Reduced-order stable stabilizing controllers for remotely driven acrobot: Existence and design method

This paper concerns reduced-order stable controllers for the remotely driven acrobot (RDA) moving in a vertical plane, which is a 2-link planar underactuated robot whose second link is remotely driven by an actuator mounted at a fixed base through a belt. When the angles of two links are only measurable, first, this paper proves via a constructive procedure that stable controllers exist for a local stabilization of the upright equilibrium point of RDA by designing a specific output with an adjustable parameter and employing the pole-zero relation of the linearized model around the equilibrium point. Second, the paper presents a design method to obtain explicitly a formula of second-order (reduced-order) stable controllers by choosing the adjustable parameter. The obtained results for the RDA are compared with those of the directly driven acrobot (DDA) and the Pendubot in the literature. Simulation results are presented to validate the theoretical results.