ADP-Based $\mathcal {H}_{\boldsymbol{\infty }}$ Optimal Decoupled Control of Single-Wheel Robots With Physically Coupling Effects, Input Constraints, and Disturbances

摘要

This article investigates a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\boldsymbol{\mathcal {H}}_{\boldsymbol{\infty }}}$</tex-math></inline-formula> optimal decoupled control scheme for single-wheel (unicycle) robots with unknown physical coupling effects, input constraints, and external disturbances. First, by presenting the dynamics of the roll and pitch axes as a strict-feedback nonlinear system with physical interconnection effects, the feedforward control is proposed to decompose the centralized dynamics into decentralized dynamics. Second, based on the requirement of cooperation between roll and pitch dynamics, value functions are defined, and the Hamilton–Jacobi–Isaacs equations are derived, to which the solutions are estimated online by the adaptive dynamic programming principle and the two-player game differential theory. From the Lyapunov theory, the optimal control policies and disturbance compensation policies are established. The tracking and approximation errors are proven to be ultimately uniformly bounded. Finally, the effectiveness of the proposed control scheme is validated through comparative simulation and experimental results.