Optimal planar leg geometry in robots and crabs for idealized rocky terrain

Yang Chen; Glenna Clifton; Nicole M Graf; Kayla Durand; Jennifer Taylor; Yifeng Gong; John E Grezmak; Kathryn A Daltorio

doi:10.1088/1748-3190/ac8f04

Optimal planar leg geometry in robots and crabs for idealized rocky terrain

Bioinspir Biomim. 2022 Oct 11;17(6). doi: 10.1088/1748-3190/ac8f04.

Authors

Yang Chen¹, Glenna Clifton², Nicole M Graf¹, Kayla Durand², Jennifer Taylor³, Yifeng Gong¹, John E Grezmak¹, Kathryn A Daltorio¹

Affiliations

¹ Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, United States of America.
² Biology Department, University of Portland, Portland, OR, United States of America.
³ Marine Biology Research Division, Scripps Institution of Oceanography, UC San Diego, CA, United States of America.

PMID: 36055245
DOI: 10.1088/1748-3190/ac8f04

Abstract

Natural terrain is uneven so it may be beneficial to grasp onto the depressions or 'valleys' between obstacles when walking over such a surface. To examine how leg geometry influences walking across obstacles with valleys, we (1) modeled the performance of a two-linkage leg with parallel axis 'hip' and 'knee' joints to determine how relative segment lengths influence stepping across rocks of varying diameter, and (2) measured the walking limbs in two species of intertidal crabs,Hemigrapsus nudusandPachygrapsus crassipes, which live on rocky shores and granular terrains. We idealized uneven terrains as adjacent rigid hemispherical 'rocks' with valleys between them and calculated kinematic factors such as workspace, limb angles with respect to the ground, and body configurations needed to step over rocks. We first find that the simulated foot tip radius relative to the rock radius is limited by friction and material failure. To enable force closure for grasping, and assuming that friction coefficients above 0.5 are unrealistic, the foot tip radius must be at least 10 times smaller than that of the rocks. However, ratios above 15 are at risk of fracture. Second, we find the theoretical optimal leg geometry for robots is, with the distal segment 0.63 of the total length, which enables the traversal of rocks with a diameter that is 37% of the total leg length. Surprisingly, the intertidal crabs' walking limbs cluster around the same limb ratio of 0.63, showing deviations for limbs less specialized for walking. Our results can be applied broadly when designing segment lengths and foot shapes for legged robots on uneven terrain, as demonstrated here using a hexapod crab-inspired robot. Furthermore, these findings can inform our understanding of the evolutionary patterns in leg anatomy associated with adapting to rocky terrain.

Keywords: Hemigraspsus nudus; Pachygraspsus crassipes; amphibious crab robots; distributed inward gripping; grasping uneven terrain; leg design optimization; sideways walking.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Animals
Biomechanical Phenomena
Brachyura*
Foot
Robotics* / methods
Walking