Multiparameter Bifurcation and Stability Analysis in Resource Allocation Problems of Swarm Robotic Systems

Resource allocation is a pivotal concern in swarm robotic systems. This study delves into the chaotic dynamics within the yield game process of resource-providing robots in such systems, analyzing system bifurcation and stability across multiple parameters. We propose a market-based model for swarm robotic systems, employing game theory to formulate a yield game model among resource-providing robots. Through numerical analysis and simulation, we identify stable regions of system parameters and present bifurcation diagrams under varied parameters. Our findings indicate that increasing cost parameters or decreasing decision parameters stabilizes the yield and utility of resource-providing robots, while the opposite destabilizes them. Moreover, we examine the intricate influence of cost parameters on system stability by comparing linear and exponential resource cost functions. Results reveal that exponential cost functions lead to heightened system chaos and parameter sensitivity. These insights offer crucial theoretical groundwork and practical directions for the development and deployment of swarm robot systems.