Cusp catastrophe embedded in gait transition of a quadruped robot driven by nonlinear oscillators with phase resetting

In this paper, we investigated the dynamic locomotion of a quadruped robot. This robot is controlled by a locomotion control system composed of nonlinear oscillators, which was constructed based on the physiological concept of central pattern generator and phase resetting. In our previous work, we revealed that the quadruped robot produces the walk and trot gaits depending on the locomotion speed through dynamic interactions among the robot mechanical system, the oscillator control system, and the environment. In addition, we showed that it generates the walk-trot transition with a hysteresis, similar to that observed in locomotion of quadrupeds. To further clarify the gait transition mechanism, the present study investigated the dependence of the gait transition not only on the locomotion speed, but also on the physical conditions, such as the body mass. Our simulation results show that the codimension-2 cusp bifurcation appears in the gait transition, which further elucidates the dynamic structure inherent in quadrupedal locomotion.