A framework for geometric reasoning about tools in assembly

When assembling a product, humans, robots, and other automation employ a variety of tools to manipulate, attach, and test parts and subassemblies. This paper proposes a framework to represent and reason about geometric accessibility constraints for a wide variety of assembly tools. Central to the framework is a volume encoding a minimum space that must be free in an assembly state to apply a given tool, and constraints on the placement of that volume relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is an instance of the FINDPLACE problem. In addition, we present more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method preprocesses a single tool application for all possible states of assembly. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. We describe experiments with an initial implementation of the framework and a library of eight tools