ABTWEAK: Abstracting a Nonlinear, Least Commitment Planner

We present the system ABTWEAK, which extends the precondition-elimination abstraction of ABSTRIPS to hierarchical planners using the nonlinear plan representation as defined in TWEAK. We show that ABTWEAK satisfies the monotonic property, whereby the existence of a lowest level solution II implies the existence of a highest level solution that is structurally similar to II. This property enables one to prune a considerable amount of the search space without loss of completeness. Abstracting Planning Systemsing Planning Systems Abstraction in planning systems can be viewed as a mapping from one problem description (at a concrete level) to another(at the abstract level). There has been a considerable amount of research recently in formalizing intuitions regarding abstraction and the hierarchical problem solving strategies that abstraction gives rise to [Fikes et al., 1972; Knoblock, 1988; Korf, 1985b; Nau, 1987; Sacerdoti, 1974; Tate, 1977; Tenenberg, 1988; Wilkins, 1984; Yang, 19891. However, there has been little work in extending the formal results from linear STRIPS-like planners to richer temporal planners, such as the nonlinear planners of Sacerdoti [1977] and Chapman [1985]. The advantage of these planners over linear planners is that they allow temporal order and operator instantiations to be only partially specified through the posting of constraints; any fully specified plan consistent withion in planning systems can be viewed as a mapping from one problem description (at a concrete level) to another(at the abstract level). There has been a considerable amount of research recently in formalizing intuitions regarding abstraction and the hierarchical problem solving strategies that abstraction gives rise to [Fikes et al., 1972; Knoblock, 1988; Korf, 1985b; Nau, 1987; Sacerdoti, 1974; Tate, 1977; Tenenberg, 1988; Wilkins, 1984; Yang, 19891. However, there has been little work in extending the formal results from linear STRIPS-like planners to richer temporal planners, such as the nonlinear planners of Sacerdoti [1977] and Chapman [1985]. The advantage of these planners over linear planners is that they allow temporal order and operator instantiations to be only partially specified through the posting of constraints; any fully specified plan consistent with *This work was supported in part by an interim research grant to Qian g Yang, from the Faculty of Mathematics at the University of Waterloo, and by grants to Josh D. Tenenberg in part from the Air Force Systems Command, Rome Air Development Center, Griffiss Air Force Base, New York 13441-5700, and the Air Force Office of Scientific Research, Boiling AFB, DC 20332, under Contract Num. F30602-85-C-0008 which supports the Northeast Artificial Intelligence Consortium (NAIC), in part by ONR/DARPA research contract #N00014-80-C-0197, and in part by US Army Communication-Electronics Command grant #DAABlO-87-D-022. 204 AUTOMATED REASONING Josh D. Tenenberg Computer Science Department University of Rochester Rochester, New York, U.S.A., 14627 [email protected] these constraints is guaranteed to solve the given problem. One particular type of abstraction that we have previously formalized [Tenenberg, 19881, involves the elimination of a subset of the predicates in the language as one ascends the abstraction hierarchy (a generalization of the precondition elimination strategy of ABSTRIPS [Sacerdoti, 19741). The predicates of the planning system are partitioned, which induces a partition on the preconditions of the operators, and each partition is assigned an integer value, a criticality. Each abstract level i is derived from the previous level by eliminating those preconditions having criticality < i, otherwise being identical. We define the system ABTWEAK, and demonstrate in this paper that precondition-elimination abstraction can be naturally extended to nonlinear least commitment planners, and thus benefit from the advantages of both abstraction and nonlinearity. Most importantly, we show that each ABTWEAK system has a monotonically expandable abstraction space, whereby the existence of a lowest level solution II implies the existence of a highest level solution that is structurally similar to II. This property enables one to prune a considerable amount of the search space without loss of completeness. In addition, the abstraction space is monotonic regardless of the criticality assignment, i.e., it does not depend upon obtaining the “right” assignment of criticality values to preconditions. We first present brief descriptions of TWEAK and ABSTRIPS, and then define ABTWEAK. We demonstrate that ABTWEAK has the monotonic property, and show how this affects search. All lemmas and theorems are presented without proofs. These proofs can be found in the longer version of this paper [Yang and Tenenberg, 19901. Nonlinear Planning: TWEAK Chapman [1985] p rovides a formalization of a least commitment, nonlinear planner, TWEAK. TWEAK extends STRIPS by allowing for