manipulators are mostly control objects with joint redundancy, and the accuracy mainly depends on the control performance of joints [6]. However, due to the nonlinear, time-variation of dynamic properties and other factors (i.e., external disturbances such as ocean current disturbance) [7,8], the system dynamic model has uncertainties, which will affect the joint control of the manipulator based on the dynamic model. Besides, for most hydraulic manipulators, the joint control performance is also affected by joint lag [6,9,10], which means that the joint lag will affect the control accuracy of manipulator joint. In conclusion, under the influence of the above factors, it has great research significance and practical value to develop the joint control technology of underwater manipulators for improving the accuracy and efficiency of underwater operation.Currently, many methods have achieved high control accuracy, which uses the online approximation to deal with the uncertainty factors, and determine the controller and adaptive law of parameter through stability analysis [11,12]. Among them, in view of the nonlinear and uncertain identification ability [11][12][13][14][15][16], neural network and fuzzy control has b...

Combined dynamics and kinematics networked fuzzy task priority motion planning for underwater vehicle-manipulator systems

“…17 Sadly, they cannot satisfy this strict condition in real time. 30 In this article, adopting the weight form of equation (22) to achieve that each secondary task's errors are zero. And K si e si in equation ( 29) as a compensator under the external disturbance is uncertain.…”

“…It is worth noticing that the problem of uncertainty and external disturbance, as the precondition of UVMS coordinated motion planning, is based on a sliding mode controller. 22 Given the EE desired velocity _ x E , the SMC eliminates the error in velocity space. Unfortunately, the EE's desired trajectory is unachievable, reflecting in the static error of position space.…”

“…Solving the lumped uncertainty for the controller of UVMS has attracted many scholars to study. [21][22][23][24][25][26] In a complex environment, the variety of disturbances include (a) ocean current, (b) payload changes, (c) lift or resistance, (d) noise (noise caused by the sensor and actuator error), (e) time delay or joint lag, and (f) friction and other disturbances. Simultaneously, uncertainty generally includes model parameter uncertain item (mainly generated by model inaccuracy) and parameter uncertain item (often not directly reflected as model parameters).…”

“…The abovementioned classification of disturbance terms is the basis to provide a compelling for the optimization of the controller. Similarly, the parameter uncertainty term in the uncertainty is passed through Legendre polynomial, 22 EKF, 8,10 respectively, achieved online estimation. Sadly, the kinematics redundancy of UVMS is less reflected in the controller designed with lumped uncertainty.…”

“…Considering (b) and (d), Mohan and Kim 8 adopted the extended Kalman filter (EKF) algorithm to construct disturbance compensation; Salloom et al 9 analyzed (c) as an unknown external disturbance and considered the nonparametric uncertainties as (f); the literature 5,9-13 designed EKF, adaptive algorithm, and observer compensation, respectively, for (d). Before using the time delay estimator, Yang et al 22 summarized (e) as (d). The abovementioned classification of disturbance terms is the basis to provide a compelling for the optimization of the controller.…”