The puzzles in Figure 1.1 can be easily discretized because of the regularity and symmetries involved in moving the parts. Figure 1.2 shows a problem that lacks these properties and requires planning in a continuous space. Such problems are solved by using the motion planning techniques of Part II. This puzzle was designed to frustrate both humans and motion planning algorithms. It can be solved in a few minutes on a standard personal computer (PC) using the techniques in Section 5.5. Many other puzzles have been developed as benchmarks for evaluating planning algorithms.
Steven M LaValle 2012-04-20