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

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.

Sideways crab-walking is faster and more efficient than forward walking for a hexapod robot.

Articulated legs enable the selection of robot gaits, including walking in different directions such as forward or sideways. For longer distances, the best gaits might maximize velocity or minimize the cost of transport (COT). While animals often have morphology suited to walking either forward (like insects) or sideways (like crabs), hexapod robots often default to forward walking. In this paper, we compare forward walking with crab-like sideways walking. To do this, a simple gait design method is introduced for determining forward and sideways gaits with equivalent body heights and step heights. Specifically, the frequency and stride lengths are tuned within reasonable constraints to find gaits that represent a robot's performance potential in terms of speed and energy cost. Experiments are performed in both dynamic simulation in Webots and a laboratory environment with our 18 degree-of-freedom hexapod robot, Sebastian. With the common three joint leg design, the results show that sideways walking is overall better (75% greater walking speed and 40% lower COT). The performance of sideways walking was better on both hard floors and granular media (dry play sand). This supports development of future crab-like walking robots for future applications. In future work, this approach may be used to develop nominal gaits without extensive optimization, and to explore whether the advantages of sideways walking persist for other hexapod designs.

Dactyls and inward gripping stance for amphibious crab-like robots on sand.

Sandy beaches are areas that challenge robots of all sizes, especially smaller scale robots. Sand can hinder locomotion and waves apply hydrodynamic forces which can displace, reorient, or even invert the robot. Crab-like legs and gaits are well suited for this environment and could be used as inspiration for an improved design of robots operating in this terrain. Tapered, curved feet (similar to crab dactyl shape) paired with a distributed inward gripping method are hypothesized to enable better anchoring in sand to resist hydrodynamic forces. This work demonstrates that crab-like legs can withstand vertical forces that are larger than the body weight (e.g. in submerged sand, the force required to lift the robot can be up to 138% of the robot weight). Such legs help the robot hold its place against hydrodynamic forces imparted by waves (e.g. compared to displacement of 42.7 mm with the original feet, crab-like feet reduced displacement to 1.6 mm in lab wave tests). These feet are compatible with walking on sandy and rocky terrain (tested at three speeds: slow, medium, and fast), albeit at reduced speeds from traditional feet. This work shows potential for future robots to utilize tapered and curved feet to traverse challenging surf zone terrain where biological crabs thrive.