  The main constraint on relative position of geometric objects, used in
spatial planning for computing the C-space maps (for example, in robotics, CAD,
and packaging), is the relative non-overlapping of objects. This is the
simplest constraint in which the minimum translational distance between objects
is greater than zero, or more generally, than some positive value. We present a
technique, based on the Minkowski operations, for generating the translational
C-space maps for spatial planning with more general and more complex
constraints on the relative position of geometric objects, such as constraints
on various types (not only on the minimum) of the translational distances
between objects. The developed technique can also be used, respectively, for
spatial planning with constraints on translational distances in a given
direction, and rotational distances between geometric objects, as well as for
spatial planning with given dynamic geometric situation of moving objects.
