Equivalence of Closed Chains to Open Chains: Virtual Decomposition Control Combined With Adaptive RBF Neural Network for Hydraulic Robot Legs

The joints of the hydraulic robot, driven by linear cylinders, form triangular closed-chain structures composed of the cylinders and passive rotational joints. This configuration complicates the complete dynamic modeling and increases the system's nonlinearity. To simplify the modeling process, conventional model-based controllers often disregard the rigid-body dynamics of the cylinders, treating the robot's legs or arms as open-chain systems. However, this introduces modeling errors that adversely affect control performance, especially in systems with heavier cylinders or high dynamic requirements. To address this issue, this study takes a typical hydraulic robot leg as an example and proposes a controller that combines virtual decomposition control (VDC) with an adaptive radial basis function neural network (RBFNN). We first model the closed-chain leg system as consisting of an open-chain subsystem and a coupling subsystem solely related to cylinder dynamics. In this way, the closed-chain system can be regarded as an open-chain system driven by coupled motors. Subsequently, the VDC control equations are designed for the open-chain subsystem, while an adaptive RBFNN is developed for the coupling subsystem to compensate for the effects of cylinder dynamics. Stability analysis is conducted for the entire system. The effectiveness and advantages of the proposed controller is validated through a series of prototype experiments.