Bearing-Only Cooperative-Localization and Path-Planning of Ground and Aerial Robots

140 Pages·2016·3.68 MB·English

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Theses and Dissertations
2011-11-16
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Rajnikant Sharma
Brigham Young University - Provo
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Bearing-onlyCooperative-LocalizationandPath-Planning
ofGroundandAerialRobots
RajnikantSharma
Adissertationsubmittedtothefacultyof
BrighamYoungUniversity
inpartialfulfillmentoftherequirementsforthedegreeof
DoctorofPhilosophy
RandalW.Beard,Chair
WynnC.Stirling
TimW.McLain
MarkB.Colton
D.J.Lee
DepartmentofElectricalandComputerEngineering
BrighamYoungUniversity
December2011
Copyright©2011RajnikantSharma
AllRightsReserved

ABSTRACT
Bearing-onlyCooperative-LocalizationandPath-Planning
ofGroundandAerialRobots
RajnikantSharma
DepartmentofElectricalandComputerEngineering,BYU
DoctorofPhilosophy
In this dissertation, we focus on two fundamental problems related to the navigation of
ground robots and small Unmanned Aerial Vehicle (UAVs): cooperative localization and path
planning. The theme running through in all of the work is the use of bearing only sensors, with a
focusonmonocularvideocamerasmountedongroundrobotsandUAVs.
To begin with, we derive the conditions for the complete observability of the bearing-only
cooperative localization problem. The key element of this analysis is the Relative Position Mea-
surementGraph(RPMG).ThenodesofanRPMGrepresentvehiclestatesandtheedgesrepresent
bearing measurements between nodes. We show that graph theoretic properties like the connec-
tivity and the existence of a path between two nodes can be used to explain the observability of
the system. We obtain the maximum rank of the observability matrix without global information
and derive conditions under which the maximum rank can be achieved. Furthermore, we show
that for the complete observability, all of the nodes in the graph must have a path to at least two
different landmarks of known location. The complete observability can also be obtained without
landmarks if the RPMG is connected and at least one of the robots has a sensor which can mea-
sure its global pose, for example a GPS receiver. We validate these conditions by simulation and
experimental results. The theoretical conditions to attain complete observability in a localization
system is an important step towards reliable and efficient design of localization and path planning
algorithms. With such conditions, a designer does not need to resort to exhaustive simulations
and/or experimentation to verify whether a given selection of a control strategy, topology of the
sensor network, and sensor measurements meets the observability requirements of the system. In
turn,thisleadstodecreasedrequirementsoftime,cost,andeffortfordesigningalocalizationalgo-
rithms. We use these observability conditions to develop a technique, for camera equipped UAVs,
to cooperatively geo-localize a ground target in an urban terrain. We show that the bearing-only
cooperative geo-localization technique overcomes the limitation of requiring a low-flying UAV to
maintain line-of-sight while flying high enough to maintain GPS lock. We design a distributed
path planning algorithm using receding horizon control that improves the localization accuracy of
thetargetandofalloftheUAVswhilesatisfyingtheobservabilityconditions.
Next, we use the observability analysis to explicitly design an active local path planning
algorithm for UAVs. The algorithm minimizes the uncertainties in the time-to-collision (TTC)
and bearing estimates while simultaneously avoiding obstacles. Using observability analysis we
show that maximizing the observability and collision avoidance are complementary tasks. We
providesufficientconditionsoftheenvironmentwhichmaximizesthechancesobstacleavoidance
and UAV reaching the goal. Finally, we develop a reactive path planner for UAVs using sliding
mode control such that it does not require range from the obstacle, and uses bearing to obstacle to

avoid cylindrical obstacles and follow straight and curved walls. The reactive guidance strategy is
fast,computationallyinexpensive,andguaranteescollisionavoidance.
Keywords: cooperative localization, path planning, graph theory, nonlinear system theory, sliding
modecontrol,extendedkalmanfilter,liederivatives,visionbasedestimationandcontrolnolistofta-
bles

ACKNOWLEDGMENTS
Iwouldliketothankmyadvisorandcommitteechair,Prof. RandyBeard,forhisguidance,
funding, and enthusiasm for the research. Special thanks to Dr. Clark Taylor for inviting me to
come to BYU for the PhD programme and providing the initial help for my research. Prof. Tim
McLain was a great help in completing the work in this dissertation, and I thank him for being on
my committee and providing me funding through TA opportunities. Also, thanks to Prof. Wynn
C.Sterling,Prof. D.J.Lee,andProf. MarkColtonforbeingonmycommittee
Thanks very much to the other graduate students of MAGICC Lab who have helped me
to mature as a researcher. In particular: Travis Millet, Stephen Quebe, John MacDonald, Huili
Yu, and Solomon Sun. I especially thank the department staff for making the administrative life
of every ECEN student easy. Also I would like to thank Dr. P.B Sujit for the important research
relateddiscussions.
I would not be here if it wasn’t for my family, and I would not be able to stay if it weren’t
for my beautiful wife, Suruchi. This work is dedicated to my wife and the glorious memories I
haveofmyuncleKrishanKumar.

TABLEOFCONTENTS
LISTOFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Singlevehiclelocalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Cooperativelocalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Pathplanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Researchoverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Organizationofthemanuscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter2 Graph-basedobservabilityanalysisofbearing-only
cooperativelocalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Bearing-onlycooperativelocalization . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Cooperativelocalizationimplementation . . . . . . . . . . . . . . . . . . 14
2.2.2 Liederivativesandnonlinearobservability . . . . . . . . . . . . . . . . . 16
2.3 Graph-basedobservabilityanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Rowsintheobservabilitymatrixduetoanedge . . . . . . . . . . . . . . . 18
2.3.2 Observabilityanalysiswithoutlandmarks . . . . . . . . . . . . . . . . . . 27
2.3.3 Observabilityanalysiswithknownlandmarks . . . . . . . . . . . . . . . . 30
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.1 Simulationresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.2 Experimentalresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Chapter3 Bearing-onlycooperativegeo-localization . . . . . . . . . . . . . . . . . . 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Problemformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.1 Bearing-onlycooperativelocalization . . . . . . . . . . . . . . . . . . . . 51
3.3 Graph-basedobservabilityanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1 Rowsintheobservabilitymatrixduetoanedge . . . . . . . . . . . . . . . 55
3.3.2 Rowsintheobservabilitymatrixofa3-nodeRPMG . . . . . . . . . . . . 59
3.4 Controllerforgeo-localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Chapter4 Observabilitybasedpathplanning . . . . . . . . . . . . . . . . . . . . . . 73
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Observabilityanalysisofstateestimation . . . . . . . . . . . . . . . . . . . . . . 75
4.3 Observability-basedpathplanning . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
ix