Parking cars and trailers

Figure 1.11: Some parking illustrations from government manuals for driver testing: (a) parking a car (from the 2005 Missouri Driver Guide); (b) parking a tractor trailer (published by the Pennsylvania Division of Motor Vehicles). Both humans and planning algorithms can solve these problems.

The planning problems discussed so far have not involved differential constraints, which are the main focus in Part IV. Consider the problem of parking slow-moving vehicles, as shown in Figure 1.11. Most people have a little difficulty with parallel parking a car and much greater difficulty parking a truck with a trailer. Imagine the difficulty of parallel parking an airport baggage train! See Chapter 13 for many related examples. What makes these problems so challenging? A car is constrained to move in the direction that the rear wheels are pointing. Maneuvering the car around obstacles therefore becomes challenging. If all four wheels could turn to any orientation, this problem would vanish. The term nonholonomic planning encompasses parking problems and many others. Figure 1.12a shows a humorous driving problem. Figure 1.12b shows an extremely complicated vehicle for which nonholonomic planning algorithms were developed and applied in industry.

Figure 1.12: (a) Having a little fun with differential constraints. An obstacle-avoiding path is shown for a car that must move forward and can only turn left. Could you have found such a solution on your own? This is an easy problem for several planning algorithms. (b) This gigantic truck was designed to transport portions of the Airbus A380 across France. Kineo CAM developed nonholonomic planning software that plans routes through villages that avoid obstacles and satisfy differential constraints imposed by 20 steering axles. Jean-Paul Laumond, a pioneer of nonholonomic planning, is also pictured.