Dynamic properties of VDP-CPG model in rhythmic movement with delay

Area of Science:

• Robotics and Control Systems
• Nonlinear Dynamics
• Computational Neuroscience

Background:

• Central Pattern Generators (CPGs) are neural circuits responsible for rhythmic motor activities.
• Van der Pol (VDP) oscillators are a classic model for self-sustained oscillations, applicable to biological and artificial systems.
• Quadruped robots require sophisticated control systems for stable and versatile locomotion.

Purpose of the Study:

• To develop a VDP oscillator-based CPG network for controlling quadruped robot gaits.
• To analyze the stability and existence conditions of different gaits using bifurcation theory.
• To determine the necessary coupling strengths between VDP oscillators for achieving walk, trot, pace, and bound gaits.

Main Methods:

• Modeling a quadruped robot's CPG system using coupled Van der Pol (VDP) oscillators.
• Applying Hopf bifurcation analysis to identify the conditions for gait transitions.
• Calculating the permissible ranges of coupling strengths between oscillators for each gait.
• Conducting numerical simulations to validate the theoretical findings.

Main Results:

• Established a VDP-CPG network model for quadruped locomotion.
• Derived the existence conditions for Hopf bifurcations in the VDP-CPG system for four gaits.
• Obtained specific coupling strength ranges for the VDP oscillators corresponding to walk, trot, pace, and bound gaits.
• Numerical simulations confirmed the theoretical analysis of gait stability and transitions.

Conclusions:

• The VDP-CPG network effectively generates and controls four distinct gaits in quadruped robots.
• Bifurcation analysis provides a robust framework for understanding gait control in CPG systems.
• The identified coupling strength ranges are crucial for designing and implementing stable locomotion controllers for quadruped robots.