Spatiotemporal Pattern of Periodic Rhythms in Delayed Van der Pol Oscillators for the CPG-based Locomotion of Snake-like Robot

Abstract

Abstract This is the further research on the DHCO (delayed half-center oscillato) neural system presented in our previous paper (Song, Z., Xu, J. Self-/mutual-symmetric rhythms and their coexistence in a delayed half-center oscillator of the CPG neural system. Nonlinear Dyn (2022). https://doi.org/10.1007/s11071-022-07222-y), which is used to construct the CPG (central pattern generator) neural system to control the snake robot. In this paper, we construct a CPG (central pattern generator) neural network system to control locomotion of snake-like robot with pitch-yaw connecting configuration by using the delay-coupling Van der Pol (VDP) oscillators. To this end, we firstly give an improved model of the VDP oscillator to adjust amplitude and frequency of periodic rhythm. Employing mutually coupled delay, two VDP oscillators are connected to produce an HCO (half-center oscillator) module with time delay that is called as a DHCO (delayed HCO) model. Based on the analysis of Hopf bifurcation, periodic rhythm and spatiotemporal patterns of the DHCO are illustrated in different regions of parameters. The DHCO module presents periodic rhythms with synchronous and anti-synchronous patterns, which is used to control the joint actuators combined in the snake-like robot with pitch-yaw connecting configuration. To realize the snake-like robotic locomotion, based on the DHCO modules, we construct a chain-type of the CPG neural system combined with a new unidirectional delay in which phase difference can be regulated. Numerical simulations are illustrated that the CPG neural system can control snake-like robot to move with serpentine, rectilinear, and side-winding patterns in the forward and backward directions.