Research On Mathematical Model Of Swarm Robotics System

With the development of robot technology and the needs of practical application, the study on behavior analysis of swarm robotics system has become a hot research at home and abroad. System designers can design an efficient system in a short time with the help of simple and effective behavior analysis method, and improve the operating efficiency in practical application scene. In the traditional analysis methods, Researchers had a choice of two options to study the behavior of swarm robotics system: experiment or simulation. Experiments with real robots, allow observing swarms under real conditions and fully verifying the effectiveness of control strategies. However, experiments are very costly and time consuming and systematically varying individual agent parameters to study their effect on the swarm behavior is often impractical. Though simulations are much faster and less costly than experiments, they suffer from many of the same limitations, namely, they are tedious, and it is often still impractical to systematically explore the parameter space.This paper proposes a stochastic macroscopic model to analyze the group behavior of swarm robotics. In this method, swarm robotics is viewed as a random system in which individual robots switch between different states. And then, rate equations are used to describe dynamic of robot's number in various states. At last, mathematical equations are established to describe the whole swarm system. Using mathematical analysis we can study dynamics of multi-agent systems, predict long term behavior of even very large systems, gain insight into system design.The paper's main achievements include:1. Swarm robotics Cooperative foraging scene: the robot explore with a random strategy. When robot encountered a food, it stops and waits for the help. If no help within the time specified, the robot leave the food and continue exploring.2. Modeling Cooperative foraging using differential equations: The paper uses rate equation to describe dynamic of robot's number in various states. Add all the rate equations together and they become differential equations. These differential equations can describe the whole system.3. Analytic differential equations using MATLAB: Analysis the differential equations, predict long term behavior of even very large systems and gain insight into system design.4. Analytic Running the Cooperative foraging task in Emulator: Completing the cooperative forage task in the emulator, collecting experimental data and verify the correctness of the mathematical model.The study in this paper proves that the mathematical model can quickly and efficiently describe the swarm robotics system and achieve the role of system performance prediction and evaluation. In addition, the experimental data from the simulation prove the correctness of the mathematical model method.