Robust Nonlinear Control for BipedWalking with a Variable Step Size

This paper presents the design of dynamic surface control (DSC) with application to the biped walking with a variable step size. Under the assumption that the biped robot consists of five links connected by four rotating joints, a three-phase model including double support phase is used for the controller design. Once the DSC is applied to the biped robot model, 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 tracking. 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