On the optimal spine morphology of rapidly accelerating quadrupeds

Abstract

Animals exploit spine actuation during rapid locomotion, however this has only recently become a focal point in robotics. Roboticists have used a multitude of spine configurations in their platforms but the optimal design for rapid acceleration and deceleration maneuvers is yet to be discovered. In this paper, we endeavour to find this optimal spine morphology by using large-scale Monte Carlo trajectory optimization simulations on long-time-horizon minimum time problems (start and end at rest while travelling a fixed distance of 30 spine lengths). Broad applicability of the results was ensured by generating 100 sets of robot parameters at random from a carefully selected design space, comparing the performance of the rigid, revolute and prismatic spine morphology. Using bootstrapping techniques, it was determined with a 78.8% probability that the prismatic spine morphology was the optimal spine for these long-time-horizon trajectories. These results will serve as a guide for designers of future, agile quadruped robots.

Modeling and Trajectory Optimization for Standing Long Jumping of a Quadruped with A Preloaded Elastic Prismatic Spine

“…Many existing works abstract the biological evidence of the spine bending [33], [35] during locomotion with one or more revolute joints [23], [25], [30], [47]- [56]. Yet, the resulting considerable change in body length along the sagittal axis also implies the possibility of a prismatic joint interpretation, which has been verified as being effective for facilitating some quadrupedal dynamical gaits [25], [51]. Notwithstanding the direct deployment of any linear actuator as the actuated prismatic spine, passively compliant spine actuation remains an attractive alternative because the compliance may introduce high-density energy storage in lightweight components and high-frequency response through mechanical feedback [23], [54].…”

“…Spines with a revolute joint in either sagittal, frontal, or transverse planes have been widely studied numerically and empirically for their contribution to motion regularity [23], [25], [30], [47], [48], [50], [52], [53], [56] and transport efficiency [48], [49], [53]- [55], [57]. Although spine bending also implies the linear change in vertebrae morphology, spines embodied with a prismatic joint have been explored only scarcely, with most of the work [23], [25], [51], [56] conducted in numerical settings.…”