Series Elastic Behavior of Biarticular Muscle-Tendon Structure in a Robotic Leg

Abstract

We investigate the role of lower leg muscle-tendon structures in providing serial elastic behavior to the hip actuator. We present a leg design with physical elastic elements in leg angle and virtual leg axis direction, and its impact onto energy efficient legged locomotion. By testing and comparing two robotic lower leg spring configurations, we can provide potential explanations of the functionality of similar animal leg morphologies with lower leg muscle-tendon network structures. We investigate the effects of leg angle compliance during locomotion. In a proof of concept, we show that a leg with a gastrocnemius inspired elasticity possesses elastic components that deflect in leg angle directions. The leg design with elastic elements in leg angle direction can store hip actuator energy in the series elastic element. We then show the leg's advantages in mechanical design in a vertical drop experiment. In the drop experiments the biarticular leg requires 46% less power. During drop loading, the leg adapts its posture and stores the energy in its springs. The increased energy storing capacity in leg angle direction reduces energy requirements and cost of transport by 31% during dynamic hopping to a cost of transport of 1.2 at 0.9 kg body weight. The biarticular robot leg design has major advantages, especially compared to more traditional robot designs. Despite its high degree of under-actuation, it is easy to converge into and maintain dynamic hopping locomotion. The presented control is based on a simple-to-implement, feed-forward pattern generator. The biarticular legs lightweight design can be rapidly assembled and is largely made from elements created by rapid prototyping. At the same time it is robust, and passively withstands drops from 200% body height. The biarticular leg shows, to the best of the authors' knowledge, the lowest achieved relative cost of transport documented for all dynamically hopping and running robots of 64% of a comparable natural runner's COT.

Effective Viscous Damping Enables Morphological Computation in Legged Locomotion

“…Stiffness, in comparison, has been studied extensively in legged locomotion. Its benefits have been shown both in numerical simulations, e.g., through spring-loaded inverted pendulum (SLIP) models (Mochon and McMahon, 1980 ; Blickhan et al, 2007 ), and physical springy leg implementations (Spröwitz et al, 2013 ; Hutter et al, 2016 ; Ruppert and Badri-Spröwitz, 2019 ).…”

Morphological Computation Increases From Lower- to Higher-Level of Biological Motor Control Hierarchy

“…This way, even simple piecewise constant control signals will result in smooth dynamic movements (Driess et al, 2018 ), very similar to what is known from simulation results (Kistemaker et al, 2007a ; Stollenmaier et al, 2020a , b ; Wochner et al, 2020 ), and are hypothesized to be a control principle of goal-directed arm movements (Feldman and Levin, 2009 ). Furthermore, as mechanical (visco-)elastic morphological characteristics are also known to benefit robotic locomotion (Iida et al, 2009 ; Shepherd et al, 2011 ; Niiyama et al, 2012 ; Hutter et al, 2013 ; Manfredi et al, 2013 ; Sprowitz et al, 2013 ; Nurzaman et al, 2015 ; Hubicki et al, 2016 ; Ruppert and Badri-Spröwitz, 2019 ), we expect that such a hierarchy in morphological control may be present in such systems too. This will become especially interesting if hierarchical control systems learn to exploit these morphological contributions to efficiently generate movements (e.g., Manoonpong et al, 2007 ; Driess et al, 2018 ; Büchler et al, 2020 ).…”

“…This is not only relevant for the understanding of biological systems, but also for bio-inspired and bio-mimetic robotics. Much effort has been taken to develop new robotic design concepts exploiting material properties (Kim et al, 2013 ; Rus and Tolley, 2015 ; Polygerinos et al, 2017 ), such as viscoelastic muscle-like actuators in arm movements (Boblan et al, 2004 ; Driess et al, 2018 ), elasticity in legged locomotion (Iida et al, 2009 ; Niiyama et al, 2012 ; Hutter et al, 2013 ; Sprowitz et al, 2013 ; Hubicki et al, 2016 ; Ruppert and Badri-Spröwitz, 2019 ) or morphology which empowers hopping (Nurzaman et al, 2015 ), goal-directed swimming (Manfredi et al, 2013 ), crawling Shepherd et al ( 2011 ), or even grasping (Deimel and Brock, 2016 ). However, also in these approaches, the hierarchy of morphological computation has not yet been quantified.…”

Hybrid Parallel Compliance Allows Robots to Operate With Sensorimotor Delays and Low Control Frequencies

“…Serial and parallel elastic-legged robots can locomote by feed-forward control and without system state knowledge from feedback ( Iida and Pfeifer, 2004 ; Narioka et al, 2012 ; Spröwitz et al, 2018 ; Ruppert and Spröwitz, 2019 ). However, passive, compliant designs are under-actuated and show limited controllability.…”