Hysteresis in the gait transition of a quadruped investigated using simple body mechanical and oscillator network models

Abstract

We investigated the dynamics of quadrupedal locomotion by constructing a simple quadruped model that consists of a body mechanical model and an oscillator network model. The quadruped model has front and rear bodies connected by a waist joint with a torsional spring and damper system and four limbs controlled by command signals from the oscillator network model. The simulation results reveal that the quadruped model produces various gait patterns through dynamic interactions among the body mechanical system, the oscillator network system, and the environment. They also show that it undergoes a gait transition induced by changes in the waist joint stiffness and the walking speed. In addition, the gait pattern transition exhibits a hysteresis similar to that observed in human and animal locomotion. We examined the hysteresis mechanism from a dynamic viewpoint.

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

“…Simple physical systems constructed by extracting the fundamentals of locomotion dynamics have enabled us to explain the essential characteristics of gait generation and have provided meaningful insights into biological sciences [14,16,23,41,[83][84][85]. Our robot mechanical and oscillator network systems are simple since they extract the essential aspects of locomotion from biomechanical and physiological findings.…”

“…The RG network generates the basic rhythm, and the PF network shapes the rhythm into spatio-temporal patterns of motor commands. We used an oscillator network model to control our robot (figure 3); it was constructed based on a two-layer network model composed of RG and PF models [23].…”

“…Physiological findings have enabled reasonably adequate models of the nervous system to be constructed, while robots have become effective tools for testing hypotheses of locomotor mechanisms by demonstrating real-world dynamic characteristics. We have demonstrated hysteresis in a walk-trot transition using a simple body mechanical model of a quadruped and an oscillator network model based on the physiological concept of the central pattern generator (CPG) [23]. In the present study, we design a quadruped robot to examine its gaits by varying the locomotion speed.…”

Emergence of hysteresis in gait transition of a hexapod robot driven by nonlinear oscillators with phase resetting

“…The hysteresis in the walk-trot transition of quadrupeds has also been investigated using simple body mechanical and oscillator network models [7]. Hysteresis is a typical characteristic of nonlinear dynamic systems, as observed in the periodically forced Duffing equation [17].…”

“…For the numerical simulation, we derived the equation of motion of the robot model using Lagrangian equations as in [7] and solved the equation of motion using the fourth order Runge-Kutta method with step size of 0.1 ms. Table I shows the physical parameters of the robot.…”