Out-of-Plane Vibration Control of a Planar Cable-Driven Parallel Robot

A robust MIMO sliding mode control strategy is proposed for out-of-plane stabilization of the endeffector of a planar cable-driven parallel robot using an underactuated multibody multiaxis reaction system governed by nonlinear equations of motion. Low manipulator stiffnesses in the nonplanar directions is one of the concerns regarding accurate positioning of the end effector for planar cable-driven robots since the out-of-plane directions are uncontrollable via cable actuation. Therefore, an additional inertia-based reaction system is added to the end effector, consisting of two mirrored pendulum actuator systems, in order to elevate the system to a level of full controllability. A five-dimensional multibody model of the end effector with added multiaxis reaction system is presented and its equations of motion are derived. Sliding mode control is a robust nonlinear control approach that is capable of handling disturbances and parameter uncertainties. The sliding surfaces, one per actuated degree of freedom, are defined as a linear combination of the tracking position and velocity errors of both actuated and unactuated coordinates. The proposed sliding mode control law for the multiaxis reaction system has shown to perform well in both simulation and experiments.