Point-to-Point Motion Control of an Underactuated Planar Cable Driven Robot

Despite being vastly investigated for underactuated serial robots, there is less attention paid to controller design of underactuated parallel robots in the literature. This paper studies regulation of an underactuated planar parallel cable-driven robot with three degrees of freedom. First, kinematic and dynamic equations of the robot are derived, then equilibrium points of the robot are investigated. By analyzing dynamics of the under-constrained robot, it is shown that zero dynamic is oscillatory, thus a control law is proposed by a composition of damping injection and sliding mode control. One of the greatest advantages of the proposed controller is that after convergence of the robot to the desired point, which is proven by Lyapunov theorem, it is chattering free. Finally, simulation results shows the effectiveness of the controller in practice.