Abstract
This chapter presents the analysis and design of Dynamic Surface Control (DSC) with the application to biped walking with a variable step size. Under the assumption that the biped model consists of a single-leg support, a double impact, and a double-leg support phase model, the DSC is applied to the model which is a piecewise multi-input multi-output nonlinear system. Once the system becomes closed-loop with DSC, piecewise augmented error dynamics with provable stability properties are derived in the form of a piecewise linear system subject to exogenous inputs. Based on the error dynamics, a convex optimization problem is formulated to estimate the ellipsoidal error bound to guarantee the piecewise quadratic boundedness. Finally, the performance of DSC for the biped walking with a variable step size will be estimated by calculating a piecewise ellipsoidal error bound numerically and validated via simulation.
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