Coverage Control with Information Decay in Dynamic Environments Nico H¨ ubel ∗ S. Hirche ∗∗ A. Gusrialdi ∗∗ T. Hatanaka ∗∗ M. Fujita ∗∗ O. Sawodny ∗ ∗ Institute for System Dynamics, Universit¨at Stuttgart ∗∗ Fujita Laboratory, Dept. of Mechanical and Control Engineering, Tokyo Institute of Technology Abstract: In this paper a method for coverage control for a convex region D⊂ R 2 in a dynamic environment is studied. An information map is introduced in which the information about each point is decaying with respect to time s.t. the robots must revisit them periodically. Also a time- varying density function is used for modeling moving points of interest. The considered gradient based control approach causes the cost function to stay within the desired bounds. But due to the non-stationary problem setup caused by the information decay it does not converge to a single point but to a bounded set, such that the robots keep gathering information continuously. With this method it is possible to gather information about several points of interest within the region D with only a few robots. In the end simulation results are presented to outline the effectiveness of the proposed control law. 1. INTRODUCTION Natural disasters with their need for quick humanitarian help as well as military and surveillance operations and tasks in hazardous environments are major application for robots. In these kind of applications we often have to deal with additional difficulties like an adversarial environment, constraints (e.g. time restrictions, limited communication capabilities, etc.) and changing mission objectives. But for the use of robots in these scenarios they also must be economically reasonable. This is the motivation for the approach of this paper to use only a few robots, which should gather information in a specified area. Recently a lot of research results came up for the area of coverage control. A very nice introductory overview can be found in Mart´ ınes [2007]. Most of the results rely on Voronoi tessellations. For example in Cort´ es [2004] a gra- dient descent to reach the optimal Voronoi configuration is proposed and in Mart´ ınes [2004] coverage control al- gorithms for robot groups with limited-range interactions are presented. Other results use some explicit information measures to express a gain of information. For instance Olfati-Saber [2007] proposes an algorithm which causes mobile agents with a dynamic network topology to im- prove their estimation of a moving target. In Mart´ ınez [2005] motion coordination algorithms which maximize the determinant of a Fisher Information Matrix are presented and in Basir [1995] a solution to an active sensing task is given which minimizes the variance of the estimation error and thus reduces the uncertainty of the target state. In addition there are also results like Ahmadzadeh [2007] which are based on receding horizon control or MPC. In this paper the problem of gathering information and monitoring an area with only a few robots is addressed. The aim was to derive results, which are applicable for infinite time and therefore not converge to a single point but to a bounded set. In order to achieve that, an idea similar to the effective coverage function in Hussein [2007] but with the novel concept of an information model with information decay is introduced. The paper is organized as follows. In section 2 the problem setup and the necessary definitions are presented and explained. Then the control law will be introduced and discussed in section 3. The results were validated by ex- tensive simulations. In section 4 a simulation for covering a square area with a moving point of interest is presented before a conclusion and the possible extensions of this work are stated in section 5. 2. PROBLEM SETUP In this paper Q = R 2 denotes the configuration space of the agents. Let D be the area which should be monitored by the agents. D must be a convex subset of Q. Throughout the paper R + = {a ∈ R | a ≥ 0} is used. 2.1 Agent model Let A = {A i | i ∈ S = {1, 2, 3,...,N }} be the set of agents consisting of the single agents A i with N being the number of agents and S being the index set of the fully connected network which means that it contains the indices of all agents. Let q i ∈ Q denote the position of agent A i . All agents A i satisfy the kinematic equation ˙ q i = u i , i ∈ S (1) with u i ∈ R 2 as the control input of agent A i . It is assumed that the underlaying dynamics of the agents are controlled by low level controllers which use u i as reference input. 2.2 Measurement function The measurement function M i (s i ): D× Q → R + with s i = ‖p − q i ‖ 2 (2) of the agent A i is defined as a C 1 -continuous map that describes the sensing performance of that agent. Sensing