Interference-free polyhedral configurations for stacking

This paper uses a configuration space (c-space) based method to compute interference-free configuration for stacking polyhedral sheet metal parts. This work forms the interference analysis module of a stacking planner developed by us. Parts in a stack should not interfere with each other and should also satisfy stability, grasping, and stacking plan feasibility related constraints. We present two techniques to speed up the expensive step of c-space obstacle computation. The first technique identifies orientation intervals (for a convex pair of solids) within which the topology of face-edge-vertex graph of an obstacle stays the same. Within this interval, c-space obstacle geometry for one orientation can be extrapolated from obstacle geometry for another orientation. Our experiments show that extrapolation takes an order of magnitude less than the time taken to compute an obstacle from scratch. The second technique computes near optimal interference-free positions for a discrete orientation without having to compute the complete c-space obstacle. Our experiments show that, for complex sheet metal parts, less than 0.1% of the convex component pairs are evaluated in order to compute an interference-free configuration. We describe a configuration space-based method to compute a list of interference-free configurations that can be tested to see if they satisfy the above mentioned constraints. The cost function is a weighted sum of components that penalize floor space utilization and height of center of gravity of parts. The algorithm is able to pick nested stacks that tend to be stable and compact without having to explicitly enumerate features that can be nested. It is also able to accommodate flanges in holes to reduce the value of the user specified cost function. We use three test parts to illustrate the effect of the two techniques to speed up c-space obstacle computation. We also show the stacking plans generated for three different values of the weighting parameter in the cost function used by the stacking planner