Emergent gait transitions of a quadrupedal robot under obstacle modulation

Biological gaits are results of both neural control signals and mechanical feedback. Recent biological studies (Wilshin et al., 2017) demonstrated that when moving from flat ground to rough terrains, dogs would shift from walk-like gaits to trot-like gaits. Inspired by this result, we use a quadrupedal robot as a robophysics model, to study how a ''soft’’ feedforward gait is affected by repeated ''phase perturbations’’, as the robot traverses an array of evenly spaced half-cylindrical obstacles. We modelled the feedforward quadrupedal gait as relative phases between the leg pairs, (Φ₁, Φ₂, Φ₃), with a ''gait stiffness'', K. Here Φ₁, Φ₂, Φ₃ denote the phase differences between the left and right front legs, left rear and right front legs, right rear and right front legs, respectively. Upon each leg-obstacle collision, a phase perturbation, L, is applied to the contacting robot leg, causing the leg to delay or advance its phase based on the contact position on the obstacle, and therefore modulates the robot gait. Simulation results with a feedforward ''trot’’ gait, (Φ₁, Φ₂, Φ₃) = (0.5,0,0.5), suggested that with a relatively small phase perturbation as compared to the gait stiffness, the robot could converge to a new stable gait under repeated phase perturbations. Two distinct groups of converged gaits were observed: (i) (0.5-C₁, 0, 0.5-C₁), and (ii) (0.5,1-C₂, 0.5-C₂), where C₁ and C₂ are primarily governed by the ratio of the phase perturbation, L, to the gait stiffness, K.