The world according to MARP

166 Pages·2010·1.41 MB·English

The world according to MARP
Multi-Agent Route Planning
Adriaan W. ter Mors

The world according to MARP
Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof.ir. K.C.A.M. Luyben,
voorzitter van het College van Promoties,
in het openbaar te verdedigen op maandag 15 maart 2010 om 15:00 uur
door Adriaan Willem TER MORS
informatica ingenieur
geboren te Zoetermeer
Dit proefschrift is goedgekeurd door de promotor:
Prof.dr. C. Witteveen
Copromotor: Dr.ir. F.A. Kuipers
Samenstelling van de promotiecommissie:
Rector Magnificus voorzitter
Prof.dr. C. Witteveen Technische Universiteit Delft, promotor
Dr.ir. F.A. Kuipers Technische Universiteit Delft, copromotor
Prof.dr.-ing. I.J. Timm Goethe-Universit¨at
Prof.dr. M. Fox University of Strathclyde
Prof.dr.ir. S.P. Hoogendoorn Technische Universiteit Delft
Prof.dr.ir. J.A. La Poutr´e Technische Universiteit Eindhoven
Dr. A.H. Salden Almende BV
SIKS Dissertation Series No. 2010-11. The research reported in this thesis has been
carried out under the auspices of SIKS, the Dutch Research School for Information and
Knowledge Systems.
ThisresearchhasbeenfundedbytheDutchMinistryofEconomicAffairs,projectnumber
CSI4006.
ISBN: 978-90-8559-937-1
Copyright (cid:13)c 2009 A.W. ter Mors
Contents
1 Introduction 1
1.1 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Research question. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 From Motion Planning to Route planning 9
2.1 Robot motion planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 Kinodynamic motion planning . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Motion planning with moving obstacles . . . . . . . . . . . . . . . 12
2.1.3 Multi-robot motion planning . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 Multi-agent route planning in robotics . . . . . . . . . . . . . . . . 14
2.1.5 Lessons learned from motion planning . . . . . . . . . . . . . . . . 16
2.2 The automated guided vehicle domain . . . . . . . . . . . . . . . . . . . . 17
2.3 Multi-agent route planning . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Decoupled path and velocity planning . . . . . . . . . . . . . . . . 19
2.3.2 Prioritized route planning . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.3 Optimal multi-agent route planning . . . . . . . . . . . . . . . . . 24
2.3.4 Robust route planning . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 A Model for Multi-Agent Route Planning 31
3.1 Basic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.1 Agent plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Additional constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Simultaneous resource exchanges . . . . . . . . . . . . . . . . . . . 36
3.2.2 Resource traversal constraints . . . . . . . . . . . . . . . . . . . . . 40
3.2.3 Agent plan properties . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Problem complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.1 PSPACE-complete routing . . . . . . . . . . . . . . . . . . . . . . 48
3.4 The prioritized approach to MARP . . . . . . . . . . . . . . . . . . . . . . 50
vi CONTENTS
4 Sequential Route Planning 53
4.1 Reservations and free time windows . . . . . . . . . . . . . . . . . . . . . 54
4.1.1 Free time window and model configuration . . . . . . . . . . . . . 55
4.2 Route planning from A to B . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.1 Algorithm specification . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.2 Algorithm complexity . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Route planning from A to Z . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.1 Naive multi-stage algorithm . . . . . . . . . . . . . . . . . . . . . . 70
4.3.2 Algorithm specification . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5 Priority-Based Schedule Repair 77
5.1 Plan execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.1.1 Incidents in plan execution . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Planstep-Priority Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3 Priority-changing algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.1 Algorithm description . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3.2 Extending the IAP algorithm . . . . . . . . . . . . . . . . . . . . . 92
5.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Usability of Prioritized Route Planning 97
6.1 Robustness of route plans . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.1.1 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.1.2 Robustness under fixed priorities . . . . . . . . . . . . . . . . . . . 101
6.1.3 Robustness with flexible priorities . . . . . . . . . . . . . . . . . . 113
6.2 Priorities and global plan quality . . . . . . . . . . . . . . . . . . . . . . . 118
6.2.1 Agent ordering assumption . . . . . . . . . . . . . . . . . . . . . . 118
6.2.2 Schiphol experiments. . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.3 Experiments on random infrastructures . . . . . . . . . . . . . . . 121
6.3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7 Conclusions 125
7.1 Finding conflict-free route plans . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2 Efficiency of route plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.3 Robustness of route plans . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.4 Computational complexity of route planning. . . . . . . . . . . . . . . . . 128
7.5 Answering the research question . . . . . . . . . . . . . . . . . . . . . . . 128
7.6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Summary 139
Samenvatting 143
Acknowledgements 147
Curriculum Vitae 149
CONTENTS vii
SIKS dissertation series 151
viii CONTENTS
Chapter 1
Introduction
The day is November 13, 1994. The streets of Adelaide, Australia are empty except for
twenty-six autonomous agents that drive around a 3.78km track for a total of 81 laps.
On lap 35, agent 5 and agent 0 try to occupy a piece of track that has room for only one.
The resulting collision immediately puts agent 5 out of the race, while agent 0 manages
to limp back to the pit lane, where he retires with a broken suspension. Having scored
more points in previous races, agent 5 is World Champion; agent 0 misses the title by a
single point.
The subject of this thesis is multi-agent route planning (MARP), in which each agent
(acomputationalentitywithadegreeofautonomytochooseitsactions—seesection1.2)
has to plan a route from a current location to a destination location, while avoiding
conflicts with the plans of the other agents. The scope of MARP is not quite as broad
as to encompass Formula 1 racing, at least not until the FIA1 allows non-human drivers
to enter the championship. Until that time, there are many interesting situations in
whichmulti-agentrouteplanningis arelevantproblem,includingplanningtaxiroutesfor
airplanes at airports [33], and coordinating the movements of automated guided vehicles
in flexible manufacturing systems [7]. In addition, research into the complexity of multi-
agent route planning has revealed similarities with other planning problems, including
moving pianos (out of a room of movable objects) [82], dodging asteroids, and escaping
from prison (by evading detection from search beam lights) [25].
The main applications we will consider in this thesis are taxiway route planning and
route planning for automated guided vehicles. In airport taxi routing, aircraft (agents)
have to taxi from a runway to a gate, and then, after all ground handling services have
beenperformed,theyhavetotaxifromthegatetotherunwayfortake-off. Theseaircraft
drive around a shared infrastructure of taxiways, runways, gates, aprons, parking places,
etc., and they may never come into contact with (or even close to) another aircraft.
Also, agents are self-interested in the sense that they care little whether the planes of
rival airlines arrive on time, as long as they are on time themselves. Although at many
airportstaxirouteshavebeenspecifiedinadvance,routeplanningalgorithmscanimprove
performance, because the pre-specified routes may not be optimal (for example with
1TheF´ed´erationInternationaledel’Automobileisthegoverningbodyforworldmotorsport.
2 Introduction
regard to the minimization of delay). In addition, new routes have to be found in case
the standard taxiways are covered with snow or are otherwise obstructed. Also, wintry
conditionssometimesrequiresnowandicetoberemovedfromairplanespriortotake-off.
This de-icing process usually occurs at a de-icing station, which means that an agent
cannot take its regular route to the runway, but it must first taxi from the gate to the
de-icingstation. Moreover,anaircraftmusttakeoffwithinacertaintimelimitofde-icing
(called the holdover time, which is typically 15 minutes), to prevent ice from re-forming.
Hence, we need algorithms to plan along a sequence of locations, possibly with timing
constraints between different locations.
Other application domains of multi-agent route planning are those in which Auto-
matedGuidedVehicles(AGVs)aredeployed. OnfactoryfloorsandinwarehousesAGVs
are used to transport materials between locations of the facility. The AGV routing prob-
lem is typically but one of the optimization problems involving AGVs. It must also be
decidedwhichtransportationtasktoallocatetowhichAGV[38],whattodowithanAGV
onceithascompletedatransportationtask(e.g. theidle-vehiclepositioningproblem[8]),
what the optimal AGV fleet size is [79], when an AGV should recharge its battery [62],
etc. All of these problems interact with the problem of determining the best routes for
the AGVs. Another prominent area where AGVs are used is at container terminals (e.g.
in Singapore, Rotterdam, or Hamburg), where AGVs carry containers to and from ships.
1.1 Problem description
In multi-agent route planning, there are a number of autonomous agents (in the above
examples: (auto-)pilots in taxiing aircraft, and automated guided vehicles), each with its
own transportation task, which implies that each agent has a start location and one or
more destination locations2. In the example domains, an aircraft has to taxi to the gate
afterlanding,whileanAGVmayhavetopickupapalletatthewarehouseandtransport
it to a production station. We assume that agents traverse a road map. That is, rather
than moving around in free space, an agent must keep to pre-specified roads. A taxiing
aircraft, for instance, can no longer travel as the crow flies.
With more than one agent active on the infrastructure, the agents need to coordinate
theirmovementstoavoidcollisions, bothduringrouteplanningandduringtheexecution
of the route plans. In multi-agent route planning, the coordination between the agents
mustensurethatnoneoftheresources oftheinfrastructure(e.g. roadsandintersections)
are ever occupied by more agents than the capacities of the resources allow. Planning-
time coordination should ensure that coordination during the plan execution phase (e.g.,
maintaining sufficient distance between the agents) is no longer a difficult problem. The
challenge is to coordinate the agents while enabling them to efficiently perform their
transportation tasks, by which we mean that they want to finish their transportation
tasks as quickly as possible. In the airport domain, where delays can be very costly, an
aircraftshouldspendaslittletimeaspossibletraversingthetaxiways. Formanufacturing
systems that use AGVs for materials handling, efficient transportation is important to
2We will only consider the case where destination locations have to be visited in a particular order
that is known in advance. Otherwise, a Traveling Salesperson Problem (TSP) (see e.g. [26]) has to be
solved.