Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001
One problem that tends to paralyse most methods is the expansion to multilink systems. The first implementation of most techniques is made with a simple mobile robot. When the method is increased by adding oddly sized links, and then a payload, the complexity grows at a more than exponential rate.
The number of degrees of freedom also play in the applications of the robot. If a manipulator has 6 degrees of freedom, then it can obtain any position or orientation in space. Some specific cases of problems require only 3 or 4 degrees of freedom. This can be a great time saver. When an environment becomes cluttered then it may be desirable to have a higher number of degrees of freedom than six, so that the redundancy of the robot can move through the environment. The complexity of most routines increases exponentially with the number of degrees of freedom, thus it is best to match the manipulator degrees of freedom to the complexity of the task to be done.
One assumption that helps reduce the problem complexity is the approximation of motion in a single plane. The net result of this effort is that the robot is reduced to 2 or 3 degrees of freedom. The payload may also be neglected, or fixed, and thus the degrees of freedom are reduced. A second approach is to approximate the volume of the links swept out over a small volume in space. This volume is then checked against obstacles for collisions. A payload on a manipulator may sometimes be approximated as part of the robot if, it is small, or it is symmetrical. This means that the number of degrees of freedom for a manipulator may be reduced, and thus the problem simplified in some cases.
Figure 2.4 Multi-Link Approaches
Multilink manipulators also come in a variety of configurations. These configurations lend themselves to different simplifications, which may sometime provide good fast solutions in path planning.
- Cartesian (i.e. X, Y, Z motions)
- Spherical (Stanford Manipulator)
The various robot configurations are fundamentally different. Many approaches have tried to create general solutions for all configurations, or alternate solutions for different specific manipulators. The fastest solutions are the ones which have been made manipulator specific. With a manipulator it is also possible to describe motions in both Joint Space (Manipulator Space), and Cartesian Space (Task Space). There are approaches which use one, or both of these.