Dynamic Walking 2010. Anton Shiriaev. VHC Tools for Gait Analysis and Control.
Stable gaits of passive walking mechanisms often have narrow and strangely shaped regions of attraction, which are difficult both to estimate analytically and to enlarge using feedback from just a few actuators. For instance, linearization of the first-return Poincaré map, being decisive for exponential orbital stability of a limit cycle, can be used for estimating neither its region of attraction nor possible deviations from a nominal trajectory in response to small parametric perturbations. In this talk, we reiterate and refine the arguments presented in 2008 and describe a procedure for constructing such estimates based on the notions of virtual holonomic constraints and transverse linearization. The method allows: (a) revealing mechanisms of instability of cycles when dynamics of an underactuated biped is perturbed by imperfections of a walking surface; (b) developing tools for planning gaits insensitive to certain perturbations; (c) designing robustly stabilizing feedback controllers. The results are presented on the examples of a compass-gait biped and a quadruped.