A Cascade MIMO Control for Trajectory Tracking of Hydraulic Multi‐Closed‐Loop Robotic Manipulators

ABSTRACT This paper proposes a cascade multiple‐input–multiple‐output (MIMO) control framework for trajectory tracking of hydraulic robotic manipulators with multi‐closed‐loop kinematic chains. A dynamic modeling method integrating screw theory with reduced system dynamics is first developed to derive standard Lagrangian equations of motion for such manipulators. As large flow‐rate cartridge valves or combined flow control valves are commonly employed in these systems for heavy‐duty operation, a non‐affine nonlinear model is formulated to characterize the hydraulic actuation dynamics. A cascade control algorithm is then proposed, integrating a MIMO approximate nonlinear internal model with a feedback controller to achieve accurate trajectory tracking. The proposed approach tightly couples a computationally efficient screw‐theory‐based dynamic model of the multi‐closed‐loop mechanism with a MIMO approximate internal model control (AIMC) structure tailored to the system's non‐affine actuation characteristics. Whereas existing IMC implementations have predominantly focused on SISO or input‐affine systems, this paper develops a systematic methodology for deriving and implementing discrete‐time MIMO AIMC for non‐affine hydraulic systems, providing a principled framework for handling the inherent nonlinearities and model uncertainties of hydraulic manipulators with non‐affine valve actuation. Experimental results confirm that the proposed controller achieves high trajectory tracking performance on the hydraulic multi‐closed‐loop manipulator platform.