Locomotory behaviour of the intertidal marble crab (Pachygrapsus marmoratus) supports the underwater spring-loaded inverted pendulum as a fundamental model for punting in animals

Abstract

In aquatic pedestrian locomotion the dynamics of terrestrial and aquatic environments are coupled. Here we study terrestrial running and aquatic punting locomotion of the marine-living crab Pachygrapsus marmoratus. We detected both active and passive phases of running and punting through the observation of crab locomotory behaviour in standardized settings and by three-dimensional kinematic analysis of its dynamic gaits using high-speed video cameras. Variations in different stride parameters were studied and compared. The comparison was done based on the dimensionless parameter the Froude number (Fr) to account for the effect of buoyancy and size variability among the crabs. The underwater spring-loaded inverted pendulum (USLIP) model better fitted the dynamics of aquatic punting. USLIP takes account of the damping effect of the aquatic environment, a variable not considered by the spring-loaded inverted pendulum (SLIP) model in reduced gravity. Our results highlight the underlying principles of aquatic terrestrial locomotion by comparing it with terrestrial locomotion. Comparing punting with running, we show and increased stride period, decreased duty cycle and orientation of the carapace more inclined with the horizontal plane, indicating the significance of fluid forces on the dynamics due to the aquatic environment. Moreover, we discovered periodicity in punting locomotion of crabs and two different gaits, namely, long-flight punting and short-flight punting, distinguished by both footfall patterns and kinematic parameters. The generic fundamental model which belongs to all animals performing both terrestrial and aquatic legged locomotion has implications for control strategies, evolution and translation to robotic artefacts.

Models of benthic bipedalism

“…The foot-ground contact was modelled as a perfectly inelastic impact, which dissipates any velocity component that violates the constraint at foot placement, consistent with a range of previously used simple models of locomotion [9][10][11]. In the absence of slip, upon leg contact with the ground, the velocity of the body v is perpendicular to the leg vector r c , which points from body to contact point c. It may be useful here to contrast our model with other commonly adopted models for walking and running on land [12,13] and punting in water [14] that rely on spring-mass systems, known collectively as SLIP models. These spring models are particularly useful in their ability to model energy recovery in such instances as running dynamics.…”

Underwater legged robotics: review and perspectives

“…A comparison of crab locomotion in air and water revealed a novel gait characterised by backward directed pushes and great variability in leg patterns [94]. This gait was called underwater punting and its main features can be predicted by adapting the widely used single legged SLIP model either through reduced gravity or including the contributions of the underwater environment such as drag, lift, buoyancy and added mass [69,80,81,118]. ULRs featuring several DoFs can employ several types of gaits to adapt to different situations.…”

Learning to stop: a unifying principle for legged locomotion in varying environments

“…While this assumption is perfectly sensible in the case of terrestrial legged locomotion, the same cannot be said underwater, where the drag imposed on the body by a dense fluid introduces significant dissipation. Biological studies revealed fundamentals changes in the gait employed by crabs while running in water [8,10] that simply cannot be obtained through SLIP solutions. At the same time, there has been a growing interest towards underwater legged vehicles (ULR) [11,12,[38][39][40][41][42], which can extend the capabilities of traditional underwater robots thanks to their improved interaction with the seabed.…”

“…However, significant changes in the dynamics of the latter are difficult to explain by the SLIP model alone and, indeed, animals employ a slightly different gait in the underwater environment, which is referred to as punting [8]. An extension of the SLIP model, called underwater SLIP (USLIP, [9]), which takes into account the non-conservative nature of the system, the buoyancy, drag, and added mass effects of the punting gait, captures the dynamic of such locomotion [10], and it is successfully employed as a reference for the locomotion of underwater robots [11,12].…”