Clustering-Based Robot Navigation and Control

204 Pages·2016·5.55 MB·English

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Departmental Papers (ESE) Department of Electrical & Systems Engineering
8-1-2016
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Omur Arslan
University of Pennsylvania, [email protected]
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Omur Arslan, "Clustering-Based Robot Navigation and Control", Dissertation, University of Pennsylvania .
August 2016.
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For more information, please contact [email protected].
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In robotics, it is essential to model and understand the topologies of configuration spaces in order to
design provably correct motion planners. The common practice in motion planning for modelling
configuration spaces requires either a global, explicit representation of a configuration space in terms of
standard geometric and topological models, or an asymptotically dense collection of sample
configurations connected by simple paths, capturing the connectivity of the underlying space. This
dissertation introduces the use of clustering for closing the gap between these two complementary
approaches. Traditionally an unsupervised learning method, clustering offers automated tools to discover
hidden intrinsic structures in generally complex-shaped and high-dimensional configuration spaces of
robotic systems. We demonstrate some potential applications of such clustering tools to the problem of
feedback motion planning and control.
The first part of the dissertation presents the use of hierarchical clustering for relaxed, deterministic
coordination and control of multiple robots. We reinterpret this classical method for unsupervised
learning as an abstract formalism for identifying and representing spatially cohesive and segregated
robot groups at different resolutions, by relating the continuous space of configurations to the
combinatorial space of trees. Based on this new abstraction and a careful topological characterization of
the associated hierarchical structure, a provably correct, computationally efficient hierarchical navigation
framework is proposed for collision-free coordinated motion design towards a designated multirobot
configuration via a sequence of hierarchy-preserving local controllers.
The second part of the dissertation introduces a new, robot-centric application of Voronoi diagrams to
identify a collision-free neighborhood of a robot configuration that captures the local geometric structure
of a configuration space around the robot’s instantaneous position. Based on robot-centric Voronoi
diagrams, a provably correct, collision-free coverage and congestion control algorithm is proposed for
distributed mobile sensing applications of heterogeneous disk-shaped robots; and a sensor-based
reactive navigation algorithm is proposed for exact navigation of a disk-shaped robot in forest-like
cluttered environments.
These results strongly suggest that clustering is, indeed, an effective approach for automatically
extracting intrinsic structures in configuration spaces and that it might play a key role in the design of
computationally efficient, provably correct motion planners in complex, high-dimensional configuration
spaces.
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Motion planning, Robot control, Clustering, Configuration spaces, Sampling-based motion planning,
Geometry, Topology, Voronoi Diagrams, Hierarchical Clustering, Collision Avoidance, Local free space
DDiisscciipplliinneess
Controls and Control Theory | Control Theory | Discrete Mathematics and Combinatorics | Dynamic
Systems | Electrical and Computer Engineering | Engineering | Geometry and Topology | Non-linear
Dynamics | Robotics | Systems Engineering
This thesis or dissertation is available at ScholarlyCommons: https://repository.upenn.edu/ese_papers/722
CLUSTERING-BASED ROBOT NAVIGATION AND CONTROL
Omur Arslan
A DISSERTATION
in
Electrical and Systems Engineering
Presented to the Faculties of the University of Pennsylvania
in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
2016
Supervisor of Dissertation
Daniel E. Koditschek, Professor of Electrical and Systems Engineering
Graduate Group Chairperson
Alejandro Ribeiro, Associate Professor of Electrical and Systems Engineering
Dissertation Committee
Alejandro Ribeiro, Associate Professor of Electrical and Systems Engineering
George J. Pappas, Professor of Electrical and Systems Engineering
Vijay Kumar, Professor of Mechanical Engineering and Applied Mechanics
Yuliy Baryshnikov, Professor of Mathematics and Electrical and Computer Engineering,
University of Illinois at Urbana-Champaign
CLUSTERING-BASED ROBOT NAVIGATION AND CONTROL
COPYRIGHT
2016
Omur Arslan
To my family
iii
Acknowledgments
This thesis would not have been possible without the encouragement and support of many
people. It is a pleasure to thank those who made this unforgettable journey possible.
First and foremost, I would like to express my sincere appreciation and gratitude to
my advisor, Daniel E. Koditschek, for his endless support, patience, and encouragement
throughout my graduate studies. It was a great opportunity to work under his guidance
and to learn from his research expertise. His constant enthusiasm and dedication to basic
research has been a source of inspiration to reach for excellence in my own work.
I would also like to thank Alejandro Ribeiro, George Pappas, Vijay Kumar, and Yuliy
Baryshnikov for serving on my dissertation committee, despite their busy schedules, and
for their encouragement and insightful comments, but also for their hard questions. I am
always deeply impressed with and inspired by the quality of their research. My special
thanks go to Yuliy for introducing me to the space of trees and for discussions on clustering
methods and the topology of configuration spaces. I would also like to express my deepest
gratitude to my former advisor, Uluc Saranli, for encouraging and inspiring me to pursue a
doctoral degree and providing guidance to achieve my goals.
I would like to gratefully acknowledge the funding sources that made this research work
possible. This work was supported in part by the Air Force Office of Scientific Research
under CHASE MURI FA9550-10-1-0567 and in part by the Office of Naval Research under
the HUNT MURI N00014-07-0829, and I greatly appreciate the generous support of the
UniversityofPennsylvaniathroughtheAlfredFitlerMooreChairEndowment. Thesupport
fromAFOSRwasnotonlyfinancial — wealsohaveagreatopportunitytocollaboratewith
the researchers at the Air Force Research Laboratory. In particular, I would like to thank
Jared Culbertson and Bernard Abayowa for our intellectually stimulating conversations.
I would also like to thank my fellow lab members, past and present, for many intellec-
tual and scientific discussions and for their assistance and support over the years: Dan P.
Guralnik, Haldun Komsuoglu, Paul Reverdy, Aaron Johnson, Avik De, Gavin Kenneally,
Sonia Roberts, Jeff Duperret, Turner Topping, Feifei Qian, Vasileios Vasilopoulos, Wei-Hsi
Chen, and Arunkumar Byravan. Especially, I am very much indebted to Dan Guralnik for
many fruitful and enlightening discussions and his critical and very valuable feedback to
my work. I am very thankful for his guidance, encouragement and support. I would also
like to thank our lab coordinator, Diedra Krieger, for her kind assistance.
Of course, getting through graduate school requires more than academic support, and
colleagues and friends made my life at Penn much more enjoyable and valuable. I thank
Nikolay Atanasov, Shahin Shahrampour, Shaudi Mahdavi, and Hadi Afrasiabi for their
personalsupportto cope with theups and downs of graduate school and for the great times
iv
we worked together on projects and assignments. I thank Santiago Segarra and Santiago
Paternain for our numerous useful discussions on clustering and robot motion planning. I
thank Selman Sakar, Ceyhun Eksin, Tolga Ozaslan, Basak Taraktas, Selman Erol, Fatih
Karahan and Fazil Pac, whose company and great conversation over bad coffee helped me
a lot to endure and survive the graduate school experience. I cannot fully express my
gratitude and appreciation for their friendship.
Lastbutnottheleast, Iwouldliketothankmyfamily. Imustexpressmyvery profound
gratitude to my parents, Arife and Ali, and to my brother, Onur, and to my sister, Arzu,
for their love and for always being there for me in my life and supporting me throughout
my doctoral studies. Most importantly, I thank my loving partner, Alyona, for her under-
standing, kindness and support during the years of this study. This dissertation would not
have been possible without her. Thank you!
v
ABSTRACT
CLUSTERING-BASED ROBOT NAVIGATION AND CONTROL
Omur Arslan
Daniel E. Koditschek
Inrobotics,itisessentialtomodelandunderstandthetopologies ofconfigurationspaces
in order to design provably correct motion planners. The common practice in motion plan-
ning for modelling configuration spaces requires either a global, explicit representation of a
configuration space in terms of standard geometric and topological models, or an asymp-
totically dense collection of sample configurations connected by simple paths, capturing
the connectivity of the underlying space. This dissertation introduces the use of cluster-
ing for closing the gap between these two complementary approaches. Traditionally an
unsupervised learning method, clustering offers automated tools to discover hidden intrin-
sic structures in generally complex-shaped and high-dimensional configuration spaces of
robotic systems. We demonstrate some potential applications of such clustering tools to
the problem of feedback motion planning and control.
The first part of the dissertation presents the use of hierarchical clustering for relaxed,
deterministic coordination and control of multiple robots. We reinterpret this classical
method for unsupervised learning as an abstract formalism for identifying and represent-
ing spatially cohesive and segregated robot groups at different resolutions, by relating the
continuousspaceofconfigurationstothecombinatorialspaceoftrees. Basedonthisnewab-
straction and a careful topological characterization of the associated hierarchical structure,
a provably correct, computationally efficient hierarchical navigation framework is proposed
for collision-free coordinated motion design towards a designated multirobot configuration
via a sequence of hierarchy-preserving local controllers.
Thesecondpartofthedissertationintroducesanew,robot-centricapplicationofVoronoi
diagrams to identify a collision-free neighborhoodof arobotconfiguration that captures the
local geometric structure of a configuration space around the robot’s instantaneous posi-
tion. Based on robot-centric Voronoi diagrams, a provably correct, collision-free coverage
and congestion control algorithm is proposed for distributed mobile sensing applications
of heterogeneous disk-shaped robots; and a sensor-based reactive navigation algorithm is
proposed for exact navigation of a disk-shaped robot in forest-like cluttered environments.
These results strongly suggest that clustering is, indeed, an effective approach for au-
tomatically extracting intrinsic structures in configuration spaces and that it might play
a key role in the design of computationally efficient, provably correct motion planners in
complex, high-dimensional configuration spaces.
vi
Contents
Acknowledgments iv
Abstract vi
Contents vii
List of Tables x
List of Figures xi
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 What Does Clustering Offer? . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Prior Literature on the Use of Clustering in Robot Motion Planning . . . . 4
1.4 Contributions and Organization of the Thesis . . . . . . . . . . . . . . . . . 6
2 Coordinated Robot Navigation via Hierarchical Clustering 9
2.1 Hierarchical Abstraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Configuration Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Cluster Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3 Configuration Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.4 Graphs On Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Hierarchical Navigation Framework . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Generic Components of Hierarchical Navigation . . . . . . . . . . . . 17
2.2.2 Specification and Correctness of the Hierarchical Navigation Control
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Hierarchical Navigation of Euclidean Spheresvia Bisecting K-means Clustering 21
2.3.1 Hierarchical Strata of HC2-means . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Hierarchy-Preserving Navigation . . . . . . . . . . . . . . . . . . . . 24
2.3.3 Navigation in the Space of Binary Trees . . . . . . . . . . . . . . . . 28
2.3.4 Portal Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
vii
3 Navigation in Tree Space 38
3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1.1 Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1.2 Some Operations on Trees . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.3 Dissimilarities, Metrics and Ultrametrics . . . . . . . . . . . . . . . . 45
3.2 Quantifying Incompatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1 The Cluster-Cardinality Distance . . . . . . . . . . . . . . . . . . . . 47
3.2.2 The Crossing Dissimilarity . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Navigation in the Space of Trees . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 A Discrete-Time Dynamical System Perspective . . . . . . . . . . . 54
3.3.2 Special Crossings of Clusters . . . . . . . . . . . . . . . . . . . . . . 54
3.3.3 NNI Control Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.4 Resolving Incompatibilities with the Root Split . . . . . . . . . . . . 65
3.4 The NNI Navigation Dissimilarity . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4.2 Relations with Other Tree Measures . . . . . . . . . . . . . . . . . . 74
3.5 Discussion and Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . 77
3.5.1 Consensus Models and Median Trees . . . . . . . . . . . . . . . . . . 77
3.5.2 Sample Distribution of Dissimilarities . . . . . . . . . . . . . . . . . 77
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Sensor-Based Reactive Navigation in Unknown Convex Sphere Worlds 80
4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2 Encoding Collisions via Separating Hyperplanes . . . . . . . . . . . . . . . . 83
4.2.1 Separating Hyperplane Theorem . . . . . . . . . . . . . . . . . . . . 83
4.2.2 The Safe Neighborhood of a Disk-Shaped Robot . . . . . . . . . . . 85
4.3 Robot Navigation via Separating Hyperplanes . . . . . . . . . . . . . . . . . 87
4.3.1 Feedback Robot Motion Planner . . . . . . . . . . . . . . . . . . . . 87
4.3.2 Qualitative Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.3 Extensions for Limited Range Sensing Modalities . . . . . . . . . . . 91
4.3.4 An Extension for Differential Drive Robots . . . . . . . . . . . . . . 97
4.4 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Voronoi-Based Coverage Control of Heterogeneous Disk-Shaped Robots102
5.1 Coverage Control of Point Robots . . . . . . . . . . . . . . . . . . . . . . . 103
5.1.1 Location Optimization of Homogeneous Robots . . . . . . . . . . . . 103
5.1.2 Location Optimization of Heterogeneous Robots . . . . . . . . . . . 105
5.2 Occupancy Defects of Power Diagrams . . . . . . . . . . . . . . . . . . . . . 106
5.3 Combining Coverage Control and Collision Avoidance . . . . . . . . . . . . 106
5.3.1 Encoding Collisions via Body Diagrams . . . . . . . . . . . . . . . . 107
5.3.2 Coverage Control of Heterogeneous Disk-Shaped Robots . . . . . . . 109
5.3.3 Congestion Control of Unassigned Robots . . . . . . . . . . . . . . . 112
5.3.4 Coverage Control of Differential Drive Robots . . . . . . . . . . . . . 113
5.4 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
viii