A Unified Dynamic Approach for Dealing with Temporal Uncertainty and Conditional Planning

In temporal planning, Temporal Constraint Networks allow to check the temporal consistency of a plan, but it has to be extended to deal with tasks which effective duration is uncertain and will only be observed during execution. The Contingent TCN models it: in which Dynamic ontrollability has to be dmcked, i.e.: during execution, will the system be able to consistently release tasks according to the observed durations of already completed tasks ? This behaviour is a reactive one suggesting the plan is conditional in some sense. A Timed Game Automaton model has been specifically designed to check the Dynamic ontrollability. This paper furthermore discusses the use of such a model with respect to conditional and reactive planning, and its strength with respect to execution supervision needs, and suggests improving efficiency by partitioning the plan into subparts~ introducing so-called waypoints with fixed time of occurrence. Last we show that the expressive power of automata might allow to address more elaborate reactive planning features, such as preprocessed subplans, information gathering, or synchronization constraints. Background and overview Temporal Constraint .Networks (TCN) (Schwalb Dechter 1997) rely on qualitative (or symbolic) constraint algebras (Vilain, Kautz, & van Beek 1989) but mort. specifically tackle quantitative (ornumerical) constraints. They are now at the heart of many application domains, especially scheduling (Dubois, Fargier: & Prade 1993) and planning (Morris: Muscettola, Tsamardinos 1998; Fargier et al. 1998)~ where a TCN might allow one to incrementally (i.e. at each addition of a new constrainQ check the temporal consistency of the plan. In realistic applications theinherent uncertain nature of some task durations must be accounted for, distinguishing between contingent constraints (whose ffective duration is only observed at execution time, e.g. the duration of a task) and controllable ones (which instanciation is controlled by the agent, e.g. a delay between starting times of tasks): the problem becomes Copyright (~ 2000, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. a decision-making process under uncertainty, and consistency nmst be redefined interms of controUabilities, especially the Dynamic ontrollability that encompasses the reactive nature of the solution building process in dynamic domains: this property allows one to check if it is feasible tobuild a solution i the process oftime, each assignment depending only on the situation observed so far, and still needing to account for all the future unknown observations. In (Vidal & Fargier 1999) partial results about complexity and tractable subclasses were given and a first ad hoc algorithm was provided, based on a discretization of time. This work has been recently completed by the introduction of the Waypoint controllability feature (Morris & Muscettola 1999) (i.e. there are some time-points which cazl be assigned the same time of occurrence in all solutions). Adding wait periods in a plan allows to get this property checked, and then the problem may lie in a subclass in which Waypoint and Dynamic controllabilities are equivalent. This paper goes further: relying on a Dynamic controllability checking method through an equivalent Timed Game Automaton, we will show that a small set of waypoints might also be used to partition the plan into subparts in which small size automata can be built to check Dynamic controllability only locally, hence providing a nice tradeoff between expressiveness, optimality" of the plan and efficiency. The other contribution of this paper is to situate the automaton approach within the conditional and reactive planning area. The paper is organized as follows. Section 2 provides the basic constraint network model and the Dynamic and Waypoint controllability definitions, and Section 3 gives the complete automaton-based Dynamic controUability checking method (those two sections being developped in more details in (Vidal 2000)). Then section 4 gives evidence of the pros and cons of the approach in planning, with respect to efficiency, reactive behaviours in presence of temporal uncertainty and execution supervision needs, before proposing the combined framework of partitioned Dynamic controllability. Section 5 eventually describes how the full expressiveness of timed automata may be used to address more complex features such as preprocessed subplans, information gathering, or synchronization constraints. Vidal 395 From: AIPS 2000 Proceedings. Copyright © 2000, AAAI (www.aaai.org). All rights reserved. Contingent TCN and Controllability In temporal planning, the planning process produces a Temporal Constraint Network to represent the temporal informations captured by the plaal. This model relies on a rcified logic framework (Vila & Reichgelt ̄ 1993) that separates the atemporal logical propositions from their temporal qualification, which are then interpretcd in a temporal algebra framework (in our casc a time-point based one), for which one uses a graphbased model on which we will focus in this so(:tion. This model is used for checking the temporal consistency of the plan. VCe will barely recall here the Contingent TCN model mid focus on the Dynanfic controllalfility property, both being "already dcscribed in (Vidal & Fargicr 1999), and we will re(:all as well the Waypoint controllability property introduced in (Morris & Muscettola 1999). We will use the, extended expressiveness and the unified characterization that appear in more details in (Vidal 2000). We first recall the basics of TCNs (Schwalb & Dechter 1997). At the qualitative level, we rely on the timepoint continuous algebra (Vilain, Kautz, & van Beck 1989), where time-points are related by a number of relatkms, that can be be represented through a graph where nodes are time-points and edges correspond to precedence (-<) relations. We can use the same timepoint graph to represent quantitative constraints as well, thanks to the TCN formalism (Schwalb & Dechter 1997). Here continuous binary constraints define the possible durations between two time-points by means of temporal intervals. A basic constraint between x and y is l~g _< (y x) < u,.v equally expressed c,~ = [l~u,u~u] in the TCN. TCN a priori allow disjunctions of intervals, but we will restrict ourselves to the so-called STP (Simple Temporal Problem) where disjunctions are not permitted. A TCN is said to be consistent if one can C[IOOSE for each time-point a value such that ̄ all the constraints are satisfied, the rcsulting instanciatioxl being a solution of the STP modelled by the TCN. Then consistency checking of such a restricted TCN can be made through complete and polynomialtime propagation algorithms. The TCN suits well the cases in which effective dates of time-points and effective durations of constraints are always chosen by the agent. If not, the problem has to bc redefined in the following way. A typology of temporal constraints One needs first distinguishing between two different kinds of time-points: the time of occurrence of an activated time-point can be freely assigned by the agent, while received time-points are those which effective time of occurrencc is out of control and can only be observed. This raises a corresponding distinction between socalled controllable and contingent constraints ( Clb and Ctg for short): the former can be restricted or instanciated by the agent while values for the latter will be provided (within allowed bounds) by the e~ernal world (see (Vidal & Fargier 1999) for details). 396 AIPS-2000 For instance, in planning, a task which duration is uncertain and will only be known when the task is completed at execution time will be nmdelled by a Ctg between the beginning time-point which is an activated one and thc ending one whicaa is a received one. As far as Clbs are concerned, we need to further distinguish