Adaptive Dynamic Programming-Based Cross-Scale Control of a Hydraulic-Driven Flexible Robotic Manipulator

Featured Application The proposed method is suitable for application in robotic arm systems. This paper focuses primarily on adaptive dynamic programming (ADP)-based tracking control of the hydraulic-driven flexible robotic manipulator system (HDFRMS) with varying payloads and uncertainties via singular perturbation theory (SPT). Firstly, the dynamics is derived using a driven Jacobin matrix, which represents the coupling between the hydraulic servo-driven system and rigid-flexible manipulator established using the assumed mode method and Lagrange principle. Furthermore, the whole dynamic model of the manipulator system is decoupled into a second slow subsystem (SSS), a second fast subsystem (SFS) and a first fast subsystem (FFS). The three subsystems can describe a large range of movement, flexible vibration and electro-hydraulic servo control, respectively. Hereafter, an adaptive dynamic programming trajectory tracking control law with a critic-only policy iteration algorithm is presented in the second slow timescale, while both robust optimal control (ROC) in the second first timescale and adaptive sliding mode control (ASMC) in the first fast timescale are also designed using the Lyapunov stability theory. Finally, the numerical simulations are carried out to illustrate the rightness and robustness of the singular perturbation decomposition and proposed composite control algorithm.

Automated summary

The proposed method in this paper is suitable for application in robotic arm systems. It focuses on adaptive dynamic programming-based tracking control of the hydraulic-driven flexible robotic manipulator system (HDFRMS) with varying payloads and uncertainties via singular perturbation theory (SPT). The dynamics of the manipulator system is derived using a driven Jacobian matrix, and the whole dynamic model is decoupled into three subsystems. An adaptive dynamic programming trajectory tracking control law, a robust optimal control, and an adaptive sliding mode control are designed using Lyapunov stability theory. Numerical simulations are carried out to validate the singular perturbation decomposition and proposed control algorithm.