MOBILE ROBOT LOCALIZATION UNDER PROCESSING AND COMMUNICATION CONSTRAINTS A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY ESHA NERURKAR IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY STERGIOS ROUMELIOTIS, ADVISOR March, 2016 c ESHA NERURKAR 2016 ALL RIGHTS RESERVED Acknowledgements This work would not have been possible without the guidance and support of my adviser, Professor Stergios Roumeliotis. He epitomizes the ideal teacher; one who teaches by example and passes along not only his knowledge and experience, but also his passion for his work. I am immensely grateful to him for his constant encouragement and invaluable advice, for pushing me beyond my limits, and for providing outstanding research and career opportunities. I am thankful for the time and valuable inputs from my committee members, Professor Saad, Professor Giannakis, Professor Isler, and Professor Kumar. During my time at the MARS lab, I got the opportunity to work with many amazing people, Tassos, Niko, Sam, Faraz, Ke, Joel, Paul, Gian Luca, Agostino, Kejian, Dimitri, Chao, Igor, Luis, Jack, Ahmed, Elliot, Ruipeng, and Ryan. Thank you all for providing such a wonderful work environment filled with stimulating research discussions and laughter in equal measures. I owe a lot to the vibrant city of Minneapolis, with its mighty Mississippi and numerous lakes, trails, eating joints, and watering holes, for creating a welcoming home away from home. I made many great friends here, DK, Raghav, Ajay, Vinu, Shantanu, Nihar, Neha, Salil (x2), Pu(oo)rva, Aditya, Vinita, Shraddha, Sajal, Anay, Siddharth, Erika, Shameek, Nikhil (x2) (and others, who I am surely forgetting here), with whom I have shared many happy hours full of laughter, food, and play. I am immensely thankful to Aniket, my wonderfully quirky friend, and Manasi, my partner-in-crime since childhood, for single-handedly upholding our friendships through graduate school; their insanity went a long way in keeping me sane. This work would be incomplete without acknowledging the unwavering support and unconditional love of my family. Even though they are so far away, my parents have been a constant source of inspiration and guidance. They have never failed to believe in i me and have done everything in their power (and then some more) so that I could have this opportunity today. My husband, Rahul, with his seemingly boundless kindness and patience, has been my companion through the everyday ups and downs of graduate school. I am thankful to him for still loving me at the end of this; without him by my side, I would not be writing these words. Last but not the least, I gratefully acknowledge financial support from the National Science Foundation, the University of Minnesota Department of Computer Science and Engineering, the Digital Technology Center at the University of Minnesota, and the University of Minnesota Graduate School Doctoral Dissertation Fellowship. ii Abstract Mobile robot localization is one of the most fundamental problems in robotics. For robots assisting humans in tasks such as surveillance, search and rescue, and space ex- ploration, accurate localization, that is, precisely estimating the robot's pose (position and orientation), is a prerequisite for autonomous operation. The system resources (processing and communication) for localization, however, are often limited, and their availability varies widely depending upon the application and the operating environ- ment. Therefore, the objective of this work is to develop resource-aware estimators for robot localization, which optimally utilize all available resources in order to maximize estimation accuracy. In the first part of this thesis, we address the problem of robot localization under processing constraints, focusing on the key applications of single-robot Simultaneous Lo- calization and Mapping (SLAM) and multi-robot Cooperative Localization (CL). For SLAM, we propose two resource-aware approaches, the approximate Minimum Mean Squared Error (MMSE) estimator-based Power-SLAM algorithm and the approximate batch Maximum A Posterior (MAP) estimator-based Constrained Keyframe-based Lo- calization and Mapping (C-KLAM). When approximations are inevitable due to process- ing constraints, both approaches aim to minimize the information loss while generating consistent estimates. For CL, we exploit the sparse structure of the batch MAP esti- mator to develop a resource-aware, fully-distributed multi-robot localization algorithm, that harnesses the processing, storage, and communication resources of the entire team, to obtain substantial speed-up. The second part of this thesis focuses on CL under communication constraints, in particular, asynchronous communication and bandwidth constraints. Due to limited communication range or the presence of obstacles, robots communicate asynchronously, that is, they can only interact with different sub-teams over time and exchange informa- tion intermittently. For this scenario, we develop a family of resource-aware information- exchange rules for the robots, in order to ensure optimal and consistent localization per- formance. Lastly, this thesis investigates the problem of decentralized estimation under stringent communication-bandwidth constraints. Here, robots can communicate only iii a severely quantized version (few or only one bit), of their real-valued sensor measure- ments, to the team. Existing estimation frameworks, however, are designed to process either real-valued or quantized measurements. To overcome this drawback, we propose a paradigm shift in estimation methodology by focusing on the design and performance evaluation of the first-ever, resource-aware, hybrid estimators. The proposed hybrid estimators are able to process both locally-available real-valued information, along with the quantized information received from the team, in order to maximize localization accuracy. Finally, we note that mobile robot applications are no longer limited to special- ized and expensive robots. Commonly-available hand-held devices such as cell phones, PDAs, and even cars, are equipped with processing, sensing, and networking capabil- ities. Therefore, when coupled with the proposed innovative, scalable, and resource- aware algorithms, these ubiquitous mobile devices can lead to a proliferation of novel location-based services. iv Contents Acknowledgements i Abstract iii List of Tables ix List of Figures x 1 Introduction 1 1.1 Robot Localization . 1 1.2 Resource-Constrained Robot Localization . 4 1.2.1 Processing Constraints . 4 1.3 Research Objectives . 6 1.3.1 SLAM under processing constraints . 7 1.3.2 Distributed CL under processing constraints . 8 1.3.3 Asynchronous Multi-Centralized CL . 8 1.3.4 Hybrid Estimation Framework for bandwidth-constrained CL . 9 1.4 Organization of the manuscript . 9 2 Power-SLAM: A linear-complexity, anytime algorithm for EKF-based SLAM 10 2.1 Introduction . 10 2.2 Related Work . 12 2.2.1 Standard EKF-based SLAM . 13 2.2.2 Approximate EKF-based SLAM . 13 v 2.3 Algorithm Description . 15 2.3.1 Standard EKF-based SLAM . 15 2.3.2 Global Map Postponement SLAM . 19 2.3.3 Low-Rank Approximation . 25 2.3.4 Linear-Time, Rank-2 Covariance Updates . 30 2.4 Simulations . 34 2.4.1 Simulation Setup . 34 2.4.2 Simulation Results . 34 2.5 Experiments . 40 2.5.1 Experimental Setup . 40 2.5.2 Experimental Results . 41 2.6 Summary . 43 3 C-KLAM: Constrained Keyframe-based Localization and Mapping 45 3.1 Introduction and Related Work . 45 3.2 Algorithm Description . 48 3.2.1 Batch MAP-based SLAM . 48 3.2.2 Marginalization and Na¨ıve Approximation-based SLAM . 52 3.2.3 C-KLAM Algorithm . 55 3.3 Experimental and Simulation Results . 58 3.3.1 Experimental Results . 58 3.3.2 Simulation Results . 59 3.4 Summary . 60 4 Distributed MAP-based CL 65 4.1 Introduction . 65 4.2 Related Work . 67 4.2.1 Centralized Cooperative Localization . 67 4.2.2 Decentralized Cooperative Localization . 68 4.2.3 Overview of the Proposed Approach . 70 4.3 Problem Formulation . 71 4.3.1 Problem Setup . 71 4.3.2 Maximum A Posteriori Estimator Formulation for CL . 72 vi 4.3.3 Structure of the Minimization Problem . 74 4.4 Centralized Cooperative Localization . 76 4.5 Distributed Cooperative Localization . 77 4.5.1 Distributed Data Storage and Updating . 77 4.5.2 Distributed Conjugate Gradient . 78 4.5.3 Marginalization . 84 4.6 Simulation Results . 93 4.7 Experimental Results . 95 4.8 Summary . 96 5 Multi-centralized CL under Asynchronous Communication Constraints103 5.1 Introduction and Related Work . 103 5.2 Problem Formulation . 106 5.3 Information Transfer Schemes . 109 5.3.1 Scheme 1: Own Information Transfer only . 109 5.3.2 Scheme 2: Information Transfer from q oldest time steps . 116 5.4 Simulations . 123 5.5 Summary . 127 6 MMSE-based Hybrid Estimation Framework for CL 128 6.1 Introduction and Related Work . 128 6.2 Problem Formulation . 131 6.2.1 Real vs. Quantized Measurements . 132 6.3 Hybrid Estimation Framework . 134 6.3.1 Batch Quantization . 135 6.3.2 Iterative Quantization . 139 6.4 Simulations and Experiment . 143 6.4.1 Simulation Results . 143 6.4.2 Experimental Results . 144 6.5 Summary . 145 7 MAP-based Hybrid Estimation Framework for CL 150 7.1 Introduction and Related Work . 150 vii 7.2 Problem Formulation . 152 7.2.1 Real vs. Quantized Measurements . 153 7.3 Hybrid Estimation Framework . 154 7.3.1 Quantization Rule . 155 7.3.2 BQMAP and H-BQMAP Estimators . 156 7.4 Simulation Results . 158 7.5 Summary . 158 8 Concluding Remarks 161 8.1 Summary of contributions . 161 8.2 Future research directions . 163 References 166 Appendix A. Appendices for Chapter 4 181 ∗ ∗ A.1 Derivation of D1 and c1 . 181 ∗ ∗ A.2 Derivation of Dp and cp . 182 Appendix B. Appendices for Chapter 6 189 B.1 Proof of Proposition 2 . 189 B.2 Proof of Proposition 3 . 197 viii List of Tables 2.1 Dimensions of terms appearing in EKF-based SLAM .