Control of 2R underactuated manipulator with friction

Manipulators with free joists are typical underactuated mechanisms. The constraints are second-order nonholonomic, and control of such systems is quite difficult. Many researches have been made on control of such systems without considering friction at free joints, In this paper, we analyze the behaviors of 2R underactuated manipulators with friction at free joints by the averaging method in response to a periodic input. We define an energy-like function from analyses of frictionless systems and utilize it to the system with friction for feedback stabilization onto an invariant elliptic manifold. We also propose a control method to stabilize it to a stable manifold for systems with friction. The effectiveness of the method is verified by experiments.