Time-Minimal Motion: Applications
We have shown some basic properties of accessibility in Chap. 3. In this chapter, we describe a number of extensions and applications that make use of the concept of accessibility. Some results can be derived using the Time-Minimal Motion theorem proved in Chap. 3 by making some modifications to, or observations about, Propositions 1 and 3. For example, we show that some speedup is possible for the case in which all the obstacles are convex. Also, we further extend the use of accessibility to deal with more complex classes of dynamic environments. They involve time-minimal motion when the destination point can move faster than the robot, motion planning in the presence of obstacles that have piecewise linear motions, motion planning in the environment that contains rotating obstacles, motion planning among obstacles that split and merge, etc.
KeywordsAccessible Point Motion Planning Destination Point Split Point Split Time
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