Chapter 7

Extensions of Basic Motion Planning

This chapter presents many extensions and variations of the motion planning prob- lem considered in Chapters 3 to 6. Each one of these can be considered as a “spin-off” that is fairly straightforward to describe using the mathematical con- cepts and algorithms introduced so far. Unlike the previous chapters, there is not much continuity in Chapter 7. Each problem is treated independently; therefore, it is safe to jump to whatever sections in the chapter you find interesting without fear of missing important details.

In many places throughout the chapter, a state space X will arise. This is con- sistent with the general planning notation used throughout the book. In Chapter 4, the C-space, , was introduced, which can be considered as a special state space: It encodes the set of transformations that can be applied to a collection of bodies. Hence, Chapters 5 and 6 addressed planning in X = . The C-space alone is insufficient for many of the problems in this chapter; therefore, X will be used because it appears to be more general. For most cases in this chapter, however, X is derived from one or more C-spaces. Thus, C-space and state space terminology will be used in combination.

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