Magnus Egerstedt

Executive Director
Institute for Robotics and Intelligent Machines
Professor and Julian T. Hightower Chair in Systems and Control
School of Electrical and Computer Engineering
Georgia Institute of Technology

Phone +1 404 894-3484
Fax +1 404 894-4641 (School of ECE)
Office TSRB 436B
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, GA 30332, USA

GRITS Lab Group Members
Sean Wilson (Postdoc)
Pietro Pierpaoli (Postdoc)
Li Wang (Ph.D. student)
Sebastian Ruf (Ph.D. student)
Maria Santos (Ph.D. student)
Paul Glotfelter (Ph.D. student)
Siddharth Mayya (Ph.D. student)
Gennaro Notomista (Ph.D. student)
Eric Squires (Ph.D. student)
Ian Buckley (Ph.D. student)
Christopher Banks (Ph.D. student)
Anqi Li (Ph.D. student)
Kyle Slovak (M.S. student)
Mark Olsen (M.S. student)

Former Ph.D. Students
Matt Hale (Ph.D. Spring 2017)
Thesis: Mixed Centralized/Decentralized Coordination Protocols for Multi-Agent Systems
Abstract: This thesis uses a mixture of centralized and decentralized architectures and algorithms to develop coordination strategies for multi-agent systems. Conventionally, centralized and decentralized methods are viewed as belonging to distinct paradigms, each with its own features and drawbacks, and multi-agent coordination algorithms are typically classified as being exclusively one or the other. However, emerging technologies such as cloud computing make it feasible to incorporate some centralization into an otherwise decentralized system, and one may ask how to embrace this mix of centralized and decentralized information that is rapidly being integrated into various systems such as the smart power grid, swarms of robots, and cyber- physical systems. To address this question, two problem domains are considered. The first is that of asynchronous coordination, in which agents generate and share information with arbitrary timing. The second concerns private coordination, in which teams of agents must work together without revealing sensitive information. In both cases, mixing centralized and decentralized information enables successful coordination despite the challenges imposed by asynchrony and privacy, and theoretical performance guarantees are derived for each algorithm that is developed. Complementing these theoretical developments, robotic experiments are included that demonstrate the utility of these algorithms in practice.

Tina Setter (Ph.D. Spring 2017)
Thesis: Psychologically Consistent Coordinated Control of Multi-Agent Teams
Abstract: The objective of this research is to describe both human-robot interactions and inter-robot interactions and analyze the behavior of the resulting multi-agent systems, while drawing comparisons to psychological studies regarding human team behavior. In particular, we look at the effects of trust, energy, and manipulability on these interactions. We first address the problem of modeling trust evolution and describing how it affects the states of agents in a system - whether they be human or robot. We introduce two different types of trust models - self-centered and team-oriented - and show, through simulations and theoretical analyses, under what initial trust conditions these systems achieve their objectives. We show our models to be psychologically consistent in that they exhibit group polarization, belief polarization, and a positive trust-performance correlation. In the second part of this work, we look at the effect of energy on inter-robot interactions by solving an energy-constrained coordination problem in which robots must determine where and when to meet given differing initial battery levels to do so in the least amount of time. This is formulated as a constrained optimization problem where the constraints arise from solving for a single agent's optimal control input. Lastly, we address the effect of manipulability on human-robot interactions through a haptic human-swarm interaction user study. Manipulability, a notion describing how effective a leader robot is at controlling the follower robots, is provided as force feedback on a haptic joystick that a human operator uses to control a swarm of robots. Ten subjects complete the experiment in which they move the group of robots through a series of waypoints and different mappings between manipulability and the haptic feedback force are investigated.

Usman Ali (Ph.D. Summer 2016)
Thesis: Optimal Control of Constrained Hybrid Dynamical Systems: Theory, Computation and Applications
Abstract: Hybrid dynamical systems arise in a number of application areas such as power converters, autopilots, manufacturing, process control, hybrid cars, mobile and humanoid robotics etc., to name a few and as such the optimal control of these systems has been an area of active research. These systems are characterized by two components: subsystems (modes) with continuous or discrete dynamics and a switching law which determines which of these subsystems is active at a given time. While in theory, we can switch infinitely many times between different modes in a finite amount of time, physical systems need to spend some minimum time in a mode before they can switch to another mode due to mechanical reasons, power constraints, information delays, stability considerations etc and must spend some minimum amount of time in a mode before they can switch to another mode. This minimum time is known as the dwell time, a term first used in the context of stability of hybrid systems, and the optimal control of hybrid systems under these constraints is the main focus of this thesis.

Thiagarajan Ramachandran (Ph.D. Spring 2016)
Thesis: Algorithmically Induced Architectures for Multi-Agent System
Abstract: The objective of this thesis is to understand the interactions between the computational mechanisms, described by algorithms and software, and the physical world, described by differential equations, in the context of networked systems. Such systems can be denoted as cyber-physical nodes connected over a network. In this work, the power grid is used as a guiding example and a rich source of problems which can be generalized to networked cyber-physical systems. We address specific problems that arise in cyber-physical networks due to the presence of a computational network and a physical network as well as provide directions for future research.

Yancy Diaz-Mercado (Ph.D. Spring 2016)
Thesis: Interactions in Multi-Robot Systems
Abstract: The objective of this research is to develop a framework for multi-robot coordination and control with emphasis on human-swarm and inter-agent interactions. We focus on two problems: in the first we address how to enable a single human operator to externally influence large teams of robots. By directly imposing density functions on the environment, the user is able to abstract away the size of the swarm and manipulate it as a whole, e.g., to achieve specified geometric configurations, or to maneuver it around. In order to pursue this approach, contributions are made to the problem of coverage of time-varying density functions. In the second problem, we address the characterization of inter-agent interactions and enforcement of desired interaction patterns in a provably safe (i.e., collision free) manner, e.g., for achieving rich motion patterns in a shared space, or for mixing of sensor information. We use elements of the braid group, which allows us to symbolically characterize classes of interaction patterns. We further construct a new specification language that allows us to provide rich, temporally-layered specifications to the multi-robot mixing framework, and present algorithms that significantly reduce the search space of specification-satisfying symbols with exactness guarantees. We also synthesize provably safe controllers that generate and track trajectories to satisfy these symbolic inputs. These controllers allow us to find bounds on the amount of safe interactions that can be achieved in a given bounded domain.

Daniel Pickem (Ph.D. Spring 2016)
Thesis: Self-Reconfigurable Multi-Robot Systems
Abstract: Self-reconfigurable robotic systems are variable-morphology machines capable of changing their overall structure by rearranging the modules they are composed of. Individual modules are capable of connecting and disconnecting to and from one another, which allows the robot to adapt to changing environments. Optimally reconfiguring such systems is computationally prohibitive and thus in general self-reconfiguration approaches aim at approximating optimal solutions. Nonetheless, even for approximate solutions, centralized methods scale poorly in the number of modules. Therefore, the objective of this research is the development of decentralized self-reconfiguration methods for modular robotic systems. Building on completeness results of the centralized algorithms in this work, decentralized methods are developed that guarantee convergence to a given target shape. A game-theoretic approach lays the theoretical foundation of a novel potential game-based formulation of the self-reconfiguration problem. Stochastic convergence guarantees are provided for a large class of utility functions used by purely self-interested agents. Furthermore, two extensions to the basic game-theoretic learning algorithm are proposed that enable agents to modify the algorithms' parameters during runtime and improve convergence times. The flexibility in the choice of utility functions together with runtime adaptability makes the presented approach and the underlying theory suitable for a range of problems that rely on decentralized local control to guarantee global, emerging properties. The experimental evaluation of the presented algorithms relies on a newly developed multi-robotic testbed called the "Robotarium" that is equipped with novel custom-designed miniature robots, the "GRITSBots". The Robotarium provides hardware validation of self-reconfiguration on robots but more importantly introduces a novel paradigm for remote accessibility of multi-agent testbeds with the goal of lowering the barrier to entrance into the field of multi-robot research and education.

Rowland O'Flaherty (Ph.D. Spring 2016)
Thesis: A Control Theoretic Perspective on Learning in Robotics
Abstract: For robotic systems to continue to move towards ubiquity, robots need to be more autonomous. More autonomy dictates that robots need to be able to make better decisions. Control theory and machine learning are fields of robotics that focus on the decision making process. However, each of these fields implements decision making at different levels of abstraction and at different time scales. Control theory defines low-level decisions at high rates, while machine learning defines high-level decision at low rates. The objective of this research is to integrate tools from both machine leaning and control theory to solve higher dimensional, complex problems, and to optimize the decision making process.

Zak Costello (Ph.D. Spring 2016)
Thesis: Distributed Computation in Networked Systems
Abstract: The objective of this thesis is to develop a theoretical understanding of computation in networked dynamical systems and demonstrate practical applications supported by the theory. We are interested in understanding how networks of locally interacting agents can be controlled to compute arbitrary functions of the initial node states. In other words, can a dynamical networked system be made to behave like a computer? In this thesis, we take steps towards answering this question with a particular model class for distributed, networked systems which can be made to compute linear transformations.

Smriti Chopra (Ph.D. Spring 2015)
Thesis: Spatio-Temporal Multi-Robot Routing
Abstract: In this dissertation, we analyze spatio-temporal routing under various constraints specific to multi-robot applications. Spatio-temporal routing requires multiple robots to visit spatial locations at specified time instants, while optimizing certain criteria like the total distance traveled, or the total energy consumed. Such a spatio-temporal concept is intuitively demonstrable through music (e.g. a musician routes multiple fingers to play a series of notes on an instrument at specified time instants). As such, we showcase much of our work on routing through this medium. Particular to robotic applications, we analyze constraints like maximum velocities that the robots cannot exceed, and information-exchange networks that must remain connected. Furthermore, we consider a notion of heterogeneity where robots and spatial locations are associated with multiple skills, and a robot can visit a location only if it has at least one skill in common with the skill set of that location. To extend the scope of our work, we analyze spatio-temporal routing in the context of a distributed framework, and a dynamic environment. We demonstrate the entirety of our work through simulations and hardware implementations, centered around the premise of music. We conclude this dissertation with a graphical user-interface that allows humans to interact with multiple robots through the creation of different musical compositions.

Jean-Pierre de la Croix (Ph.D. Spring 2015)
Thesis: Characterizing and Facilitating Human Interactions with Swarms of Mobile Robots
Abstract: Since humans and robots often share workspaces and interact with each other to complete tasks cooperatively, as is the case, for example, in automated warehouses and assembly lines, much of the focus has been centered on supporting human interactions with one or a few robots. As the number of robots involved in a task grows large, scalable abstractions are needed to support interactions with larger numbers of robots. Consequently, there has been a growing effort to understand human-swarm interactions (HSIs) and devise abstractions that are amenable to having humans interact with swarms of robots easily and effectively. In this dissertation, we investigate what it means to impose a control structure on a swarm of robots for the purpose of supporting a specific HSI, when such a control structure is suitable for allowing a user to solve a particular task with a swarm of robots, how one can evaluate attention and effort required to interact with a swarm of robots through a particular control structure, how well attention and effort scale as the number of robots in the swarm increases, why some swarms of robots are easier to interact with than others under the same type of control structure, how to select an appropriate swarm size, and how to design new input controllers for interacting with swarm of mobile robots. Consequently, this dissertation provides a comprehensive framework for characterizing, understanding, and designing the control structures of new abstractions that will be amenable to humans interacting with swarms of networked mobile robots, as well as, a number of examples of such old and new abstractions investigated under this framework.

Yasin Yazicioglu (Ph.D. Summer 2014)
Thesis: Decentralized Graph Processes for Robust Multi-Agent Networks
Abstract: The objective of this thesis is to develop decentralized methods for building robust multi-agent networks through self-organization. Multi-agent networks appear in a large number of natural and engineered systems, including but not limited to, biological networks, social networks, communication systems, transportation systems, power grids, and robotic swarms. Networked systems typically consist of numerous components that interact with each other to achieve some collaborative tasks such as flocking, coverage optimization, load balancing, or distributed estimation, to name a few. Multi-agent networks are often modeled via interaction graphs, where the nodes represent the agents and the edges denote direct interactions between the corresponding agents. Interaction graphs play a significant role in the overall behavior and performance of multi-agent networks. Therefore, graph theoretic analysis of networked systems has received a considerable amount of attention within the last decade. In many applications, network components are likely to face various functional or structural disturbances including, but not limited to, component failures, noise, or malicious attacks. Hence, a desirable network property is robustness, which is the ability to perform reasonably well even when the network is subjected to such perturbations. In this thesis, robustness in multi-agent networks is pursued in two parts. The first part presents a decentralized graph reconfiguration scheme for formation of robust interaction graphs. Particularly, the proposed scheme transforms any interaction graph into a random regular graph, which is robust to the perturbations of their nodes/links. The second part presents a decentralized coverage control scheme for optimal protection of networks by some mobile security resources. As such, the proposed scheme drives a group of arbitrarily deployed resources to optimal locations on a network in a decentralized fashion.

Greg Droge (Ph.D. Spring 2014)
Thesis: Behavior-Based Model Predictive Control for Networked Multi-Agent Systems
Abstract: We present a motion control framework which allows a group of robots to work together to decide upon their motions by minimizing a collective cost without any central computing component or any one agent performing a large portion of the computation. When developing distributed control algorithms, care must be taken to respect the limited computational capacity of each agent as well as respect the information and communication constraints of the network. To address these issues, we develop a distributed, behavior-based model predictive control (MPC) framework which alleviates the computational difficulties present in many distributed MPC frameworks, while respecting the communication and information constraints of the network. In developing the multi-agent control framework, we make three contributions. First, we develop a distributed optimization technique which respects the dynamic communication restraints of the network, converges to a collective minimum of the cost, and has transients suitable for robot motion control. Second, we develop a behavior-based MPC framework to control the motion of a single-agent and apply the framework to robot navigation. The third contribution is to combine the concepts of distributed optimization and behavior-based MPC to develop the mentioned multi-agent behavior-based MPC algorithm suitable for multi-robot motion control.

Hassan Jaleel (Ph.D. Fall 2013)
Thesis: Power-Aware Control Strategies in Wireless Sensor Networks
Abstract: As the trends towards decentralization, miniaturization, and longevity of deployment continue in many domains, power management has become increasingly important. In sensing and communications networks, power management has long been a part of the design paradigm. However, an underlying assumption in most of the existing work is that the performance of the sensing devices remain the same throughout their lifetime, which is not always true. Moreover, when mobility is added to the mix, power management is not well understood. Thus, the research presented in this thesis is focused on developing power-aware control strategies for maximizing the lifetime of wireless sensor networks, spanning two broad classes of wireless sensor networks, namely, static networks (comprising of agents with no mobility) and mobile networks (comprising of agents with mobility). For the case of static networks, the problem of the effects of power decay on the performance of an individual sensor and on the entire network is identified and is addressed for networks in which sensing devices are randomly deployed in a region of interest. For the case of mobile networks, this research proposes a solid framework for distributed power-aware mobility strategies that can achieve any desired global objective while minimizing total energy consumption.

Waseem Abbas (Ph.D. Fall 2013)
Thesis: Network-Centric Methods for Heterogeneous Multiagent Networks
Abstract: We present tools for a network topology based characterization of heterogeneity in multiagent systems, thereby providing a framework for the analysis and design of heterogeneous multiagent networks from a network structure view-point. In heterogeneous networks, agents with a diverse set of resources coordinate with each other. Coordination among different agents and the structure of the underlying network topology have significant impacts on the overall behavior and functionality of the system. Using constructs from graph theory, a qualitative as well as a quantitative analysis is performed to examine an inter-relationship between the network topology and the distribution of agents with various capabilities in heterogeneous networks. Our goal is to allow agents maximally exploit heterogeneous resources available within the network through local interactions, thus exploring a promise heterogeneous networks hold to accomplish complicated tasks by leveraging upon the assorted capabilities of agents. For a reliable operations of such systems, the issue of security against intrusions and malicious agents is also addressed. We provide a scheme to secure a network against a sequence of intruder attacks through a set of heterogeneous guards. Moreover, robustness of networked systems against noise corruption and structural changes in the underlying network topology is also examined.

Amy LaViers (Ph.D. Summer 2013)
Thesis: Choreographic Abstractions for Style-Based Robotic Motion
Abstract: What does it mean to do the disco? Or perform a cheerleading routine? Or move in a style appropriate for a given mode of human interaction? Answering these questions requires an interpretation of what differentiates two distinct movement styles and a method for parsing this difference into quantitative parameters. Furthermore, such an understanding of principles of style has applications in control, robotics, and dance theory. This thesis present a definition for “style of motion” that is rooted in dance theory, a framework for stylistic motion generation that separates basic movement ordering from its precise trajectory, and an inverse optimal control method for extracting these stylistic parameters from real data. On the part of generation, the processes of sequencing and scaling are modulated by the stylistic parameters enumerated: an automation that lists basic primary movements, sets which determine the final structure of the state machine that encodes allowable sequences, and weights in an optimal control problem that generates motions of the desired quality. This generation framework is demonstrated on a humanoid robotic platform for two distinct case studies – disco dancing and cheerleading. In order to extract the parameters that comprise the stylistic definition put forth, two inverse optimal control problems are posed and solved -- one to classify individual movements and one to segment longer movement sequences into smaller motion primitives. The motion of a real human leg (recorded via motion capture) is classified in an example. Thus, the contents of the thesis comprise a tool to produce and understand stylistic motion.

Peter Kingston (Ph.D. Spring 2012)
Thesis: Multi-Agent Coordination: Fluid-Inspired and Optimal Control Approaches
Abstract: Multiagent coordination problems arise in a variety of applications, from satellite constellations and formation flight, to air traffic control and unmanned vehicle teams. We investigate the coordination of mobile agents using two kinds of approaches. In the first, which takes its inspiration from fluid dynamics and algebraic topology, control authority is split between mobile agents and a network of static infrastructure nodes – like wireless base stations or air traffic control towers – and controllers are developed that distribute their computation throughout this network. In the second, we look at networks of interconnected mechanical systems, and develop novel optimal control algorithms, which involve the computation of optimal deformations of time- and output- spaces, to achieve approximate formation tracking. Finally, we investigate algorithms that optimize these controllers to meet subjective criteria of humans.

Philip Twu (Ph.D. Spring 2012)
Thesis: Control of Multi-Agent Networks: From Network Design to Decentralized Coordination
Abstract: This dissertation presents a suite of design tools for multi-agent systems that address three main areas: network design, decentralized controller generation, and the synthesis of decentralized control strategies by combining individual decentralized controllers. First, a new metric for quantifying heterogeneity in multi-agent systems is presented based on combining different notions of entropy, and is shown to overcome the drawbacks associated with existing diversity metrics in various scientific fields. Moreover, a new method of controlling multi-agent networks through the single-leader network paradigm is presented where by directly exploiting the homogeneity of agent capabilities, a network which is not completely controllable can be driven closer to a desired target configuration than by using traditional control techniques. An algorithm is presented for generating decentralized control laws that allow for agents to best satisfy a desired global objective, while taking into account network topological constraints and limitations on how agents can compute their control signals. Then, a scripting tool is developed to aid in specifying sequences of decentralized controllers to be executed consecutively, while helping ensure that the required network topological requirements needed for each controller to execute properly are maintained throughout mode switches. Finally, the underlying concepts behind the developed tools are showcased in three example applications: distributed merging and spacing for heterogeneous aircraft during terminal approaches, collaborative multi-UAV convoy protection in dynamic environments, and an educational tool used to teach a graduate-level networked controls course at the Georgia Institute of Technology.

Rahul Chipalkatty (Ph.D. Spring 2012)
Thesis: Human in the Loop Control for Cooperative Human-Robot Tasks
Abstract: Even with the advance of autonomous robotics and automation, many automated tasks still require human intervention or guidance to mediate uncertainties in the environment or to execute the complexities of a task that autonomous robots are not yet equipped to handle. As such, robot controllers are needed that utilize the strengths of both autonomous agents, adept at handling lower level control tasks, and humans, superior at handling higher-level cognitive tasks. To address this need, we develop a control theoretic framework that incorporates user commands such that user intention is preserved while an automated task is carried out by the controller. This is a novel approach in that system theoretic tools allow for analytic guarantees of feasibility and convergence to goal states which naturally lead to varying levels of autonomy. We develop a model predictive controller that takes human input, infers human intent, then applies a control that minimizes deviations from the intended human control while ensuring that the lower-level automated task is being completed.

Jonghoek Kim (Ph.D. Spring 2011)
Thesis: Simultaneous Cooperative Exploration and Networking
Abstract: This thesis provides strategies for multiple vehicles to explore unknown environments in a cooperative and systematic manner. These strategies are called Simultaneous Cooperative Exploration and Networking (SCENT) strategies. As the basis for development of SCENT strategies, we first tackle the motion control and planning for one vehicle with range sensors. In particular, we develop the curve-tracking controllers for autonomous vehicles with rigidly mounted range sensors, and a provably complete exploration strategy is proposed so that one vehicle with range sensors builds a topological map of an environment. The SCENT algorithms introduced in this thesis extend the exploration strategy for one vehicle to multiple vehicles. The enabling idea of the SCENT algorithms is to construct a topological map of the environment, which is considered completely explored if the map corresponds to a complete Voronoi diagram of the environment. To achieve this, each vehicle explores its local area by incrementally expanding the already visited areas of the environment. At the same time, every vehicle deploys communication devices at selected locations and, as a result, a communication network is created concurrently with a topological map. This additional network allows the vehicles to share information in a distributed manner resulting in an efficient exploration of the workspace.

Musad Haque (Ph.D. Fall 2010)
Thesis: Biologically Inspired Heterogeneous Multi-Agent Systems
Abstract: Many biological systems are known to accomplish complex tasks in a decentralized, robust, and scalable manner - characteristics that are desirable to the coordination of engineered systems as well. Inspired by nature, we produce coordination strategies for a network of heterogenous agents and in particular, we focus on intelligent collective systems. Bottlenose dolphins and African lions are examples of intelligent collective systems since they exhibit sophisticated social behaviors and effortlessly transition between functionalities. Through preferred associations, specialized roles, and self-organization, these systems forage prey, form alliances, and maintain sustainable group sizes. In this thesis, we take a three-phased approach to bioinspiration: in the first phase, we produce agent-based models of specific social behaviors observed in nature. The goal of these models is to capture the underlying biological phenomenon, yet remain simple so that the models are amenable to analysis. In the second phase, we produce bio-inspired algorithms which are based on the simple biological models produced in the first phase. Moreover, these algorithms are developed in the context of specific coordination tasks, e.g., the multi-agent foraging task. In the final phase of this work, we tailor these algorithms to produce coordination strategies that are ready to be deployed in target applications.

Patrick Martin (Ph.D. Spring 2010)
Thesis: Motion Description Languages: From Specification to Execution
Abstract: Many emerging controls applications have seen increased operational complex- ity due to the deployment of embedded, networked systems that must interact with the physical environment. In order to manage this complexity, we design different control modes for each system and use motion description languages (MDL) to specify a sequence of these controllers to execute at run-time. Unfortunately, current MDL frameworks lose some of the important details (i.e. power, spatial, or communication capabilities) that affect the execution of the control modes. This work presents sev- eral computational tools that work towards closing MDL¢s specification-to-execution gap, which can result in undesirable behavior of complex systems at run-time. First, we develop the notion of an MDL compiler for control specifications with spatial, energy, and temporal constraints. We define a new MDL for networked systems and develop an algorithm that automatically generates a supervisor to prevent incorrect execution of the multi-agent MDL program. Additionally, we derive conditions for checking if an MDL program satisfies actuator constraints and develop an algorithm to insert new control modes that maintain actuator bounds during the execution of the MDL program. Finally, we design and implement a software architecture that facilitates the development of control applications for systems with power, actuator, sensing, and communication constraints.

Xu Chu (Dennis) Ding (Ph.D. Fall 2009)
Thesis: Real-Time Optimal Control of Autonomous Switched Systems
Abstract: In this work, we provide a real-time algorithmic optimal control framework for autonomous switched systems. Traditional optimal control approaches for autonomous switched system are open-loop in nature. Therefore, the switching times of the system can not be adjusted or adapted when the system parameters or the operational environments change. We aim to close this loop, and apply adaptations to the optimal switching strategy based on new information that can only be captured on-line. One important contribution of this work is to provide the means to allow feedback (in a general sense) to the control laws (i.e. the switching times) of the switched system so that the control law can be updated to maintain optimality of the switching-time control inputs. Furthermore, convergence analyses for the proposed algorithms are presented. Finally, we apply the real-time algorithms to an application in optimal formation and coverage control of a networked system. This application is implemented on a realistic simulation framework consisting of a number of Unmanned Aerial Vehicles (UAVs) that interact in a virtual 3D world.

Brian Smith (Ph.D. Spring 2009)
Thesis: Automatic Coordination and Deployment of Multi-Robot Systems
Abstract: We present automatic tools for configuring and deploying multi-robot networks of decentralized, mobile robots. These methods are tailored to the decentralized nature of the multi-robot network and the limited information available to each robot. We present methods for determining if user-defined network tasks are feasible or infeasible for the network, considering the limited range of its sensors. To this end, we define rigid and persistent feasibility and present necessary and sufficient conditions (along with corresponding algorithms) for determining the feasibility of arbitrary, user-defined deployments. Control laws for moving multi-robot networks in acyclic, persistent formations are defined. We also present novel Embedded Graph Grammar Systems (EGGs) for coordinating and deploying the network. These methods exploit graph representations of the network, as well as graph-based rules that dictate how robots coordinate their control. Automatic systems are defined that allow the robots to assemble arbitrary, user-defined formations without any reliance on localization. Further, this system is augmented to deploy these formations at the user-defined, global location in the environment, despite limited localization of the network. The culmination of this research is an intuitive software program with a Graphical User Interface (GUI) and a satellite image map which allows users to enter the desired locations of sensors. The automatic tools presented here automatically configure an actual multi-robot network to deploy and execute user-defined network tasks.

Meng Ji (Ph.D. Summer 2007)
Thesis: Graph-Based Control of Networked Systems
Abstract: Networked systems have attracted great interests from the control society during the last decade. Several issues rising from the recent research are addressed in this dissertation. Connectedness is one of the important conditions that enable distributed coordination in a networked system. Nonetheless, it has been assumed in most implementations, especially in continuous-time applications, until recently. A nonlinear weighting strategy is proposed in this dissertation to solve the connectedness preserving problem. Both rendezvous and formation problem are addressed in the context of homogeneous network. Controllability of heterogeneous networks is another issue which has been long omitted. This dissertation contributes a graph theoretical interpretation of controllability. Distributed sensor networks make up another important class of networked systems. A novel estimation strategy is proposed in this dissertation. The observability problem is raised in the context of our proposed distributed estimation strategy, and a graph theoretical interpretation is derived as well.

Tejas Mehta (Ph.D. Spring 2007)
Thesis: Optimal, Multi-Modal Control With Applications to Robotics
Abstract: Multi-modal control is a commonly used design tool to deal with increasing complexity associated with modern control tasks. The main idea in multi-modal control is to breakup complex control tasks into simpler tasks. In particular, number of control modes are constructed, each with respect to a particular task, and these modes are combined according to some supervisory control logic in order to complete the overall control task. This way of modularizing the control task lends itself particularly well to the control of autonomous mobile robot, as evidenced by the success of behavior-based robotics. Many challenging and interesting research issues arise when employing multi-modal control. This dissertation aims to address these issues within an optimal control framework and apply the resulting theory to develop effective navigation strategies for autonomous mobile robots. To this end, we first addressed the problem of inferring global behaviors from a collection of local rules (i.e., feedback control laws). Next, we addressed the issue of adaptively varying the multi-modal control system to further improve performance. Inspired by adaptive multi-modal control, we presented a constructivist framework for the learning from example problem. Next, we addressed the optimal control of multi-modal systems with infinite dimensional constraints. Finally, we used multi-modal control to develop effective navigation strategies for autonomous mobile robots. In closing, the main strength of multi-modal control lies in breaking up complex control task into simpler tasks. This divide-and-conquer approach helps modularize the control system. This has the same effect on complex control systems that object-oriented programming has for large-scale computer programs, namely it allows greater simplicity, flexibility, and adaptability.

David Wooden (Ph.D. Fall 2006)
Thesis: Graph-based Path Planning for Mobile Robots
Abstract: Mobile robots are increasingly moving from structured spaces (e.g. office buildings) to unstructured space (e.g. unfamiliar outdoor terrain), from plodding along (1 mph) to high speed (70 mph), and from accurate, active sensing (LIDAR, IR) to passive noisy sensing (vision). This thesis presents work on how to solve planning and navigation control problems for mobile robots in unknown unstructured environments in the presence of noisy perception. The centerpiece of this work is a sparse, combinatorial approach to path planning that is dynamic and fast. Additional work is presented that augments a standard control architecture to include a feedback mechanism that handles inconsistencies in configuration spaces. Also, a method for quickly finding globally optimal paths in a colored graph is presented, given our sense of edge coloring and optimality. All the presented methods were implemented on various real-world mobile platforms, such as the LAGR robot, iRobot Magellans, and Georgia Tech's entry to the Urban Grand Challenge; the work is presented with attention given to both theoretical and practical considerations.

Florent Delmotte (Ph.D. Fall 2006)
Thesis: Multi-Modal Control: From Motion Description Languages to Optimal Control
Abstract: The goal of the proposed research is to provide efficient methods for defining, selecting and encoding multi-modal control programs. To this end, modes are recovered from system observations, i.e. quantized input-output strings are converted into consistent mode sequences within the Motion Description Language (MDL) framework. The design of such modes can help identify and predict the behaviors of complex systems (e.g. biological systems such as insects) and inspire the design and control of robust semi-autonomous systems (e.g. navigating robots). In this work, the efficiency of a method will be defined by the complexity and expressiveness of specific control programs. The insistence on low-complexity programs is originally motivated by communication constraints on the computer control of semi-autonomous systems, but also by our belief that, as complex as they may look, natural systems indeed use short motion schemes with few basic behaviors. The attention is first focused on the design of such short-length, few-distinct-modes mode sequences within the MDL framework. Optimal control problems are then addressed. In particular, given a mode sequence, the question of deciding when the system should switch from one mode to another in order to achieve some reachability requirements is studied. Finally, we propose to investigate how sampling strategies affect complexity and reachability, and how an acceptable trade-off between these conflicting entities can be reached.

Henrik Axelsson (Ph.D. Spring 2006)
Thesis: Optimal Control of Switched Autonomous Systems: Theory, Algorithms, and Robotic Applications
Abstract: As control systems are becoming more and more complex, system complexity is rapidly becoming a limiting factor in the efficacy of established techniques for control systems design. To cope with the growing complexity, control architectures often have a hierarchical structure. At the base of the system pyramid lie feedback loops with simple closed-loop control laws. These are followed, at a higher level, by discrete control logics. Such hierarchical systems typically have a hybrid nature. A common approach to addressing these types of complexity consists of decomposing, in the time domain, the control task into a number of modes, i.e. control laws dedicated to carrying out a limited task. This type of control generally involves switching laws among the various modes, and its design poses a major challenge in many application domains. The primary goal of this thesis is to develop a unified framework for addressing this challenge. To this end, the contribution of this thesis is threefold: 1. An algorithmic framework for how to optimize the performance of switched autonomous systems is derived. The optimization concerns both the sequence in which different modes appear in and the duration of each mode. The optimization algorithms are presented together with detailed convergence analyses. 2. Control strategies for how to optimize switched autonomous systems operating in real time, and when the initial state of the system is unknown, are presented. 3. A control strategy for how to optimally navigate an autonomous mobile robot in real-time is presented and evaluated on a mobile robotics platform. The control strategy uses optimal switching surfaces for when to switch between different modes of operations (behaviors).

Abubakr Muhammad (Ph.D. Fall 2005)
Thesis: Graphs, Simplicial Complexes and Beyond: Topological Tools for Multi-agent Coordination
Abstract: In this work, connectivity graphs have been studied as models of local interactions in multi-agent robotic systems. A systematic study of the space of connectivity graphs has been done from a geometric and topological point of view. Some results on the realization of connectivity graphs in their respective configuration spaces have been given. A complexity analysis of networks, from the point of view of intrinsic structural complexity, has been given. Various topological spaces in networks, as induced from their connectivity graphs, have been recognized and put into applications, such as those concerning coverage problems in sensor networks. A framework for studying dynamic connectivity graphs has been proposed. This framework has been used for several applications that include the generation of low-complexity formations as well as collaborative beamforming in sensor networks. The theory has been verified by generating extensive simulations, with the help of software tools of computational homology and semi-definite programming. Finally, several open problems and areas of further research have been identified.

Mohamed Babaali (Ph.D. Spring 2004)
Thesis: Switched Linear Systems: Observability and Observers
Abstract: Switched linear systems have long been subject to high interest and intense research efforts, not only because many real world systems happen to exhibit switching behaviors, but also because the control of many complex systems is only possible via the combination of classical continuous control laws with supervisory switching logic. A particularly important problem is that of estimator and observer design, since the state of a system is usually only available through partial, often noise-corrupted, measurements. Even though hybrid estimation has been around for at least thirty years, a veil of mystery has surrounded the concept of ``observability' in switched linear systems. It is not until recently, with the recent renewal of interest toward deterministic hybrid systems, that observer design and observability analysis have fuelled sustained research efforts. It is in this context that this work is grounded. More precisely, the objective of this research is twofold: - To define proper concepts of observability in discrete-time switched linear systems, to characterize them, and to analyze their main properties, among which decidability is of special importance. - To propose and analyze observers - deadbeat and asymptotic - for such systems. The main contributions of this dissertation are as follows. It is shown that pathwise observability, i.e. state observability under arbitrary mode sequences, is decidable. Furthermore, the Kalman-Bertram sampling criterion is carried over to switched linear systems. Under unknown modes, mode and state observability are both characterized through simple linear algebraic tests, and are shown to be decidable in the autonomous case. As for asymptotic observers, a direct algebraic approach is proposed for the class of linear systems subjected to switching in the measurement equation.

Leandro Barajas (Ph.D. Spring 2003)
Thesis: Process Control in High-noise Environments Using a Limited Number of Measurements
Abstract: The topic of this dissertation is the derviation, development, and evaluation of novel hybrid algorithms for process control that use a limited number of measurements and that are suitable to operate in the presence of large amounts of process noise. As an initial step, affine and neural network statistical process models are developed in order to simulate the steady-state system behavior. Such models are vitally important in the evaluation, testing, and improvement of all other process controllers referred to in this work. Afterwards, fuzzy logic controller rules are assimilated into a mathematical characterization of a model that includes the modes and mode transition rules that define a hybrid hierarchical process controller. The main processing entity in such a framework is a closed-loop control algorithm that performas global and then local optimizations in order to asymptotically reach minimum bias error; this is done while requiring a minimum number of iterations in order to promptly reach a desired operational windwow. The results of this research are applied to surface mount technology manufacturing-lines yield optimization. This work achieves a practical degree of control over the solder-paste volume deposition in the Stencil Printing Process (SPP). Results show that it is possible to change the operating point of the process by modifying certain machine parameters and even compensate for the difference in height due to change in print direction.

Former M.S. Students
Marius Oei (M.S. Summer 2016)
Valentin Trimaille (M.S. Summer 2015)
Matthew Rice (M.S. Spring 2015)
Sung Lee (M.S. Spring 2014)
Paul Bartholomy (M.S. Spring 2014)
Sam Ettinger (M.S. Spring 2013)
Eugene Gargas (M.S. Spring 2012)
Jeremy Shively (M.S. Spring 2012)
Daniel Pickem (M.S. Fall 2011)
Akash Verma (M.S. Fall 2011)
Edward MacDonald (M.S. Summer 2011)
Amjad Dawd (M.S. Spring 2010)
Akhil Bahl (M.S. Fall 2009)
Daniel Sinto (M.S. Spring 2009)
Jiuguang Wang (M.S. Spring 2009)
Angela Schoellig (M.S. Summer 2007)
Johan Isaksson (M.S. Spring 2006)
Lucas Osorio (M.S. Spring 2005)
Adam Austin (M.S. Spring 2003)