One important variant of multiple-robot motion planning is called assembly planning; recall from Section 1.2 its importance in applications. In automated manufacturing, many complicated objects are assembled step-by-step from individual parts. It is convenient for robots to manipulate the parts one-by-one to insert them into the proper locations (see Section 7.3.2). Imagine a collection of parts, each of which is interpreted as a robot, as shown in Figure 7.7a. The goal is to assemble the parts into one coherent object, such as that shown in Figure 7.7b. The problem is generally approached by starting with the goal configuration, which is tightly constrained, and working outward. The problem formulation may allow that the parts touch, but their interiors cannot overlap. In general, the assembly planning problem with arbitrarily many parts is NP-hard. Polynomial-time algorithms have been developed in several special cases. For the case in which parts can be removed by a sequence of straight-line paths, a polynomial-time algorithm is given in [973,974].
Steven M LaValle 2012-04-20