Synthesis of Control Stabilizing the Unstable Equilibrium of a Ball Suspended on a Manipulator

This paper addresses the problem of stabilizing the unstable equilibrium position of a ball located on a horizontal platform, which is suspended from the end-effector of a 6DOF manipulator. The primary objective of the research is to develop a stabilization algorithm that ensures the largest possible region of attraction for the unstable equilibrium point. To this end, a mathematical model of the system is first constructed, followed by an analysis of its controllability and stability. A feedback control law is proposed to stabilize the unstable equilibrium. Numerical simulations and experimental studies confirm the effectiveness of the proposed approach. The results of this work can be applied to the control of collaborative robots, as well as for testing and improving the quality of manipulators.