Decision dynamics in cooperative search based on evolutionary game theory

Abstract

This paper investigates a search problem for a robotic group to find a target which appears randomly and stays for a fixed time interval. We assume that there are two search areas and the target appears in either of them. Under the situation, it is required to make a decision on which room to search while determining a control input. For the problem, we present an evolutionary game theoretic method to decide the action of each robot and show that the method eventually achieves two types of orders: macro and micro orders. The macro order means that the population share of robots converges to an ordered value, and the micro one means that the robots' motions converge to periodic trajectories. The macro order is achieved by a probabilistic decision-making model called Win-Stay-Lose-Shift. Then, convergence of the expectation value of population share is proved for two typical payoff structures by employing knowledge of evolutionary game theory. Once the area to search is decided by the decision-making model, each robot determines a control input aiming at reduction of control energy. Finally, simulation results show the validity of the proposed method. 1. Introduction. Recently, Professor John Baillieul actively study decision dy- namics in mixed human/robot teams as a key member of the project Center for Human and Robot Decision Dynamics. Motivated by his talk in Japan (1), we started to study decision dynamics in cooperative control. In this paper, we investigate deci- sion dynamics in cooperative search problems, which is also motivated by one of his research works (2), and this paper presents a new search strategy including decision dynamics based on evolutionary game theory. As another works on decision dynam- ics, a joint human-robot decision-making task is recently studied in (3) and (4), where they design a model for sequential binary decision-making to decide whether to keep the current choice (exploit) or switch (explore), and discuss its asymptotic property. In addition, (5) presents a decision-making algorithm for a group of robots to share the information on task completion by using a consensus-like algorithm. Search theory addresses a problem of how to deploy an agent in order to find a target within limited resources. This theory is motivated by several practical ap- plications such as detection of lost objects, rescue operations and medical services. Early works on search theory was given by Koopman (6) and Stone (7) and a large amount of research works have been devoted to the problem in some research fields such as operations research, artificial intelligence and so on, which are summarized in the survey paper (8). This theory is also extended to the cooperative search in the multi-agent case (9, 10, 11, 12).