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2.      The GRT Heuristic

 

In Strips (Fikes & Nilsson, 1971), each action a is represented by three sets of facts: the precondition list Pre(a), the add-list Add(a) and the delete-list Del(a), where Del(a) Í Pre(a). A state S is defined as a finite set of facts. An action a is applicable to a state S if:

Pre(a) Í S                                                                                           (1)

The state resulting from the application of an action a to state S is defined as:

S' = res(S,a) = S \ Del(a) È Add(a)                                                                  (2)

Inductively we can define the state resulting from the application of a sequence of actions (a1, a2, ..., aN) to a state S as:

S' = res(S, (a1, a2, ..., aN)) = res( res(S, (a1, a2, ..., aN-1)), aN)                                          (3)

with the requirement that each action ai is applicable to the state res(S, (a1, a2, ..., ai-1)), for each i=1, 2, ..., N. In the formalization used henceforth, the set of problem constants is assumed to be finite and no function symbols are used, so the set of actions is finite.

A planning problem P is a triplet P=(O, Initial, Goals), where O is the set of ground actions, Initial is the initial state and Goals is a set of facts. The task is to find a sequence of actions a1, a2, ..., aN that can be applied to the initial state, so that the state resulting from their application will be a superset of Goals. The sequences of actions are called Plans. A plan that can be applied to the initial state is called a valid plan. A valid plan that achieves the Goals is called a solution of the planning problem. A planning problem may have several or no solutions. In the latter case the problem is described as unsolvable.

The next sub-section gives a brief presentation of the Asp heuristic, which was our motivation and helps to understand the following concepts, whereas the subsequent sub-sections present the Grt heuristic in detail.

 

nextupprevious
Next: The ASP Heuristic Up: The GRT Planning System Previous: Introduction

Ioannis Refanidis

14-8-2001