10.6 Continuous State Spaces

Virtually all of the concepts covered in this chapter extend to continuous state spaces. This enables them to at least theoretically be applied to configuration spaces. Thus, a motion planning problem that involves uncertainty or noncooperating robots can be modeled using the concepts of this chapter. Such problems also inherit the feedback concepts from Chapter 8. This section covers feedback motion planning problems that incorporate uncertainty due to nature. In particular contexts, it may be possible to extend some of the methods of Sections 8.4 and 8.5. Solution feedback plans must ensure that the goal is reached in spite of nature's efforts. Among the methods in Chapter 8, the easiest to generalize is value iteration with interpolation, which was covered in Section 8.5.2. Therefore, it is the main focus of the current section. For games in continuous state spaces, see Section 13.5.