Adaptive Robust Control Based on Moore-Penrose Generalized Inverse for Underactuated Mechanical Systems

Xiaolong Chen,Shengchao Zhen,Han Zhao,Hao Sun

doi:10.1109/access.2019.2950211

Abstract

To address the uncertainty existing in underactuated mechanical systems (UMSs) and their nonholonomic servo constraints, we propose a class of adaptive robust control based on the Moore-Penrose generalized inverse for UMSs in this paper. The uncertainty is considered as (possible fast) time-varying and bounded. However, the bound is unknown. To estimate the bound information, an adaptive law is designed, which combines leakage type and dead-zone type. This adaptive law can simultaneously regulate the control effort and computation speed. The proposed control can guarantee deterministic system performance, which is analyzed by using Lyapunov method. The effectiveness of proposed control is shown by an example of simplified two-wheeled self-balancing robot.

Highlights

Underactuated manipulators [1], [2], UAVs [3], surface vessels [4], spacecraft [5], [6], underwater vehicles [7] and so on have generally become active fields for the past few years, because they are all underactuated mechanical systems (UMSs) that have the advantages of low number of actuators, weight, cost and energy consumption
Complex internal dynamics, lack of feedback linearization and nonholonomic behavior accompany UMSs, which increase the difficulty of designing controller for such systems
The proposed control is designed based on the Moore-Penrose generalized inverse to deal with nonlinear time-varying underactuated system with uncertainty and nonholonomic servo constraint

Summary

INTRODUCTION

Underactuated manipulators [1], [2], UAVs [3], surface vessels [4], spacecraft [5], [6], underwater vehicles [7] and so on have generally become active fields for the past few years, because they are all underactuated mechanical systems (UMSs) that have the advantages of low number of actuators, weight, cost and energy consumption. The proposed control is designed based on the Moore-Penrose generalized inverse to deal with nonlinear time-varying underactuated system with uncertainty and nonholonomic servo constraint. The proposed adaptive robust control is able to deal with nonlinear time-varying UMSs and nonholonomic servo constraints. The adaptive law merged leakage type and dead-zone type is designed to estimate the bound of the uncertainty and regulate the control effort and speed up the algorithm practice.

PRELIMINARY OF MOORE-PENROSE

ADAPTIVE ROBUST CONTROL DESIGN

AN ILLUSTRATIVE EXAMPLE