Planning and Scheduling in Temporally Uncertain Domains Andrea Micheli

389 Pages·2015·2.53 MB·English

DEPARTMENT OF INFORMATION ENGINEERING AND COMPUTER SCIENCE
ICT International Doctoral School
Planning and Scheduling in
Temporally Uncertain Domains
Andrea Micheli
Advisor
Dr. Alessandro Cimatti
Head of Embedded Systems Unit,
Fondazione Bruno Kessler, Trento
Co-Advisor
Dr. Marco Roveri
Fondazione Bruno Kessler, Trento
January 2016

Abstract
Any form of model-based reasoning is limited by the adherence of the model
to the actual reality. Scheduling is the problem of finding a suitable tim-
ing to execute a given set of activities accommodating complex temporal
constraints. Planning is the problem of finding a strategy for an agent
to achieve a desired goal given a formal model of the system and the en-
vironment it is immersed in. When time and temporal constraints are
considered, the problem takes the name of temporal planning.
A common assumption in existing techniques for planning and schedul-
ing is controllability of activities: the agent is assumed to be able to control
the timing of starting and ending of each activity. In several practical ap-
plications, however, the actual timing of actions is not under direct control
of the plan executor.
In this thesis, we focus on this temporal uncertainty issue in scheduling
and in temporal planning: we propose to natively express temporal uncer-
tainty in the model used for reasoning. We first analyze the state-of-the-art
on the subject, presenting a rationalization of existing works. Second, we
show how Satisfiability Modulo Theory (SMT) solvers can be exploited to
quickly solve different kinds of query in the realm of scheduling under un-
certainty. Finally, we address the problem of temporal planning in domains
featuring real-time constraints and actions having duration that is not un-
der the control of the planning agent.
Keywords
[Temporal Planning with Uncontrollable Durations, Scheduling under Un-
certainty, Temporal Problems with Uncertainty, Temporal Uncertainty,
Satisfiability Modulo Theory]
Acknowledgments
Many people deserve my gratitude for their support and their contribution
to this thesis.
First of all, I want to thank my advisor, Alessandro Cimatti, and my co-
advisor, Marco Roveri, for the help, the guidance and the support they
always provided me during the PhD. They taught me what good research
is and how to do it, how to approach a problem and how to think critically.
I will never thank them enough for these lessons and their friendship.
Then, I would like to thank David E. Smith for giving me the possibility
of working in a thrilling environment such as NASA Ames for six months;
it has been a wonderful and enriching experience. I am deeply thankful to
him, to Minh Do and to Jeremy Frank for all the interesting discussions
and the inputs they provided.
I have to thank all my close friends from the Embedded Systems Unit
in FBK, their support and their glee brightened my days: Marco Gario,
Alessandro Mariotti, Cristian Mattarei, Sergio Mover and Gianni Zampedri.
Thanks to Daniela, Jessica, Marta, Matteo and Samuel for being my closest
friends and always encouraging me and listening to me during our Saturday
nights.
Finally, this thesis is dedicated to my family: I am who I am thanks only
to their example and love. To my mother for her everyday courage, to
my father for his wisdom, to my brother for his jokes and glee and to my
girlfriend Silvia for her love.

Ringraziamenti
Devo ringraziare molte persone per il loro supporto e il loro contributo a
questa tesi.
Prima di tutto, voglio ringraziare il mio supervisore, Alessandro Cimatti,
e il mio co-supervisore, Marco Roveri, per l’aiuto, la guida e il supporto
che mi hanno sempre dato durante questo periodo di dottorato. Mi hanno
insegnato cos’`e e come si fa la buona ricerca, come approcciare un problema
e come pensare criticamente. Non li ringrazier´o mai abbastanza per queste
lezioni e per la loro amicizia.
Vorrei inoltre ringraziare David E. Smith per avermi dato la possibilit´a di
lavorare in un ambiente elettrizzante come NASA Ames per sei mesi; `e stato
un periodo meraviglioso e un esperienza arricchente. Sono profondamente
grato a lui, a Minh Do e a Jeremy Frank per tutte le interessanti discussioni
e gli stimoli che mi hanno dato.
Ringrazio tutti i miei amici dell’ unita´ di Embedded Systems in FBK, il loro
supporto e la loro allegria hanno illuminato le mie giornate: Marco Gario,
Alessandro Mariotti, Cristian Mattarei, Sergio Mover e Gianni Zampedri.
Grazie a Daniela, Jessica, Marta, Matteo e Samuel per essere i miei migliori
amici e per incoraggiarmi ed ascoltarmi sempre durante le nostre serate.
Infine, questa tesi `e dedicata alla mia famiglia: io sono chi sono solo grazie
al loro esempio e al loro amore. A mia madre per il suo coraggio che
dimostra ogni giorno, a mio padre per la sua saggezza, a mio fratello per i
suoi scherzi e la sua allegria e a Silvia per il suo affetto.

Contents
1 Introduction 1
1.1 Contributions and Publications . . . . . . . . . . . . . . . 3
1.2 Experimental Evaluations . . . . . . . . . . . . . . . . . . 5
1.3 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . 6
2 Background 9
2.1 Technical Preliminaries . . . . . . . . . . . . . . . . . . . . 9
2.2 Satisfiability Modulo Theories . . . . . . . . . . . . . . . . 11
2.2.1 SMT Notation . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Quantifiers in LRA . . . . . . . . . . . . . . . . . . 14
Fourier-Motzkin Elimination . . . . . . . . . . . . . 14
Loos-Weispfenning Elimination . . . . . . . . . . . 15
2.3 Timed Game Automata . . . . . . . . . . . . . . . . . . . 16
2.4 Clocks and Time Regions . . . . . . . . . . . . . . . . . . . 20
I State-of-the-Art Survey 25
3 Execution Model 29
3.1 Plant Interface . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Plan Executor . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Formal Model . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Plant Classification . . . . . . . . . . . . . . . . . . . . . . 38
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3.5 Plan Executor Classification . . . . . . . . . . . . . . . . . 39
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6.1 Partial Observability . . . . . . . . . . . . . . . . . 44
3.6.2 Weak Executors and Predictions . . . . . . . . . . . 45
4 Scheduling Classification 47
4.1 Qualitative Scheduling . . . . . . . . . . . . . . . . . . . . 48
4.1.1 Point Algebra . . . . . . . . . . . . . . . . . . . . . 48
4.1.2 Allen Algebra . . . . . . . . . . . . . . . . . . . . . 49
4.2 Temporal Networks . . . . . . . . . . . . . . . . . . . . . . 50
4.2.1 Temporal Networks and Consistency . . . . . . . . 53
Simple Temporal Network . . . . . . . . . . . . . . 53
Disjunctive Temporal Network . . . . . . . . . . . . 55
Temporal Constraint Satisfaction Networks . . . . . 56
Minimal Networks . . . . . . . . . . . . . . . . . . 57
4.2.2 Temporal Uncertainty . . . . . . . . . . . . . . . . 57
Simple Temporal Networks with Uncertainty . . . . 60
TCSNU and DTNU . . . . . . . . . . . . . . . . . . 62
4.2.3 Discrete Non-Determinism . . . . . . . . . . . . . . 68
Conditional Temporal Networks . . . . . . . . . . . 69
Conditional STNU . . . . . . . . . . . . . . . . . . 71
5 Planning Classification 73
5.1 Temporal Planning without Uncertainty . . . . . . . . . . 74
5.1.1 Temporal Plans . . . . . . . . . . . . . . . . . . . . 75
5.1.2 Planning Language Classification . . . . . . . . . . 76
5.1.3 State Space Temporal Planning . . . . . . . . . . . 79
5.1.4 Plan Space Temporal Planning . . . . . . . . . . . 84
5.1.5 Planning as Satisfiability . . . . . . . . . . . . . . . 87
5.1.6 Planning Graph Derivations . . . . . . . . . . . . . 88
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