Reduced-order stable controllers for two-link underactuated planar robots

This paper concerns reduced-order stable controllers in a unified way for two typical examples of underactuated robots called the Acrobot and the Pendubot, which are two-link planar robots moving in a vertical plane with a single actuator at joints 1 and 2, respectively. The main contributions of this paper are threefold. First, with the aid of properties of the mechanical parameters of two-link planar robots, this paper proves constructively that stable controllers exist for stabilizing the UEP (Upright Equilibrium Point with two links being still in the upright position) of each robot by designing a single output with an adjustable parameter. Second, the paper presents a design method to obtain explicitly a formula of second-order (reduced-order) stable controllers by choosing the adjustable parameter. Third, in terms of strong stabilization, some new features of the Acrobot and the Pendubot are revealed and are compared with those of the cart–pendulum system. Simulation results for the two robots are presented to validate the theoretical results and to demonstrate that the presented stable stabilizing controllers achieve a better control performance than several other controllers.