On the surface it may appear that there is nothing unusual about the multiple-robot problem because the formulations used in Chapter 4 already cover the case in which the robot consists of multiple bodies. They do not have to be attached; therefore, can be considered as an ordinary C-space. The planning algorithms of Chapters 5 and 6 may be applied without adaptation. The main concern, however, is that the dimension of grows linearly with respect to the number of robots. For example, if there are rigid bodies for which each has , then the dimension of is . Complete algorithms require time that is at least exponential in dimension, which makes them unlikely candidates for such problems. Sampling-based algorithms are more likely to scale well in practice when there many robots, but the dimension of might still be too high.

Steven M LaValle 2012-04-20