Machine Learning Final : Learning The Structures and Predicting Behavoir of Potential Function Based Multi-Agent Formations

K eeping formation is a technique used to maintain order in multi-agent dynamical systems. Understanding formations has implications for military applications [1] as well as better understanding group behavior [2,3]. In past work, potential functions involving the distances between agents are used to maintain formation for both centralized and decentralized systems [4,5]. In [6], formations are defined rigorously using sets and the notion of formation rigidity is explained. In [2], Virtual Leaders are established as a means to move formations held together by Artificial Potentials. Artificial Potentials are also used in robotics research, like in [7]. I n this project, we developed a series of tools in order to classify groups and their structures, as well as predict a region which encompasses as many agents in a targeted group as possible, without encompassing any members from untargeted groups. Classifying groups by observing the dynamics of multi-agent groups could help distinguish between friendly and unfriendly forces in a military scenario in which it is difficult to determine the intent of certain agents. In determining the overall structure of a group (the links that define a formation), one understands which agents are maintaining distance with which other agents in order to create global, coordinated behavior the formation is predicated on. It then becomes easier to identify agents pivitol to holding the structure together and destroy it more efficiently. For instance, if the group was a cluster of satellites which were all maintaining position based on a central comm satellite, destroying the comm satellite would render the entire group useless. Finally, better predicting an area in which some targeted group will be after a delay while avoiding untargeted groups is important for military scenarios in which innocent groups are involved. Being able to accurately predict such an area would have tremendous application in today’s wars, which are more and more waged amongst civilian parties. The development of an accurate algorithm which can identify such an area with great confidence would help one predict whether to hold off on an area focused attack strategy until there is greater chance of targetted parties being affected without injuring innocent parties. We use an algorithm highly motivated by kmeans in order to distinguish each of the multi-agent groups from other groups that are operating in the same region. We also classify the structure of the multi-agent system by using logistic regression, using forward search in order to determine the best two features to use, where a group’s structure is defined by the set of links between its agents. A link implies that two agents are trying to maintain the distance between them. We model this communication as internal linear springs which push the agents apart when the agents are less than some constant chosen distance apart and pull the agents together when they are more than some fixed distance apart. The motion of each agent is damped. It is important to note that similar potential functions are commonly used in order to maintain forma-