Analysis on periodic stability of gait trajectory of biped robot generated by NMPC realtime gait planning

Analysis on robust periodic stability of stable multi-step walking considering model uncertainty and alteration of ground condition was processed for gait trajectory of anthropomorphic biped robot generated by NMPC realtime gait planning. Feedback linearization was utilized to transform the periodic stability problem of high dimensional hybrid system to that of reduced dimensional uncontrollable pattern. Based on the existent condition of fixed point in Pincare section, robust stable theorem of multi-step limit cycle is proposed and it is proved that periodic stability of multi-step and single-step is consistent. By offline integration on time domain, simulation was carried out to analyze the influences of model uncertainties and velocity jump errors to the existence of limit cycle and contractive rate. The results show that the important theoretical and practical meanings of NMPC method in applying to actual physical object.