A stability-based mechanism for hysteresis in the walk–trot transition in quadruped locomotion

Abstract

Quadrupeds vary their gaits in accordance with their locomotion speed. Such gait transitions exhibit hysteresis. However, the underlying mechanism for this hysteresis remains largely unclear. It has been suggested that gaits correspond to attractors in their dynamics and that gait transitions are non-equilibrium phase transitions that are accompanied by a loss in stability.In the present study, we used a robotic platform to investigate the dynamic stability of gaits and to clarify the hysteresis mechanism in the walk -trot transition of quadrupeds. Specifically, we used a quadruped robot as the body mechanical model and an oscillator network for the nervous system model to emulate dynamic locomotion of a quadruped. Experiments using this robot revealed that dynamic interactions among the robot mechanical system, the oscillator network, and the environment generate walk and trot gaits depending on the locomotion speed. In addition, a walk -trot transition that exhibited hysteresis was observed when the locomotion speed was changed. We evaluated the gait changes of the robot by measuring the locomotion of dogs. Furthermore, we investigated the stability structure during the gait transition of the robot by constructing a potential function from the return map of the relative phase of the legs and clarified the physical characteristics inherent to the gait transition in terms of the dynamics.

Hysteresis in the metachronal-tripod gait transition of insects: A modeling study

“…When all the elements of matrix * ij are determined based on the desired gait and large values are used for the gain constants K ij in (3), our model will establish the desired gait when the gait becomes stable. In contrast, when small values are used for K ij , this can generate a different gait from the desired one due to the sensory regulation by phase resetting (4).…”

“…In particular, hysteresis appears when the gaits change in accordance with the locomotion speed [2,[4][5][6][7][8][9][10][11]. Specifically, the gaits vary at different locomotion speeds depending on the direction of speed change.…”

“…From the observation of locomotion, hysteresis has been reported in the walk-run transition of humans [2,[6][7][8][9]11] and in the gait transitions of quadrupeds [4,5,10]. Neuromechanical models of humans and quadrupeds have been employed to investigate their gait transition mechanisms and have demonstrated that hysteresis appears in the walk-run transition of humans [21] and in the walk-trot transition of quadrupeds [12].…”

Inter-stride variability triggers gait transitions in mammals and birds

“…If the system is stable, a perturbation will not lead to a change in state variables. In locomotion, such a state change usually refers to either interlimb interference or falling [3,9,19,26,31,32]. While moving at an optimal stride length and frequency for a particular gait type is usually stable for an animal, speeding up or slowing down drives them away from this attractor state and they enter more variable, potentially unstable locomotor conditions (electronic supplementary material, figure S1b) [3,9,19,26,31,32].…”

Mechanics and energetics in tool manufacture and use: a synthetic approach

“…Robots have been used to study locomotion biomechanics [18][19][20][21][22][23], neural control strategies [24][25][26] and animal behaviours [27,28]. The robots are often reduced-order models of the animals with similarities in certain aspects that are of the interest to investigation.…”