Robust PD Control Using Adaptive Compensation for Completely Restrained Parallel-Wire Driven Robots: Translational Systems Using the Minimum Number of Wires Under Zero-Gravity Condition

A parallel-wire driven mechanism uses flexible wires instead of heavy rigid links. In this paper, we propose a robust point-to-point (PTP) position control method in the task-oriented coordinates for completely restrained parallel wire-driven robots, which are translational systems using the minimum number of wires under zero-gravity conditions. In the cases where parallel-wire driven robots are disassembled/assembled and used outdoors (also applied in space), actuator positions would be uncertain or contain some errors. The error of internal force among wires that results from such uncertainty of actuator positions deteriorates positioning performance. To overcome such a difficulty, adaptive compensation is employed for robust PD control against the error of internal force, in this paper. It is necessary for the adaptive compensation to separate the internal force term linearly into a regressor matrix and a parameter vector concerned with the errors of actuator positions. The internal force term, however, possesses the nonlinear characteristic concerned with the errors of actuator position. Noting the structure of the internal force term, this paper shows that measuring both the position of an end-effector and wire length in real time enables the linear separation. Not only does this robust PD control method ensure precise positioning using external sensors; it enhances the robustness for uncertainty of the Jacobian matrix, which results from the error of actuator installation. First, we explain the linearization of the internal force term. Next, the robust PD control for the parallel-wire driven system using the uncertain Jacobian matrix is proposed; then, we prove the motion convergence to desired points and discuss its robustness based on Lyapunov stability analysis. Finally, the usefulness of the proposed control method is demonstrated through experiments and simulations.