A Formal Planning Model for Case-Based Process Planning

Michael M. Marefat and John M. Britanik

Department of Electrical and Computer Engineering
University of Arizona
Tucson, Arizona 85721

Email: { marefat,britanik} @ece.arizona.edu

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Abstract

Case-based reasoning provides an attractive paradigm for process planning as it combines the generative and variant approaches and improves the effectiveness of the planner by applying old experiences to solving new planning problems. Our research focuses on the development of a new case-based planning methodology that extends the capability and effectiveness of previous approaches. The planner, called CBPOP, is based on domain-independent partial-order planning, and provides a formal approach to case-based process planning. In addition, the planner has the capability to use pieces of multiple old plans in the process of constructing a new plan, providing more effective utilization of the planner's previous experiences. CBPOP generates plans for the features of a part (eg: slots, pockets, holes, etc.) independently. These feature plans are then merged using a hierarchical plan merging mechanism we have developed. The objective of this plan merging is to generate a global process plan for the part while minimizing the number of fixture and tool changes.

Introduction and Objectives

Process planners operate on higher-level entities known as features. An interpretation is a collection of features which describes a part. Since a given part may have many interpretations, the process planner may plan for each interpretation and choose the best based on optimality criteria.

One of the objectives of this research has been to develop a case-based planner that is based on formal techniques and flexible in its reuse of old plans. This objective was achieved in our development of CBPOP, a case-based partial-order planner that reuses pieces of multiple old plans to construct a new plan. Another objective was to optimize the final global plan by combining the feature subplans generated by the case-based planner such that the number of fixture and tool changes was minimized. This objective was achieved through the development of a systematic hierarchical plan merging mechanism.

Approach

To generate a process plan for a part, CBPOP generates plans for the features of the part (eg: slots, pockets, holes, etc.) independently. These feature plans are then merged into a global plan for the part using a hierarchical plan merging mechanism which minimizes the number of fixture and tool changes in the global plan.

To develop a formal planning model for case-based process planning, we have combined case-based planning with partial-order planning. Case-based planning provides the utility of plan reuse while partial-order planning provides a formal framework in which plans can be proven correct with respect to the planner's domain knowledge. CBPOP develops a solution by searching the space of plans [1]. A plan is represented as a four tuple, <A,O,L,B>, for Actions (STRIPS-like), Orderings, causal Links, and variable Bindings respectively. Figure 1a shows one snapshot in planspace in which plan P2 is refined to generate plan P5 by the addition of an ordering between actions. Search continues via plan refinement (adding actions and resolving constraints) until a complete solution is found. An example process plan generated by CBPOP for machining a thru-slot is shown in figure 1b.

CBPOP represents both primitive actions and old plans identically as cases. This allows CBPOP to refine plans by seamlessly interleaving primitive actions and old plans; hence, multiple old plans can be used in generating a solution to a single planning problem. Also, this approach obviates the difficult decision of whether to solve from scratch or retrieve and old plan first.

The output of CBPOP is a set of feature subplans and a set of orderings and constraints between the subplans. We utilize a hierarchical approach to merge each of the feature subplans into a more efficient global plan for the part [2]. The advantage of this approach is that it decomposes the plan merging problem by exploiting the natural decomposition property of the process planning domain. Costly fixturing actions are merged first, exploiting alternative fixturings to minimize the total number of fixture changes. Then tooling actions are merged to minimize the number of tool changes within a fixturing. While the hierarchical plan merging mechanism we have developed is a general methodology, it also facilitates the use of deep domain knowledge during the merging process.

Figure1: (a) Planning is viewed as the search through the space of plans. (b) A plan generated by CBPOP. Each box represents an action. Terms on the top of a box represent that action's preconditions, while terms on the bottom of a box represent that action's postconditions or effects. Arcs between actions represent causal links which protect the validity of effects until they are consumed by preconditions or goals.

Click here for a larger version of figure 1.

References

[1] J. Britanik and M. Marefat. Case-based manufacturing process planning with integrated support for knowledge sharing. In International Symposium on Assembly and Task Planning, pages 107--112, Pittsburgh, PA, August 1995.
Compressed postscript paper: isatp95-cbpop.ps.gz Abstract in HTML: isatp95-cbpop-abs.html.

[2] J. Britanik and M. Marefat. Hierarchical plan merging with application to process planning. In International Joint Conference on Artificial Intelligence, pages 1677--1683, Montreal, Canada, August 1995.
Compressed postscript paper: ijcai95.ps.gz Abstract in HTML: ijcai95-abs.html.

Compressed postscript version of this paper