A Comparative Study on the L1 Optimal Event-Based Method for Biped Walking on Rough Terrains

This paper is concerned with a comparative study of biped walking on rough terrains. Given a bipedal robot capable of walking on a flat ground with periodic behavior, whose motion can be described by a limit cycle with the Poincaré map, we consider whether the robot remains stable on rough terrain, in which geometrical uncertainties of the terrain are assumed to be persistent and bounded. More precisely, the
$l_\infty $
-induced norm is defined on the Poincaré map and taken as a performance measure evaluating a robot walking with the bounded persistent uncertainties. To minimize the performance measure and achieve an optimal walking performance, we further provide a systematic controller design scheme consisting of a inner-loop continuous-time controller and a outer-loop event-based controller, in which the latter is described as a sort of the
$l_{1}$
optimal controller. Finally, the validity as well as the effectiveness of our proposed methods in biped walking on a rough terrain are demonstrated through simulation studies.