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# Quickly Approximating the Distance Between Two Objects

- Tuesday, 01 December 2009

A method of quickly approximating
the distance between two objects (one
smaller, regarded as a point; the other
larger and complexly shaped) has been
devised for use in computationally simulating
motions of the objects for the purpose
of planning the motions to prevent
collisions. The method is needed
because computer-based-graphics techniques
that have been used heretofore to
make such estimates entail amounts of
computation that are excessively large
for purposes of the simulations. The method, denoted tree-based
model learning, is an integral combination
of (1) decision-tree techniques upon
which several machine learning techniques
have been based and (2) a relatively
accurate function-approximation
technique. Each node of a decision tree
corresponds to a partition of the problem
domain — in this case, starting with one
node representing a large cubic volume
centered on the large object and dividing
and subdividing it, at symmetry planes,
into successively smaller cubes. Each
branch of the tree represents a rule-based
decision selecting one of the child nodes
of a parent node. The smallest subdivisions
(leaf nodes) contain coefficients of
a quadric equation that estimates the distance
between the objects.

*This work was done by David Hammen of
LinCom Corp. for Johnson Space Center. For
further information, contact the JSC
Innovation Partnerships Office at (281) 483-
3809. MSC-23264-1*

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