The performance of systems for human activity recognition depends heavily on the placement of cameras observing the scene. This work addresses the question of the optimal placement of cameras to maximize the performance of these types of recognition tasks. Specifically, our goal is to optimize the quality of the joint observability of the tasks being performed by the subjects in an area. We develop a general analytical formulation of the observation problem, in terms of the statistics of the motion in the scene and the total resolution of the observed actions, that is applicable to many observation tasks and multi-camera systems. A nonlinear optimization approach is used to find the internal and external (mounting position and orientation) camera parameters that optimize the recognition criteria. In these experiments, a single camera is repositioned using a mobile robot. Initial results for the problem of human activity recognition are presented.