Data-Driven Kinematic Modeling and Control of a Cable-Driven Parallel Mechanism Allowing Cables to Wrap on Rigid Bodies

Cable-Driven Parallel Mechanisms (CDPMs) are subject to collision-free constraints from birth to the present. The collision-free constraints confine the workspace of CDPMs. To expand the workspace, scholars suggested allowing cables to wrap on rigid bodies (e.g., the end-effector) in recent years, opening new perspectives for CDPMs. However, the modeling and control of a CDPM with cables wrapped on general rigid bodies remain challenging. To this end, this study investigates the necessary conditions for a path of a cable of a CDPM wrapped on a smooth and frictionless rigid body. The solvability of the necessary conditions and the kinematics of the CDPM is explored then. It is shown that the kinematics of CDPMs with cables wrapped on rigid bodies, except for certain simple rigid bodies such as cylinders and spheres, is usually analytically unsolvable. To address the analytically unsolvable kinematics, the study develops a data-driven kinematic modeling and control strategy. The study applies the strategy to control the orientation of spatial rotational CDPM prototypes with wrapped cables and compares the strategy to a classical Jacobian-based kinematic control strategy. Experimental results indicate that for a CDPM allowing cables to wrap on a cylinder, the data-driven kinematic modeling and control strategy outperforms the Jacobian-based kinematic control strategy. For a CDPM allowing cables to wrap on a deformed cylinder, the data-driven kinematic modeling and control strategy can effectively control the CDPM.