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Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-of-Squares Optimization

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Document pages: 8 pages

Abstract: Control of wire-borne underactuated brachiating robots requires a robustfeedback control design that can deal with dynamic uncertainties, actuatorconstraints and unmeasurable states. In this paper, we develop a robustfeedback control for brachiating on flexible cables, building on previous workon optimal trajectory generation and time-varying LQR controller design. Wepropose a novel simplified model for approximation of the flexible cabledynamics, which enables inclusion of parametric model uncertainties in thesystem. We then use semidefinite programming (SDP) and sum-of-squares (SOS)optimization to synthesize a time-varying feedback control with formalrobustness guarantees to account for model uncertainties and unmeasurablestates in the system. Through simulation, hardware experiments and comparisonwith a time-varying LQR controller, it is shown that the proposed robustcontroller results in relatively large robust backward reachable sets and isable to reliably track a pre-generated optimal trajectory and achieve thedesired brachiating motion in the presence of parametric model uncertainties,actuator limits, and unobservable states.

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