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An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal

Fig 8

Pseudoglobal optimal solutions (markers) are compared to a large dataset for Belgian Malinois dogs.

(A) A slowly decaying duty factor with increasing speed is predicted well by the model for medium to fast speeds, using . At slow speeds, the model remains constant, slightly above impulsive predictions, while the empirical data approaches 1. A swing duration of half the natural pendular period (T_n) of the leg (Eq 31) does not explain the discrepancy. 95% CI for empirical mean duty factor is shown as a thin dotted line. (B) The optimal phase offset matches empirical values well for walking and trotting speeds, and the optimal walk-trot transition is very close to the natural transition speed. However, the model does not transition to a gallop after the natural trot-gallop transition speed (C) Hind Lag (HL) and Fore Lag (FL) is shown against speed. A perfectly symmetrical gait would have HL = FL = 0.5; walking and trotting in dogs is highly symmetrical both naturally [50] and in the model. Galloping is an asymmetrical gait, and past the trot-gallop transition, the lowest-cost gait discovered by the model becomes asymmetrical. Empirical phase offsets are mean values for each gait. All empirical data from [40].

doi: https://doi.org/10.1371/journal.pcbi.1007444.g008