Linking Gait Dynamics to Mechanical Cost of Legged Locomotion

Abstract

For millenia, legged locomotion has been of central importance to humans for hunting, agriculture, transportation, sport, and warfare. Today, the same principal considerations of locomotor performance and economy apply to legged systems designed to serve, assist, or be worn by humans in urban and natural environments. Energy comes at a premium not only for animals, wherein suitably fast and economical gaits are selected through organic evolution, but also for legged robots that must carry sufficient energy in their batteries. Although a robot's energy is spent at many levels, from control systems to actuators, we suggest that the mechanical cost of transport is an integral energy expenditure for any legged system-and measuring this cost permits the most direct comparison between gaits of legged animals and robots. Although legged robots have matched or even improved upon total cost of transport of animals, this is typically achieved by choosing extremely slow speeds or by using regenerative mechanisms. Legged robots have not yet reached the low mechanical cost of transport achieved at speeds used by bipedal and quadrupedal animals. Here we consider approaches used to analyze gaits and discuss a framework, termed mechanical cost analysis, that can be used to evaluate the economy of legged systems. This method uses a point mass perspective to evaluate the entire stride as well as to identify individual events that accrue mechanical cost. The analysis of gait began at the turn of the last century with spatiotemporal analysis facilitated by the advent of cine film. These advances gave rise to the "gait diagram," which plots duty factors and phase separations between footfalls. This approach was supplanted in the following decades by methods using force platforms to determine forces and motions of the center of mass (CoM)-and analytical models that characterize gait according to fluctuations in potential and kinetic energy. Mechanical cost analysis draws from these approaches and provides a unified framework that interprets the spatiotemporal sequencing of leg contacts within the context of CoM dynamics to determine mechanical cost in every instance of the stride. Diverse gaits can be evaluated and compared in biological and engineered systems using mechanical cost analysis.

Competing Models of Work in Quadrupedal Walking: Center of Mass Work is Insufficient to Explain Stereotypical Gait

“…While these approximations are useful, they each implicitly ignore certain aspects of the dynamics and energetics of gait. Simplifying the system can be useful, and the metrics provide a way of quantifying gait and pointing to similarities between disparate organisms ( Cavagna et al, 1977 ; Lee and Harris, 2018 ). It is tempting to point to a descriptive parameter as a prescriptive target of locomotion (or approximation of that target).…”

“…The first is as a gait classification scheme. Pendular recovery and collision angles have been used to identify subtle changes in gait within elephants ( Ren and Hutchinson, 2008 ), birds ( Usherwood et al, 2008 ), primates ( Demes and O’Neill, 2013 ) and numerous other taxa ( Lee and Harris, 2018 ). The second is to identify what portions of the stride could be most costly ( Donelan et al, 2002b ; Lee et al, 2011 ).…”

Divergent evolution of terrestrial locomotor abilities in extant Crocodylia

“…All video data were then digitally captured (Ulead Visual Studio 9.0; Ulead Systems, Taipei, Taiwan) as video files trimmed down to individual trials for initial analysis in Virtual Dub software (http://www.virtualdub.org/), in which foot touchdown/liftoff timings (from video fields) were recorded for each visible limb for all complete strides (cycle of footfalls). We classified footfall patterns using the limb phases 1,2,28,38 as a fraction of a stride between foot touchdown events; with the left hindlimb as the “0” reference. These limb phases corresponded to categories of footfall patterns (“gaits”) coded as trot (1), lateral sequence (2), diagonal sequence (3), rotary gallop (4), transverse gallop (5), half-bound (6), and bound (7); codes 1–3 were symmetrical gaits and 4–7 asymmetrical.…”

“…Extant Crocodylia have long been known to use almost all forms of walking and running locomotor modes (e.g., footfall patterns) present in quadrupedal mammals. These gaits include symmetrical (e.g., lateral/diagonal sequence walks; walking and running trots vide 1,2 ) and asymmetrical (e.g., galloping, bounds and half-bounds) footfall patterns. Nevertheless, the diversity, scaling (body size correlations), and underlying mechanisms of this impressive locomotor repertoire are based only on a few studies of select species from the >23 extant members of Crocodylia.…”

Measuring properties of movement in populations of evolved 3D agents

“…More general studies concern tetrapod (Biewener, 2006) and hexapod (Full et al, 1991) gaits, and such bodies are often an inspiration for the development of robot body plans (Koditschek et al, 2004). Biological inspirations are also popular in modeling locomotion (Lacquaniti et al, 2002;Biknevicius and Reilly, 2006;Lee and Harris, 2018) and in experimental and evolutionary robotics (Bongard and Paul, 2000;Krasny and Orin, 2004;Sellers et al, 2004;Ijspeert et al, 2005;Kukillaya and Holmes, 2007;Aydin et al, 2019).…”