An important issue that arises in the automation of many security, surveillance, and reconnaissance tasks is that of monitoring, or 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 of this type, 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 multi-robot observation of multiple moving targets. We focus primarily on developing the distributed control strategies that allow the robot team to attempt to maximize the collective time during which each object is being observed by at least one robot in the area of interest. Our initial efforts in this problem address the aspects of distributed control in homogeneous robot teams with equivalent sensing and movement capabilities working in an uncluttered, bounded area. This paper first formalizes the problem, discusses related work, and then shows that this problem is NP-hard. We then present a distributed approximate approach to solving this problem that combines low-level multi-robot control with higher-level control. The low-level control is described in terms of force fields emanating from the targets and the robots. The higher level control is presented in the ALLIANCE formalism, which provides mechanisms for fault tolerant cooperative control, and allows robot team members to adjust their low-level actions based upon the actions of their teammates. We then present the results of the implementation of portions of our approach, both in simulation and on physical robots.