Twisting Spine or Rigid Torso: Exploring Quadrupedal Morphology via Trajectory Optimization

Modern legged robot morphologies assign most of their actuated degrees of freedom (DoF's) to the limbs and designs continue to converge to twelve DoF quadrupeds with three actuators per leg and a rigid torso often modeled as a Single Rigid Body (SRB). This is in contrast to the animal kingdom, which provides tantalizing hints that core actuation of a jointed torso confers substantial benefit for efficient agility. Unfortunately, the limited specific power of available actuators continues to hamper roboticists' efforts to capitalize on this bio-inspiration. This paper presents the initial steps in a comparative study of the costs and benefits associated with a traditionally neglected torso degree of freedom: a twisting spine. We use trajectory optimization to explore how a one-DoF, axially twisting spine might help or hinder a set of axially-active (twisting) behaviors: trots, sudden turns while bounding, and parkour-style wall jumps. By optimizing for minimum electrical energy or average power, intuitive cost functions for robots, we avoid hand-tuning the behaviors and explore the activation of the spine. Initial evidence suggests that for lower energy behaviors the spine increases the electrical energy required when compared to the rigid torso, but for higher energy runs the spine trends toward having no effect or reducing the electrical work. These results support future, more bio-inspired versions of the spine with inherent stiffness or dampening built into their mechanical design.