Self-propulsion via slipping: Frictional swimming in multilegged locomotors.

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.

Active and passive mechanics for rugose terrain traversal in centipedes.

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.

Coordinating tiny limbs and long bodies: Geometric mechanics of lizard terrestrial swimming.

Although typically possessing four limbs and short bodies, lizards have evolved diverse morphologies, including elongate trunks with tiny limbs. Such forms are hypothesized to aid locomotion in cluttered/fossorial environments but propulsion mechanisms (e.g., the use of body and/or limbs to interact with substrates) and potential body/limb coordination remain unstudied. Here, we use biological experiments, a geometric theory of locomotion, and robophysical models to investigate body-limb coordination in diverse lizards. Locomotor field studies in short-limbed, elongate lizards (Brachymeles and Lerista) and laboratory studies of fully limbed lizards (Uma scoparia and Sceloporus olivaceus) and a snake (Chionactis occipitalis) reveal that body-wave dynamics can be described by a combination of standing and traveling waves; the ratio of the amplitudes of these components is inversely related to the degree of limb reduction and body elongation. The geometric theory (which replaces laborious calculation with diagrams) helps explain our observations, predicting that the advantage of traveling-wave body undulations (compared with a standing wave) emerges when the dominant thrust-generation mechanism arises from the body rather than the limbs and reveals that such soil-dwelling lizards propel via "terrestrial swimming" like sand-swimming lizards and snakes. We test our hypothesis by inducing the use of traveling waves in stereotyped lizards via modulating the ground-penetration resistance. Study of a limbed/undulatory robophysical model demonstrates that a traveling wave is beneficial when propulsion is generated by body-environment interaction. Our models could be valuable in understanding functional constraints on the evolutionary processes of elongation and limb reduction as well as advancing robot designs.