Self-propulsion via slipping: Frictional swimming in multilegged locomotors

Abstract

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.

Multilegged matter transport: A framework for locomotion on noisy landscapes

“…As demonstrated in previous studies of dissipation-dominated multilegged locomotion on flat ground ( 27 , 28 ), because of the periodic limb lifting and landing, an effective viscous (rate-dependent) cycle-averaged thrust-velocity (the average thrust and velocity over a period, respectively) relationship emerges in frictional environments, despite such thrusts being instantaneously independent of velocity. Specifically, the relationship of cycle-averaged robot locomotion velocity is derived to be linearly correlated with the cycle-averaged thrust: v^=γ−1f^, where γ is the effective viscous drag coefficient (Fig.…”

“…We first tested our theoretical predictions by numerical simulations. We chose a saptiotemporal bac distribution pattern that was based on limb-stepping patterns of biological centipedes [and whose efficacy in generating locomotion in multilegged robots was previously studied in ( 27 , 30 )]. Each bac generates an instantaneous thrust given by f ( t ), which is independent of our choice of spatial redundancy (proof given in the SM, proposition 1).…”

“…Because the model assumes simplified environmental interactions, we next tested if our framework could predict locomotor performance in a physical system. We chose to work with a well-controlled laboratory multilegged robophysical model (movie S1) (design and control details are provided in the SM, sections 1.2 and 1.3), similar in design to those in ( 27 , 30 , 31 ). We measured the average speed and variance in such robots with different leg numbers and terrain complexity.…”

“…From the Shannon scheme for signal transmission, it is reasonable to anticipate improved performance with more elaborate coding schemes, which we define in matter transport as designing the terradynamic interaction profile of bacs (e.g., the instantaneous thrust function f ( t ) and thrust-velocity relationship). One straightforward method to modulate the bac-interaction profile is to change the body wave amplitude ( 27 ) or the number of waves on the body ( 33 ), which alters the temporal and spatial distribution of bacs and the associated body postures. To illustrate the potential of appropriate coding, we show one example of gait design modulation.…”

Classification and performance evaluation of simultaneous multithreaded architectures

“…Previous work on quasistatic legged locomotion from a geometric perspective can be divided into three factions. The first faction involves the study of the geometric mechanics of legged systems with a biologically prescribed, a priori contact trajectory [11,12]. This method provides no analysis of the local connection in each contact state, especially in a average motion-based gait generation (refer to holonomy in [2]) for which the foundations are laid out in this paper.…”