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The most difficult issue in applying either ASSF, EPB/PDO, or any two dimensional
qualitative representation to a real robot reasoning system is the
extension of the methods developed to three dimensions. The issues involved
are too complex to discuss in any depth, but some ideas of initial directions
to investigate include the following:
- Both generalised cones and boundary representation solid modelling
techniques are based on two dimensional descriptions at a certain
level. A boundary representation must include 2D faces as part of the
boundary, and the generalised cone technique requires a method for
describing two dimensional cross-sections.
- The majority of actions in a mechanical workspace involve simultaneous
motion in no more than two dimensions. People also appear to have
difficulty reasoning about motion in three independent dimensions, so
limiting a robot reasoning system to two dimensions for actual motion
planning may be an acceptable restriction if human-like performance is
the goal. These two dimensions might be in either a cartesian or polar
co-ordinate system, since simultaneous turning and linear motion in
the case of screw operation is not a difficult reasoning problem for
people.
- In two dimensions, there are only three types of possible contacts
between object boundaries: junction-junction, segment-segment, and
junction-segment. In three dimensions, there are six types of
possible contact: plane-plane, plane-edge, plane-vertex,
edge-edge, edge-vertex and vertex-vertex. This requires that planes
be explicitly represented, and also that methods of expressing
relative orientation and contact be more sophisticated. This would
require a completely different approach to defining proximity (which
must reflect potential contact).
- Wong and Fu describe a method for planning motion in three dimensions,
operating in the space of a two-dimensional orthogonal projection
[WF86].
Next: Implementations of Two Qualitative
Up: Extensions to the Two
Previous: Ordering of Angle Sizes
Alan Blackwell
2000-11-17