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2.1  The ASP Heuristic

In the Asp heuristic, for each action a and for each fact p Î Add(a), a rule C®p is formed, where C=Pre(a). Assuming a set of rules, it is said that a fact p is reachable from a state S if p Î S or there is a rule C ® p such that each fact q Î C is reachable from S.

So, a function g(p,S) is defined, which inductively assigns a number i to each fact p, where i is an estimate of the number of steps needed to achieve p from S, i.e. the distance of p from S. More specifically, g(p,S) is set to 0 for every fact p Î S, while g(p,S) is set to i+1, i ³ 0, for each fact p for which a rule C ® p exists, such that . Thus:

0,             if p Î S

(4)

i+1,          if for some C®p,

¥,            if p is not reachable from S

In the case where there are more than one rules C®p for a fact p, the rule with the minimum cost is chosen. Note that a fact p that was initially achieved by a rule C1®p, may be re-achieved, later, by another rule C2®p with smaller cost. That is because not all the preconditions of the second rule had been achieved at the time when the first rule was applied. The task of applying rules continues until no rule that can achieve a fact with smaller cost exists. The distances computed in this way are unique.

For a set of facts P, their distance from S is defined as:

(5)

The Asp planner uses g(P,S) to estimate the distances between each intermediate state S and the Goals. So, the Asp heuristic function is defined as:

(6)

The Asp heuristic does not take into account the delete lists of the actions. The simplified problem that is created by ignoring the delete lists is referred to as the relaxed problem and the corresponding actions are referred to as the relaxed actions. The complexity for constructing HASP(S) is linear, with respect to the number of ground actions and the number of ground facts.

 

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Next: Backward Heuristic Construction Up: The GRT Planning System Previous: The GRT Heuristic

Ioannis Refanidis

14-8-2001