A Formal Account of Planning with Flexible Timelines

Abstract

Planning for real world problems with explicit temporal constraints is a challenging problem. Among several approaches, the use of flexible timelines in Planning and Scheduling (P&S) has demonstrated to be successful in a number of concrete applications, such as, for instance, autonomous space systems. A flexible timeline describes an envelope of possible solutions which can be exploited by an executive system for robust on-line execution. A remarkable research effort has been dedicated to design, build and deploy software environments, like EUROPA, ASPEN, and APSI-TRF, for the synthesis of timeline-based P&S applications. Several attempts have also been made to characterize the concept of timelines. Nevertheless, a formal characterization of flexible timelines and plans is still missing.\ud \ud This paper presents a formal account of flexible timelines aiming at providing a general semantics for related planning concepts such as domains, goals, problems, constraints and flexible plans. Some basic properties of the defined concepts are also stated and proved. A simple running example inspired by a real world planning domain is exploited to illustrate the proposed formal notions. Finally, a planning tool, called Extensible Planning and Scheduling Library (EPSL), is briefly presented, which is able to generate flexible plans that are compliant with the given semantics

Timelines Are Expressive Enough to Capture Action-Based Temporal Planning

“…A first formal description of the problem has been proposed in [13], while a formalization with flexible timelines appeared in [14], later extended in [15] to account also for controllability issues. Meanwhile, the connection between timelines and Timed Game Automata has been investigated for the purpose of plan verification [16], [17] and robust plan execution [18], [19].…”

Planning and execution with flexible timelines: a formal account

“…The contribution of this work is, up to our knowledge, the first comprehensive formalization of flexible timelines with uncertainty. It combines, extends and revises the characterization of flexible timelines and plans presented by Cialdea Mayer et al [16] and Cialdea Mayer and Orlandini [15]. The paper provides a general semantics for timeline-related planning concepts such as domains, goals, problems, constraints and flexible plans, taking into account the difference between controllable and uncontrollable activities.…”

“…Example 2 Let us consider the timeline F T L pm for the state variable pm, in the satellite case study, made of the following sequence of tokens: [23,28], [20,30], c) pm 2 = (Slewing, [53, 58], [30,30] The timeline for pm made of the following sequence of tokens: [25,25], [20,30], c) pm 2 = (Slewing, [55, 55], [30,30] It is worth pointing out that often in the literature (e.g., [16,21]) a flexible token contains also a start interval. However, once a token x i is embedded in a timeline, the time interval to which its start point belongs (start time(x i )) can easily be computed like shown in the definition above.…”

“…It is worth pointing out that a more compact formulation of synchronization rules can be obtained by allowing C to be an arbitrary combination of atoms by means of both conjunctions and disjunctions (like in [16]). However, this would require a planner to be able to transform positive boolean formulae into disjunctive normal form, in order to obtain the set of possible choices (conjunctions of atoms) implying that C holds (i.e., the implicants of C).…”

“…In Bernardini's PhD thesis work [5], temporal flexibility is also considered but temporal networks are exploited in order to represent constraints and, more in general, controllability issues are not addressed. Cialdea Mayer et al [16] provide a first formal characterization of flexible timelines and plans independent of temporal networks and Cialdea Mayer and Orlandini [15] address the controllability issue.…”