Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001
When a simple mobile robot has to navigate across a factory floor, it must solve the classic 'piano movers' problem. This representation is easily done with convex polygons, and it runs quickly. This problem is referred to as the piano movers problem, because it involves having to move a very large object (like a piano) through a cluttered environment, without picking it up. The perspective is that, the obstacles can be seen from directly above, but they are assumed infinite in height. This method may be adapted for a robotic manipulator, if it is working in a clear workspace, and is performing pick and place operations. The use of this method will save time, in all applicable cases.
As a result of the speed benefit of the 2D path finding solutions, they may be used as analytical tools. A special property can make the 2D methods applicable to 3D problems. If a 2D view of a 3D work space shows a path, then the same path will also exist in the 3D workspace. This has been used in some path planning methods, and can provide a 'trick' to avoid extensive 3D calculations. Another trick which may be used, is to represent the moving object with a box or a circle. This result in a simple technique for maintaining a minimum obstacle clearance, for collision avoidance.
Figure 2.2 Simplification of 3D Problem
