Optimal Walking of an Underactuated Planar Biped with Segmented Torso

Abstract

Recently, underactuated bipeds with pointed feet have been studied to achieve dynamic and energy efficient robot walking patterns. However, these studies usually simplify a robot torso as one link, which is different from a human torsos containing 33 vertebrae. In this paper, therefore, we study the optimal walking of a 6-link planar biped with a segmented torso derived from its 5-link counterpart while ensuring that two models are equivalent when the additional torso joint is locked. For the walking, we suppose that each step is composed of a single support phase and an instantaneous double support phase, and two phases are connected by a plastic impact mapping. In addition, the controlled outputs named symmetry outputs capable of generating exponentially stable orbits using hybrid zero dynamics, are adopted to improve physical interpretation. The desired outputs are parameterized by B´ezier functions, with 5-link robot having 16 parameters to optimize and 6-link robot having 19 parameters. According to our energy criterion, the segmented torso structure may reduce energy consumption up to 8% in bipedal walking, and the maximum energy saving is achieved at high walking speeds, while leaving the criteria at low walking speeds remain similar for both robots.