Multilayer Nested Learning Optimization-Based Coordinated Control for Biped Reconfigurable Robots Under Walking Task Constraints

Abstract

This article presents an online neuro-dynamic programming (NDP)-based optimal coordinated control method of biped reconfigurable robots (BRRs) under multilayer nested learning structure. Based on the requirements of walking task, the dynamic model of BRRs is established, decomposed into two operating modes: the swing phase and the support phase. To ensure stability during the support phase, a polyhedral friction cone approximation policy is employed to describe the distribution of plantar force, with corresponding reference values obtained through a quadratic programming (QP) algorithm. A novel cost function is constructed, incorporating the interaction forces between BRRs, torso, and ground, effectively reflecting the BRRs’ stability and coordinated control performance. Then, a functional link neural network (FLNN) identifier is designed to compensate for inherent model uncertainties. Leveraging the NDP framework, a near-optimal coordinated controller is obtained through the actor–critic dual-layer neural network (NN), enabling high-performance and stable planar walking of BRRs. Furthermore, the Lyapunov stability method is utilized to demonstrate that the tracking error of closed-loop BRRs is uniformly ultimately bounded (UUB). Finally, the effectiveness of the multilayer nested learning-based optimal coordinated control method is validated through experiments conducted on the self-designed claw-type BRR platform.