Toward sensorless acquisition of multiple contact points between planar parts

A fixture is a device which immobilizes a part through a maximal set of linearly independent contacts. While many techniques exist to determine an appropriate arrangement of contacts, little research has been done on how to acquire those contacts (i.e., move the part such that it makes contact with the fixture at all intended points). In previous work, it was assumed that the gaps between the part and the fixture were infinitesimal. This allowed the use of a continuous-time model (formulated as a linear complementarity problem) to determine a set of contact wrenches, any one of which could be applied to the part to acquire all contacts simultaneously. This set was mapped to the boundary of the part to identify a pushing region on the part where one could push with a single finger to acquire the contacts. The work presented here provides two primary improvements. First, it is based on a discrete-time rigid body dynamics model that takes into account the finite motion of a part needed to close finite initial gaps between the part and the fixture. This model also allows one to determine a convex set of applicable wrenches. Second, a technique is developed whereby finite regions of the part’s boundary can be tested for membership in the pushing region, thus eliminating the need for point-wise testing.