A game-theoretic approach to timeline-based planning with uncertainty

In timeline-based planning, domains are described as sets of independent, but interacting, components, whose behaviour over time (the set of timelines) is governed by a set of temporal constraints. A distinguishing feature of timeline-based planning systems is the ability to integrate planning with execution by synthesising control strategies for flexible plans. However, flexible plans can only represent temporal uncertainty, while more complex forms of nondeterminism are needed to deal with a wider range of realistic problems. In this paper, we propose a novel game-theoretic approach to timeline-based planning problems, generalising the state of the art while uniformly handling temporal uncertainty and nondeterminism. We define a general concept of timeline-based game and we show that the notion of winning strategy for these games is strictly more general than that of control strategy for dynamically controllable flexible plans. Moreover, we show that the problem of establishing the existence of such winning strategies is decidable using a doubly exponential amount of space.

[1]  Marco Pistore,et al.  Weak, strong, and strong cyclic planning via symbolic model checking , 2003, Artif. Intell..

[2]  Angelo Montanari,et al.  Timelines Are Expressive Enough to Capture Action-Based Temporal Planning , 2016, 2016 23rd International Symposium on Temporal Representation and Reasoning (TIME).

[3]  Marco Roveri,et al.  Timelines with Temporal Uncertainty , 2013, AAAI.

[4]  Maria Fox,et al.  PDDL2.1: An Extension to PDDL for Expressing Temporal Planning Domains , 2003, J. Artif. Intell. Res..

[5]  Christian J. Muise,et al.  Non-Deterministic Planning With Conditional Effects , 2014, ICAPS.

[6]  Thierry Vidal,et al.  Handling contingency in temporal constraint networks: from consistency to controllabilities , 1999, J. Exp. Theor. Artif. Intell..

[7]  Thomas A. Henzinger,et al.  Alternating-time temporal logic , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[8]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[9]  Amedeo Cesta,et al.  A Planning-Based Architecture for a Reconfigurable Manufacturing System , 2016, ICAPS.

[10]  Michael Beetz,et al.  Improving Robot Plans During Their Execution , 1994, AIPS.

[11]  Tristan B. Smith,et al.  EUROPA : A Platform for AI Planning, Scheduling, Constraint Programming, and Optimization , 2012 .

[12]  Nicola Muscettola,et al.  HSTS: Integrating Planning and Scheduling , 1993 .

[13]  Marta Cialdea Mayer,et al.  Planning and execution with flexible timelines: a formal account , 2016, Acta Informatica.

[14]  David E. Smith,et al.  Strong temporal planning with uncontrollable durations , 2018, Artif. Intell..

[15]  Angelo Montanari,et al.  Complexity of Timeline-Based Planning , 2017, ICAPS.

[16]  Alberto Camacho,et al.  Non-Deterministic Planning with Temporally Extended Goals: LTL over Finite and Infinite Traces , 2017, AAAI.

[17]  Hector Geffner,et al.  Fair LTL Synthesis for Non-Deterministic Systems using Strong Cyclic Planners , 2013, IJCAI.

[18]  Amedeo Cesta,et al.  Developing an End-to-End Planning Application from a Timeline Representation Framework , 2009, IAAI.

[19]  Sam Steel.  Action Under Uncertainty , 1994, J. Log. Comput..

[20]  Marta Cialdea Mayer,et al.  An Executable Semantics of Flexible Plans in Terms of Timed Game Automata , 2015, 2015 22nd International Symposium on Temporal Representation and Reasoning (TIME).