Piecewise linear spine for speed–energy efficiency trade-off in quadruped robots

Abstract

h i g h l i g h t s• Effects of flexible spine on performance of bounding quadrupeds are studied.• Superiority of nonlinear spines over linear ones is shown.• High performance is explained by energy storage-release profile of nonlinear springs.• Results are justified through a behavioral analogy with biology. a r t i c l e i n f o t r a c tWe compare the effects of linear and piecewise linear compliant spines on locomotion performance of quadruped robots in terms of energy efficiency and locomotion speed through a set of simulations and experiments. We first present a simple locomotion system that behaviorally resembles a bounding quadruped with flexible spine. Then, we show that robots with linear compliant spines have higher locomotion speed and lower cost of transportation in comparison with those with rigid spine. However, in linear case, optimal speed and minimum cost of transportation are attained at very different spine compliance values. Moreover, it is verified that fast and energy efficient locomotion can be achieved together when the spine flexibility is piecewise linear. Furthermore, it is shown that the robot with piecewise linear spine is more robust against changes in the load it carries. Superiority of piecewise linear spines over linear and rigid ones is additionally confirmed by simulating a quadruped robot in Webots and experiments on a crawling two-parts robot with flexible connection.

Natural dynamics modification for energy efficiency: A data-driven parallel compliance design method

“…Realization limitation may impose other constraints like monotony on compliance profile ( [12]). In [1], we show that nonlinearity in compliance profile gives us a flexibility in energy store-release shape of compliance, and subsequently improves energy efficiency of the system. In this work, our design methodology, based on the natural dynamics, results in a nonlinear parallel compliance.…”

“…Here are some instances: in a linear system, spring constant can relocate poles of the system and subsequently affect stability. Shaping the compliance to store energy and release it in a desired manner can lead to energy efficiency [1]. In SLIP model, average forward velocity can be controlled by leg compliance [2].…”

“…In bipedal robots, adding parallel compliance to knee joints can result in energy efficiency ( [14]). Recent researches show that compliance in spinal joint of a quadruped can lead to better behavior ( [1], [15], and [16]). It is worth mentioning that in soft robotics, softness is preferred over rigidity and compliance.…”

Energy-based and biomimetic robotics

“…Previous research has shown that a spinal joint with a spring can improve the overall energy-efficiency of the robot [45]. Others have shown that a spine with nonlinear stiffness leads to even higher efficiency [77]. In our robot, the front and rear body will be made to bounce on their legs, while the flexible spine introduces a resonance that results in forward motion.…”

“…Taking their inspiration from nature, many other scientists have investigated robotic quadrupeds with a spine: studying linear or rotational spinal joints, actuated and unactuated versions, or passive slope-walkers [77,111,33,76]. It is clear that a spine can contribute positively to locomotion.…”