The polynomial modeling and analysis of a special behavior for mobile robot

This paper gives the complete mathematical model of multi-robot cooperative hunting behavior via tasks modeling and robot-environment interaction modeling. The macro mathematical model is formulated by rate equations. Each dynamic variable in the macro model corresponds to the average number of robots in that state. The evolution of robot collective behaviors represents the transition between different states of robots. The microscopic model is established based on the polynomial modeling, which reflects the relations between sensors and activators. The polynomial model of a special behavior is identified based on the local interaction of robots. The complex collective behavior is emerged via the social interaction. The mathematical model will help us to understand the mechanism of multi-robot cooperative behaviors more clearly. This paper will give a method of quantitative analysis and mathematical modeling for robots collective behaviors, and basically set up the complete theory frame of social interaction among robots, tasks and environment.