  The development of a generic and effective force model for semi-automatic or
manual virtual assembly with haptic support is not a trivial task, especially
when the assembly constraints involve complex features of arbitrary shape. The
primary challenge lies in a proper formulation of the guidance forces and
torques that effectively assist the user in the exploration of the virtual
environment (VE), from repulsing collisions to attracting proper contact. The
secondary difficulty is that of efficient implementation that maintains the
standard 1 kHz haptic refresh rate. We propose a purely geometric model for an
artificial energy field that favors spatial relations leading to proper
assembly, differentiated to obtain forces and torques for general motions. The
energy function is expressed in terms of a cross-correlation of shape-dependent
affinity fields, precomputed offline separately for each object. We test the
effectiveness of the method using familiar peg-in-hole examples. We show that
the proposed technique unifies the two phases of free motion and precise
insertion into a single interaction mode and provides a generic model to
replace the ad hoc mating constraints or virtual fixtures, with no restrictive
assumption on the types of the involved assembly features.
