Robust Phase-Space Planning for Agile Legged Locomotion over Various Terrain Topologies

Abstract

Abstract-In this study, we present a framework for phasespace planning and control of agile bipedal locomotion while robustly tracking a set of non-periodic keyframes. By using a reduced-order model, we formulate a hybrid planning framework where the center-of-mass motion is constrained to a general surface manifold. This framework also proposes phase-space bundles to characterize robustness and a robust hybrid automaton to effectively design planning algorithms. A newly defined phasespace locomotion manifold is used as a Riemannian metric to measure the distance between the disturbed state and the planned manifold. Based on this metric, a dynamic programming based hybrid controller is introduced to produce robust locomotions. The robustness of the proposed framework is validated by using simulations of rough terrain locomotion recovery from external disturbances. Additionally, the agility of this framework is demonstrated by using simulations of the dynamic locomotion over random rough terrains.

Robust optimal planning and control of non-periodic bipedal locomotion with a centroidal momentum model

“…We are less centered on dynamic balance or moving from an initial to a final location but instead on tracking desired keyframes. A preliminary version of this work is presented in our conference paper (Zhao et al, 2016a). This paper is structured as follows.…”

Multi-contact walking pattern generation based on model preview control of 3D COM accelerations

“…Assuming that the COM lies inside the static-equilibrium polygon, 3 the right-hand side of this expression is positive from (19). The inequality is then expressed in polar form as…”

“…(We dropped the argument p G of σ â to alleviate notations.) Assuming that the COM lies in the interior of the polygon 3 (σ â > 0) and that zG > −g, 3 Otherwise, center the polygon on its Chebyshev center as previously. This expression is in polar form B 3D (p G )[x ỹ] ≤ 1 for the new coordinates:…”

“…See the accompanying video [1] for demonstrations of the controller in various multi-contact scenarios. done in [3] walking in the phase-space of the center of mass (COM), the latter being constrained on predefined surfaces that conform to terrain shape.…”

“…done in [3] walking in the phase-space of the center of mass (COM), the latter being constrained on predefined surfaces that conform to terrain shape.…”