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ABSTRACT Centipedes coordinate body and limb flexion to generate propulsion. On flat, solid surfaces, the limb-stepping patterns can be characterized according to the direction in which limb-aggregates propagate, opposite to (retrograde) or with the direction of motion (direct). It is unknown how limb and body dynamics are modified in terrain with terradynamic complexity more representative of these animal's natural heterogeneous environments. Here, we investigated how centipedes that use retrograde and direct limb-stepping patterns, Scolopendra polymorpha and Scolopocryptops sexspinosus, respectively, coordinate their body and limbs to navigate laboratory environments which present footstep challenges and terrain rugosity. We recorded the kinematics and measured the locomotive performance of these animals traversing two rugose terrains with randomly distributed step heights and compared the kinematics with those on a flat frictional surface. Scolopendra polymorpha exhibited similar body and limb dynamics across all terrains and a decrease in speed with increased terrain rugosity. Unexpectedly, when placed in a rugose terrain, S. sexspinosus changed the direction of the limb-stepping pattern from direct to retrograde. Further, for both species, traversal of these rugose terrains was facilitated by hypothesized passive mechanics: upon horizontal collision of a limb with a block, the limb bent and later continued the stepping pattern. Although centipedes have many degrees of freedom, our results suggest these animals negotiate limb–substrate interactions and navigate complex terrains leveraging the innate flexibility of their limbs to simplify control. 

Locomotion is typically studied either in continuous media where bodies and legs experience forces generated by the flowing medium or on solid substrates dominated by friction. In the former, centralized whole-body coordination is believed to facilitate appropriate slipping through the medium for propulsion. In the latter, slip is often assumed minimal and thus avoided via decentralized control schemes. We find in laboratory experiments that terrestrial locomotion of a meter-scale multisegmented/legged robophysical model resembles undulatory fluid swimming. Experiments varying waves of leg stepping and body bending reveal how these parameters result in effective terrestrial locomotion despite seemingly ineffective isotropic frictional contacts. Dissipation dominates over inertial effects in this macroscopic-scaled regime, resulting in essentially geometric locomotion on land akin to microscopic-scale swimming in fluids. Theoretical analysis demonstrates that the high-dimensional multisegmented/legged dynamics can be simplified to a centralized low-dimensional model, which reveals an effective resistive force theory with an acquired viscous drag anisotropy. We extend our low-dimensional, geometric analysis to illustrate how body undulation can aid performance in non–flat obstacle-rich terrains and also use the scheme to quantitatively model how body undulation affects performance of biological centipede locomotion (the desert centipede Scolopendra polymorpha ) moving at relatively high speeds (∼0.5 body lengths/sec). Our results could facilitate control of multilegged robots in complex terradynamic scenarios. 

Snake robots have the potential to locomotethrough tightly packed spaces, but turning effectively withinunmodelled and unsensed environments remains challenging.Inspired by a behavior observed in the tiny nematode wormC.elegans, we propose a novel in-place turning gait for elongatedlimbless robots. To simplify the control of the robots’ many in-ternal degrees-of-freedom, we introduce a biologically-inspiredtemplate in which two co-planar traveling waves are superposedto produce an in-plane turning motion, theomega turn. Theomega turn gait arises from modulating the wavelengths andamplitudes of the two traveling waves. We experimentally testthe omega turn on a snake robot, and show that this turninggait outperforms previous turning gaits: it results in a largerangular displacement and a smaller area swept by the bodyover a gait cycle, allowing the robot to turn in highly confinedspaces. 

While terrestrial locomotors often contend with permanently deformable substrates like sand, soil, and mud, principles of motion on such materials are lacking. We study the desert-specialist shovel-nosed snake traversing a model sand and find body inertia is negligible despite rapid transit and speed dependent granular reaction forces. New surface resistive force theory (RFT) calculation reveals how wave shape in these snakes minimizes material memory effects and optimizes escape performance given physiological power limitations. RFT explains the morphology and waveform-dependent performance of a diversity of non-sand-specialist snakes but overestimates the capability of those snakes which suffer high lateral slipping of the body. Robophysical experiments recapitulate aspects of these failure-prone snakes and elucidate how re-encountering previously deformed material hinders performance. This study reveals how memory effects stymied the locomotion of a diversity of snakes in our previous studies (Marvi et al., 2014) and indicates avenues to improve all-terrain robots.