Sedas and Talukdar have developed an algorithm for planning disassembly of objects in two dimensions which makes use of multiple representations of the object to be disassembled [ST87]. The three representations used include a sectional view of the assembly, stored as the co-ordinates of all vertices in the section, a connection graph describing points of attachment between parts in the assembly, and a ``skeleton'' diagram which represents each part as a connected group of convex polygons, with connections between the centroids of the polygons.
Ballard describes a method for representing robot actions using ``task frames'' [Bal84]. A task frame is a special co-ordinate system based on the object being manipulated by the robot. The task frame moves with the object, and can thus be used to simply describe tasks which occur in a context that might otherwise add to the complexity of describing robot motion. One such situation would be the assembly of a workpiece while it is moving past on a conveyor. The advantages of the task frame approach are its simplicity of implementation, and the straightforward transformation that can be performed between the task frame and world co-ordinates.
Although the majority of high-level shape representation techniques are designed to be used with visual sensory information, representations can also be built from other sensory input. For example, Briot et. al. outline an object representation which describes an object in terms of the joint positions of a four fingered multiply-jointed manipulator grasping it [BRS78]. This allows objects to be recognised from grasp alone, without any visual or other sensory data. The joint-space object representation is not intended as a general purpose shape description method, but is simply used for object recognition.
These last examples are only a few from a great range of representation techniques, but they indicate some of the variation that is possible in describing shape and space for robot reasoning. The previous sections have surveyed the most influential techniques in spatial representation for robots, but it has been necessary to omit a number of interesting systems.