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15
Analysis and Implementation of Distributed algorithms for multirobot Systems
, 2008
"... Distributed algorithms for multirobot systems rely on network communications to share information. However, the motion of the robots changes the network topology, which affects the information presented to the algorithm. For an algorithm to produce accurate output, robots need to communicate rapidl ..."
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Distributed algorithms for multirobot systems rely on network communications to share information. However, the motion of the robots changes the network topology, which affects the information presented to the algorithm. For an algorithm to produce accurate output, robots need to communicate rapidly enough to keep the network topology correlated to their physical configuration. Infrequent communications will cause most multirobot distributed algorithms to produce less accurate results, and cause some algorithms to stop working altogether. The central theme of this work is that algorithm accuracy, communications bandwidth, and physical robot speed are related. This thesis has three main contributions: First, I develop a prototypical multirobot application and computational model, propose a set of complexity metrics to evaluate distributed algorithm performance on multirobot systems, and introduce the idea of the robot speed ratio, a dimensionless measure of robot speed relative to message speed in networks that rely on multihop communication. The robot speed ratio captures key relationships
Sensing and filtering: A tutorial based on preimages and information spaces. Foundations and Trends in Robotics
"... This tutorial presents a fresh perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. The guiding principle is not to sense, represent, and encode more than is necessary. The concepts and tools are motiv ..."
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Cited by 5 (3 self)
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This tutorial presents a fresh perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. The guiding principle is not to sense, represent, and encode more than is necessary. The concepts and tools are motivated by many tasks of current interest, such as tracking, monitoring, navigation, pursuitevasion, exploration, and mapping. First, an overview of sensors that appear in numerous systems is presented. Following this, the notion of a virtual sensor is explained, which provides a mathematical way to model numerous sensors while abstracting away their particular physical implementation. Dozens of useful models are given, each as a mapping from the physical world to the set of possible sensor outputs. Preimages with respect to this mapping represent a fundamental source of uncertainty: These are equivalence classes of physical states that would produce the same sensor output. Pursuing this idea further, the powerful notion of a sensor lattice is introduced, in which all possible virtual sensors can be rigorously compared. The next part introduces filters that aggregate information from multiple sensor readings. The integration of information over space and time is considered. In the spatial setting, classical triangulation methods are expressed in terms of preimages. In the temporal setting, an informationspace framework is introduced that encompasses familiar Kalman and Bayesian filters, but also introduces a novel family called combinatorial filters. Finally, the planning problem is presented in terms of filters and information spaces. The tutorial concludes with some discussion about connections to many related research fields and numerous open problems and future research directions. 1 1
Sensing and Filtering: A Fresh Perspective Based on Preimages and Information Spaces
"... This paper presents an unusual perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. Information itself is modeled using information space concepts, which originated from dynamic game theory (rather than ..."
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Cited by 3 (2 self)
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This paper presents an unusual perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. Information itself is modeled using information space concepts, which originated from dynamic game theory (rather than information theory, which was developed mainly for communication). The guiding principle in this paper is avoid sensing, representing, and encoding more than is necessary. The concepts and tools are motivated by many tasks of current interest, such as tracking, monitoring, navigation, pursuitevasion, exploration, and mapping. First, an overview of sensors that appear in numerous systems is presented. Following this, the notion of a virtual sensor is explained, which provides a mathematical way to model numerous sensors while abstracting away their particular physical implementation. Dozens of useful models are given, each as a mapping from the physical world to the set of possible sensor outputs. Preimages with respect to this mapping represent a fundamental source of uncertainty: These are equivalence classes of physical states that would produce the same sensor output. Pursuing this idea further, the powerful notion of a sensor lattice is introduced, in which all possible virtual sensors can be rigorously compared. The next part introduces filters that aggregate information from multiple sensor readings. The integration of information over space and time is considered. In the spatial setting, classical triangulation methods are expressed in terms of preimages. In the temporal setting, an informationspace framework is introduced that encompasses familiar Kalman and Bayesian filters, but also introduces a novel family called combinatorial filters. Finally, the planning problem is presented in terms of filters and information spaces. The paper concludes with some discussion about connections to many related research fields and numerous open problems and future research directions. 1 1
ScaleFree Coordinates for MultiRobot Systems with Bearingonly Sensors
"... We propose scalefree coordinates as an alternative coordinate system for multirobot systems with large robot populations. Scalefree coordinates allow each robot to know, up to scaling, the relative position and orientation of other robots in the network. We consider a weak sensing model where ea ..."
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We propose scalefree coordinates as an alternative coordinate system for multirobot systems with large robot populations. Scalefree coordinates allow each robot to know, up to scaling, the relative position and orientation of other robots in the network. We consider a weak sensing model where each robot is only capable of measuring the angle, relative to its own heading, to each of its neighbors. Our contributions are threefold. First, we derive a precise mathematical characterization of the computability of scalefree coordinates using only bearing measurements, and we describe an efficient algorithm to obtain them. Second, through simulations we show that even in graphs with low average vertex degree, most robots are able to compute the scalefree coordinates of their neighbors using only 2hop bearing measurements. Finally, we present an algorithm to compute scalefree coordinates that is tailored to lowcost systems with limited communication bandwidth and sensor resolution. Our algorithm mitigates the impact of sensing errors through a simple yet effective noise sensitivity model. We validate our implementation with realworld robot experiments using static accuracy measurements and a simple scalefree motion controller.
Dominance and equivalence for sensorbased agents
"... This paper describes recent results from the robotics community that develop a theory, similar in spirit to the theory of computation, for analyzing sensorbased agent systems. The central element to this work is a notion of dominance of one such system over another. This relation is formally based ..."
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This paper describes recent results from the robotics community that develop a theory, similar in spirit to the theory of computation, for analyzing sensorbased agent systems. The central element to this work is a notion of dominance of one such system over another. This relation is formally based on the agents ’ progression through a derived information space, but may informally be understood as describing one agent’s ability to “simulate ” another. We present some basic properties of this dominance relation and demonstrate its usefulness by applying it to a basic problem in robotics. We argue that this work is of interest to a broad audience of artificial intelligence researchers for two main reasons. First, it calls attention to the possibility of studying belief spaces in way that generalizes both probabilistic and nondeterministic uncertainty models. Second, it provides a means for evaluating the information that an agent is able to acquire (via its sensors and via conformant actions), independent of any optimality criterion and of the task to be completed.
Comparison of constrained geometric approximation strategies for planar information states
 In Proceedings of the IEEE International Conference on Robotics and Automation
, 2012
"... AbstractThis paper describes and analyzes a new technique for reasoning about uncertainty called constrained geometric approximation (CGA). We build upon recent work that has developed methods to explicitly represent a robot's knowledge as an element, called an information state, in an approp ..."
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AbstractThis paper describes and analyzes a new technique for reasoning about uncertainty called constrained geometric approximation (CGA). We build upon recent work that has developed methods to explicitly represent a robot's knowledge as an element, called an information state, in an appropriately defined information space. The intuition of our new approach is to constrain the Istate to remain in a structured subset of the Ispace, and to enforce that constraint using appropriate overapproximation methods. The result is a collection of algorithms that enable mobile robots with extreme limitations in both sensing and computation to maintain simple but provably meaningful representations of the incomplete information available to them. We present a simulated implementation of this technique for a sensorbased navigation task, along with experimental results for this task showing that CGA, compared to a highfidelity representation of the unapproximated Istate, achieves a similar success rate at a small fraction of the computational cost.
On the Topology of Plans
 WORKSHOP ON THE ALGORITHMIC FOUNDATIONS OF ROBOTICS
, 2008
"... This paper explores a topological perspective of planning. A series of examples and theorems establishes a fundamental coupling between tasks on graphs and simplicial complexes. Planning under uncertainty is one application. The paper introduces strategy and loopback complexes. The paper’s main th ..."
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Cited by 1 (1 self)
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This paper explores a topological perspective of planning. A series of examples and theorems establishes a fundamental coupling between tasks on graphs and simplicial complexes. Planning under uncertainty is one application. The paper introduces strategy and loopback complexes. The paper’s main theorem shows that tasks specified by goals in nondeterministic graphs have guaranteed solutions if and only if their loopback complexes are homotopic to spheres.
On the Topology of Discrete Strategies
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 2009
"... This paper explores a topological perspective of planning in the presence of uncertainty, focusing on tasks specified by goal states in discrete spaces. The paper introduces strategy complexes. A strategy complex is the collection of all plans for attaining all goals in a given space. Plans are like ..."
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This paper explores a topological perspective of planning in the presence of uncertainty, focusing on tasks specified by goal states in discrete spaces. The paper introduces strategy complexes. A strategy complex is the collection of all plans for attaining all goals in a given space. Plans are like jigsaw pieces. Understanding how the pieces fit together in a strategy complex reveals structure. That structure characterizes the inherent capabilities of an uncertain system. By adjusting the jigsaw pieces in a design loop, one can build systems with desired competencies. The paper draws on representations from combinatorial topology, Markov chains, and polyhedral cones. Triangulating between these three perspectives produces a topological language for describing concisely the capabilities of uncertain systems, analogous to concepts of reachability and controllability in other disciplines. The major nouns in this language are topological spaces. Three key theorems (numbered 1, 11, 20 in the paper) illustrate the sentences in this language: (a) Goal Attainability: There exists a strategy for attaining a particular goal
Local Distributed Algorithms for MultiRobot Systems
, 2012
"... The field of swarm robotics focuses on controlling large populations of simple robots to accomplish tasks more effectively than what is possible using a single robot. This thesis develops distributed algorithms tailored for multirobot systems with large populations. Specifically we focus on local d ..."
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The field of swarm robotics focuses on controlling large populations of simple robots to accomplish tasks more effectively than what is possible using a single robot. This thesis develops distributed algorithms tailored for multirobot systems with large populations. Specifically we focus on local distributed algorithms since their performance depends primarily on local parameters on the system and are guaranteed to scale with the number of robots in the system. The first part of this thesis considers and solves the problem of finding a trajectory for each robot which is guaranteed to preserve the connectivity of the communication graph, and when feasible it also guarantees the robots advance towards a goal defined by an arbitrary motion planner. We also describe how to extend our proposed approach to preserve the kconnectivity of the communication graph. Finally, we show how our connectivitypreserving algorithm can be combined with standard averaging procedures to yield a provably correct flocking algorithm. The second part of this thesis considers and solves the problem of having each
Sensor Lattices: A PreimageBased Approach to Comparing Sensors
"... Abstract — This paper addresses the sensing uncertainty associated with the manytoone mapping from a physical state space onto a sensor observation space. By studying preimages of this mapping for each sensor, a notion of sensor dominance is introduced, which enables interchangeability of sensors ..."
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Abstract — This paper addresses the sensing uncertainty associated with the manytoone mapping from a physical state space onto a sensor observation space. By studying preimages of this mapping for each sensor, a notion of sensor dominance is introduced, which enables interchangeability of sensors and a clearer understanding of their tradeoffs. The notion of a sensor lattice is also introduced, in which all possible sensor models are arranged into a hierarchy that indicates their power and gives insights into the construction of filters over time and space. I.