Using Blocks for Constraint Satisfaction

Abstract

The assembly problem is the spatial joining of separate rigid bodies within a CAD/CAM-system. The solution to the assembly does not only need to contain one consistent instantiation, but also qualitative information. In particular, this covers the localization of redundancy and remaining degrees of freedom in the mechanism. Although it is natural to model the assembly as a constraint satisfaction problem (CSP), solving remains a difficult task

In general, a CSP can be attacked by two strategies: consistency enforcement and search. Algorithms work best if they combine these strategies in a clever way. When modeling the assembly problem as a CSP, one is confronted with two special conditions. First, the variable domains are continuous. Second, constraints are not arbitrary, but are conjunctions of instantiated predefined constraint types. Thus, search is not possible because of the continuous domains and numeric iterative or interval approaches deliver no information on degrees of freedom and redundancy. Therefore, pure consistency enforcement, which has many drawbacks in general CSPs, is the best choice

In this poster, we discuss how consistency can be enforced in assembly problems while preserving redundancy information. For this purpose, we introduce k-block-consistency (k-BC), which only requires support for tuples of the same biconnected component (block).