Robust control synthesis and verification for wire-borne underactuated brachiating robots using sum-of-squares optimization

S Farzan, AP Hu, M Bick… - 2020 IEEE/RSJ …, 2020 - ieeexplore.ieee.org
S Farzan, AP Hu, M Bick, J Rogers
2020 IEEE/RSJ International Conference on Intelligent Robots and …, 2020ieeexplore.ieee.org
Control of wire-borne underactuated brachiating robots requires a robust feedback control
design that can deal with dynamic uncertainties, actuator constraints and unmeasurable
states. In this paper, we develop a robust feedback control for brachiating on flexible cables,
building on previous work on optimal trajectory generation and time-varying LQR controller
design. We propose a novel simplified model for approximation of the flexible cable
dynamics, which enables inclusion of parametric model uncertainties in the system. We then …
Control of wire-borne underactuated brachiating robots requires a robust feedback control design that can deal with dynamic uncertainties, actuator constraints and unmeasurable states. In this paper, we develop a robust feedback control for brachiating on flexible cables, building on previous work on optimal trajectory generation and time-varying LQR controller design. We propose a novel simplified model for approximation of the flexible cable dynamics, which enables inclusion of parametric model uncertainties in the system. We then use semidefinite programming (SDP) and sum-of-squares (SOS) optimization to synthesize a time-varying feedback control with formal robustness guarantees to account for model uncertainties and unmeasurable states in the system. Through simulation, hardware experiments and comparison with a time-varying LQR controller, it is shown that the proposed robust controller results in relatively large robust backward reachable sets and is able to reliably track a pre-generated optimal trajectory and achieve the desired brachiating motion in the presence of parametric model uncertainties, actuator limits, and unobservable states.
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