Abstract: Almost all living organisms exhibit autonomic oscillatory activities, which are primarily generated by the rhythmic activities of their neural systems. Several nonlinear oscillator models have been proposed to elucidate these neural behaviors and subsequently applied to the domain of robot control. However, the oscillation patterns generated by these models are often unpredictable and need to be obtained through parameter search. This study introduces a mathematical model that can be used to analyze multiple neurons connected through fast inhibitory synapses. The characteristic of this oscillator is that its stationary point is stable, but the location of the stationary point changes with the system state. Only through reasonable topology and threshold parameter selection can the oscillation be sustained. This study analyzed the conditions for stable oscillation in two-neuron networks and three-neuron networks, and obtained the basic rules of the phase relationship of the oscillator network established by this model. In addition, this study also introduces synchronization mechanisms into the model to enable it to be synchronized with the sensing pulse. Finally, this study used these theories to establish a robot single leg joint angle generation system. The experimental results showed that the simulated robot could achieve synchronization with human motion, and had better control efects compared to traditional oscillators.

Key words: Oscillator , · Phase trajectory , · Synaptic threshold , · Synchronization , · Motion generation