On the problem of multiple mobile robots cluttering a workspace

We consider the problem of multiple mobile robots navigating in a common workspace. Initially, based on the premise that the costs of operation of the robots can be ignored, results regarding the probability of collision of two point robots in the workspace are derived. Obviously, these results depend on the geometry of the workspace, and hence they are derived for workspaces with various geometries. The results are then extended for two robots of finite dimensions. The question "Are k + 1 robots better than k?" is then considered. Based on two modes of operation, namely, the batch-scheduled mode and the list-scheduled mode, various theoretical results are derived. If the costs of operation of the robots can be ignored, based on various computational results obtained, we conjecture that the answer to the question is in the affirmative in both modes of operation. Finally, by using the model of computation which includes the costs of operation of the robots, the problem is revisited. We have shown that for various geometries and revenue to cost ratios, there are optimal finite values for the number of robots that can operate within the workspace. Expressions for these optimal values have been derived