Complex switching dynamics and chatter alarm for aerial agents with artificial potential field method

Abstract

This paper presents a dynamic problem with moving discontinuous boundary for two aerial agents. One of the agents is assigned as the leader, and the other follows such a leader based on artificial potential field. The artificial potential field technique is designed to make the two agents repel each other when the relative distance is less than r1 in order to avoid collision, and such two agents will attract each other when the distance is greater than r1. The interaction between two agents becomes zero when the relative distance is greater than r2(r2>r1) to model the communication disconnected. Since the mathematic function for the artificial potential field is discontinuous, the dynamics of such two aerial agents might be also discontinuous. The main contributions of this paper are: 1) the dynamics of such two aerial agents switching on the discontinuous boundaries are firstly studied based on the complexity theory of flow switchability; 2) the “chatter” phenomenon due to the artificial potential field is explained as the onset of sliding motion on such a moving discontinuous boundary.