Van der Pol Oscillators and Phase-Locked Loops: A Transparent Model for Central Pattern Generators in Bioinspired Robotics

Central pattern generators (CPGs) are biological neural circuits that allow vertebrates to control rhythmic and motor behavior by generating rhythmic output without rhythmic input. The synthetic generation of CPGs has attracted attention to control robots for locomotion tasks. The above has led to the design of CPGs using spiking neural networks (SNNs) or systems of coupled oscillators. Nevertheless, using SNNs for CPG design has drawbacks, such as a lack of interpretability and difficult training. On the other hand, coupled oscillators require trial and error tuning of many parameters and may face stability and synchronization issues between oscillators. This study proposed utilizing Phase-Locked Loops (PLLs) combined with adjustable amplitude van der Pol (VDP) oscillators for synthetic CPG design used for locomotion tasks. Each VDP-PLL unit acts as an analog for a neuron within a biological CPG, forming a synchronized network that resembles rhythmic, coordinated movements. Furthermore, the proposed VDP-PLL was compared to classical coupled oscillators such as the Kuramoto and Hopf. The results demonstrate that the VDP-PLL method effectively overcomes the typical challenges of conventional coupled oscillator implementations in CPGs, since it benefits from a robust mathematical model utilizing four non-heuristic variables, allowing system parameterization using classical control system methodologies. The system can self-correct within an adequate time frame in response to variations in oscillation parameters. Furthermore, the VDP-PLL system has the potential to be implemented using analog electronics, thereby mitigating processing limitations in embedded systems. Our findings indicate that this method offers a promising pathway for achieving adaptable and transparent bioinspired motion.