A Method for Solving Conjunctive Goal Problem in Planning : Deducing order relations by using temporal reasoning

Abstract

Achieving a conjunctive goal is a difficult problem in robot planning. Subgoals of a conjunctive goal can't be performed by arbitrary order because the mutual interferences exist in the processes of performing subgoals. For deriving such partial orders, we propose a new technique for planning by using temporal reasoning proposed by Allen. In our system, such a conjunctive goal composed of only two subgoals is called as minimal conjunctive goal, and given conjunctive goal can be regarded as a set of minimal conjunctive goals. All minimal conjunctive goals of a given circumstance can be obtained from production rules for that circumstance. And orders of performing subgoals of those minimal conjunctive goals can be derived by using temporal reasoning. Planning proceeds by utilizing these orders and so the backtracking of planning can be avoided, and the planning algorithm is very simple. In Allen's model, the time and space complexity in a full connected interval network is prohibitive. However, the size of the interval networks in our system is limited for minimal conjunctive goals, so that it is no necessary to worry about the complexity of time and space. In this paper, we will describe the deduction process of partial orders of performing subgoals of minimal conjunctive goals at first, and then show the algorithm of the main part of planning system. Some examples also will be shown to clarify the efficiency of our system.