Controlling a Nonlinear Hierarchical Planner Using Case Replay

step concrete step relevant feature abstract planning level concrete planning level machined(rising-1) has-feature( rising-2, thread) machined(horizontal) machined(feature-1) causal link ordering relation irrelevant feature Fig. 7. Interactions from a nonlinear hierarchical plan problem. CAPlan/CbC combines both approaches by performing its retrieval phase in two steps: 1. A domain-dependent pre-selection using physical constraints and domain knowledge to obtain a small subset of cases, discarting most of the cases in the case base. 2. A domain-independent selection step using a footprint-like similarity measure (Veloso & Carbonell, 1991) which computes structural information about previous generated plans and known problem descriptions (cf. section 4.1). Given a CAD representation of a new workpiece (Fig. 1) the atomic and the complex processing areas (Fig. 2) are determined. In the next step the hierarchical representation of the planning problem (Fig. 3) and the set of initial goals and their ordering relations (Fig. 4) are computed. The initial goals and ordering relations represent a set of domain dependent technical constraints which must be satis ed by any case, e.g. the groove represented by feature-2 in Fig. 2 can only be processed after the processing areas of cylinder-1 and of the complex processing area rising-1 have been processed. In the current implementation, case retrieval in CAPlan/CbC is made by comparing the hierarchical description (Fig. 3) of a new problem with the problem description of stored cases (cf. D ej a Vu (Smyth & Cunningham, 1992)). Using the tree-based problem representation the case match is made by a tree matching algorithm (Tanaka & Tanaka, 1988). The similarity measure is computed as the weighted sum of all adding and deleting operations necessary for transforming the hierarchical problem description of the case into the description of the current problem. Every transformation step is associated with domainspeci c costs which are comparable to the e ort that is necessary for the modication of the corresponding solutions (Humm et al., 1991). 1 2 4 5 6 4 3 1 a b 3 5 2 2 6 4 1 1 2 3 5 Fig. 8. Mapping representations using a structural matching algorithm (a) and generating a reusable solution by deleting the respective nodes (b) The distance between the case and the problem description is measured as follows: First, a structure preserving match (Tanaka & Tanaka, 1988) between the hierarchical structures of the workpieces is computed (Fig. 8a). Second, the di erence between the two representations is calculated, i.e. the nodes that were not matched and the nodes that were matched, but are of di erent type (for example a geometrical primitive of type torroid is matched with one of type cylinder) are counted (Fig. 8b). During this calculation di erent domain speci c weights according to the type of the nodes are processed, since it is easier to replace an atomic processing area than a complex processing area e.g. counting a node which represents a primitive area has a smaller value than counting one which represents a complex processing area. A case quali es for solving a new problem if the computed transformation costs are smaller than a given threshold. To determine the relevance of features (Janetzko, Wess, & Melis, 1993) we compare the problem description with the annotated problem description (cf. section 4.1) of the case to determine in detail how many relevant features they have in common. This step corresponds to footprinting in Prodigy/Analogy (Veloso & Carbonell, 1991). Concretely, the groups of features in the annotated problem description of the case that are completely included in the description of the current problem are determined. The relevance of these features is de ned as the number of features that are entirely included in the problem description. 4.3 Case Replay Although CAPlan can autonomously solve problems by depthrst search, it is mainly intended as a planning assistant that provides a control interface for a human planner or external control components, such as CAPlan/CbC. The input for the case-based control component consists of the problem description of a new planning problem, the case selected (cf. section 4.2) and an associationbetween goals of the new planning problem and initial goals of the plan cannedby the case. The associations are computed by tree matching of the retrievalphase. For solving a new problem, the decisions and their rationals of a caseare used to choose from the set of alternative planning steps to satisfy a goal orto choose from the set of alternative constraints that can be added to resolve athreat of a causal link. This replaying of a decision of the case is done in foursteps. First, the planner computes the set of alternative plan steps or con ictsolving constraints that can be applied to the goal or to the con ict currentlybeing worked on. In the second step a match of the alternative chosen by thedecision of the case with the possible alternatives of the new problem is made. Ifthere is a successful match, the decision's rationals are veri ed in the context ofthe new problem. Third, if the rationals are satis ed the step is chosen and thedecision for choosing this alternative is provided with the veri ed rationals of thecase. And fourth, the new subgoals resulting from the step chosen are matchedagainst the subgoals resulting from the replayed decision. By every successfulmatch a new association between a goal of the new planning problem and a goalof the case is generated. As soon as CAPlan/CbC continues replaying for oneof the prematched subgoals the associations to the case are already available,enabling the system to repeat the four steps described above.Planning for goals that cannot be matched to a goal of the case are delayeduntil the replay process is completed. The remaining goals are solved by rst-principle planning or possibly by user interactions. Because replaying a caseand planning by rst-principles results in the same representation of a plan,all planning decisions made during case replay can be rejected if they don'tallow a completion of a partial plan. The separation of the replay phase fromsolving unmatched goals is possible because of the partially ordered plan repre-sentation and the nonlinear planning paradigm. The rst point is in contrast toProdigy/Analogy where a total-order planner is used which makes necessaryinterleaving of case replay and rst-principle planning for unmatched goals.5 ConclusionsWe have described the hybrid planning architectureCAPlan and its applicationin a process planning domain. A main characteristic of this domain is that plan-ning is driven by minimizing plan execution costs. Human planning experts inthis domain use a large number of heuristics and domain speci c reasoning. Sincethis knowledge is extremely case sensitive its usage is not su ciently supportedby known planning techniques.In our approach a general purpose planning system, CAPlan, is combinedwith a case-driven control unit CAPlan/CbC which allows to use previous ex-perience in form of recorded cases to guide the problem solving process. If thereexists a case which is useful to solve the current problem, its decisions are re-played (Veloso, 1992) in the current context, i.e., a planning decision of the caseis only reused if its rationals are compatible with the problem description of the new problem. Thus, our approach is very similar to the work of Veloso (Veloso,1992), but there are some important di erences. First, planning in CAPlan isbased on the ideas of partial-order planning (SNLP (McAllester & Rosenblitt,1991)), so the underlying planning architecture is di erent. Second, retrieval ofuseful cases in CAPlan is realized as a combination of domain-independent anddomain-dependent techniques which constrain the number of cases that have tobe inspected during the retrieval phase. The annotated problem description isan extension of the concepts of footprinting (Veloso & Carbonell, 1991) and ofinteracting goals in Prodigy. This extension is necessary due to the hierarchi-cal representation of plans in CAPlan. Third, the overall architecture of thesystem combines specialized domain dependent reasoners and a feature-basedCAD system with general purpose planning (Kambhampati et al., 1991).Contrary to other well-known case-based planning systems such as Chef(Hammond, 1986), CAPlan uses (like Prodigy) an explicit domain modelto describe the plan steps and the constraints that must be satis ed duringthe retrieval and adaptation phase. The use of domain speci c knowledge andtechniques for the retrieval of useful cases by calculating ameasure of adaptabilityin CAPlan is similar to the adaptation guided retrieval approach in D eja Vu(Smyth & Keane, 1993).AcknowledgementsThe authors want to thank Michael M. Richter, Charles Petrie, Manuela Velosoand Frank Weberskirch for their contributions as well as Ralph Bergmann andthe reviewers for helpful comments on earlier versions of this paper.ReferencesBarrett, A., & Weld, D. S. (1993). Partial-order planning. 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