Serret-Frenet Multi-Agent System with optimal control approach

Abstract

Multi-agents systems is a system consisting of several agents, from two to hundreds agents. These agents are connected to each other. The main problem is how to control such systems. This paper isnpired from some facts as follows. In nature, can be viewed animals perfom multi agent system in the land and in the air. In avionic world, can be observed that there are many cases where pilots must fly their aircrafts in some particular formation. Some ships also very often form a convoy. In smaller scales, can be viewed that there are many robot designer would like to create multi-robot system for conducting some task. In particular, this paper focuses on the robotics utilizations. That is we would like to steer the multi-agent system to go from one particular position to the other position. Moreover, the agents move in some formations is required. The first objective of this paper is to create mathematical model of multi-agent system applicable in robotic. The model would consist of Serret-Frenet control systems. The second objective is to model the performance index of the multi-agent system. Thus, we would like the multi-agent system move from one place to another and the whole group of agents works collaboratively for optimizing the performance index. This is the idea behind multi-agent control system design. The third objective is to analyze controllability the above models. The last objective is to find the optimal control of each agent. The Pontryagin Maximumm Principle is used to search this optimal control. The result of this paper, optimal control can be used to model the multi agent system Serret-Frenet system.