This paper explores the motion planning problem for multiple mov- ing objects. The approach taken consists of assigning priorities to the objects, then planning motions one object at a time. For each moving object, the planner constructs a configuration space-time that represents the time-varying constraints im- posed on the moving object by the other moving and stationary objects. The planner represents this space-time approximately, using two-dimensional slices. The space-time is then searched for a collision-free path. The paper demonstrates this approach in two domains. One domain consists of translating planar objects; the other domain consists of two-link planar articulated arms.

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.