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An important issue that arises in the automation of many security, surveillance, and reconnaissance tasks is that of observing the movements of targets navigating in a bounded area of interest. A key research issue in these problems is that of sensor placement—determining where sensors should be located to maintain the targets in view. In complex applications involving limited-range sensors, the use of multiple sensors dynamically moving over time is required. In this paper, we investigate the use of a cooperative team of autonomous sensor-based robots for the observation of multiple moving targets. In other research, analytical techniques have been developed for solving this problem in complex geometrical environments. However, these previous approaches are very computationally expensive—at least exponential in the number of robots—and cannot be implemented on robots operating in real-time. Thus, this paper reports on our studies of a simpler problem involving uncluttered environments—those with either no obstacles or with randomly distributed simple convex obstacles. We focus primarily on developing the on-line distributed control strategies that allow the robot team to attempt to minimize the total time in which targets escape observation by some robot team member in the area of interest. This paper first formalizes the problem (which we term CMOMMT for Cooperative Multi-Robot Observation of Multiple Moving Targets) and discusses related work. We then present a distributed heuristic approach (which we call A-CMOMMT) for solving the CMOMMT problem that uses weighted local force vector control. We analyze the effectiveness of the resulting weighted force vector approach by comparing it to three other approaches. We present the results of our experiments in both simulation and on physical robots that demonstrate the superiority of the A-CMOMMT approach for situations in which the ratio of targets to robots is greater than 1/2. Finally, we conclude by proposing that the CMOMMT problem makes an excellent domain for studying multi-robot learning in inherently cooperative tasks. This approach is the first of its kind for solving the on-line cooperative observation problem and implementing it on a physical robot team.