When designing swarm-robotic systems, systematic comparison of algorithms from different domains is necessary to determine which is capable of scaling up to handle the target problem size and target operating conditions. We propose a set of quantitative metrics for scalability, flexibility, and emergence which are capable of addressing these needs during the system design process. We demonstrate the applicability of our proposed metrics as a design tool by solving a large object gathering problem in temporally varying operating conditions using iterative hypothesis evaluation. We provide experimental results obtained in simulation for swarms of over 10,000 robots.
In recent years, many theoretical SR system design tools have become available @cite_22 @cite_9 @cite_8 @cite_14 . These tools have made it easier to conduct mathematical analysis of algorithms and derive analytical, rather than weakly inductive proofs of correctness @cite_25 . Despite this, there has not been a corresponding increase in the average swarm sizes used to evaluate new algorithms (Notable exceptions include @cite_8 (600 robots), @cite_11 (768 robots), @cite_7 (375 robots)). Investigation of simple behaviors such as pattern formation, localization, or collective motion, where design and computational complexity do not inherently limit scalability, is generally evaluated with relatively small scales ( robots @cite_25 ). Methods for more complex behaviors, such as foraging @cite_19 @cite_1 (20 robots), @cite_26 (30 robots), task allocation @cite_9 (25 robots) are likewise tested at similar scales.
@cite_14 @cite_26 @cite_22 @cite_7 @cite_8 @cite_9 @cite_1 @cite_19 @cite_25 @cite_11
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Distributed algorithms for multi-robot 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 multi-robot 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 multi-robot application and computational model, propose a set of complexity metrics to evaluate distributed algorithm performance on multi-robot 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 multi-hop communication. The robot speed ratio captures key relationships between communications bandwidth, mobility, and algorithm accuracy, and can be used at design time to trade off between them. I use this speed ratio to evaluate the performance of existing distributed algorithms for multi-hop communication and navigation. Second, I present a definition of boundaries in multi-robot systems, and develop new distributed algorithms to detect and characterize them. Finally, I define the problem of dynamic task assignment, and present four distributed algorithms that solve this problem, each representing a different trade-off between accuracy, running time, and communication resources. All the algorithms presented in this work are provably correct under ideal conditions and produce verifiable real-world performance. They are self-stabilizing and robust to communications failures, population changes, and other errors. All the algorithms were tested on a swarm of 112 robots. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.) As robots begin to collaborate with humans in everyday workspaces, they will need to understand the functions of tools and their parts. To cut an apple or hammer a nail, robots need to not just know the tool's name, but they must localize the tool's parts and identify their functions. Intuitively, the geometry of a part is closely related to its possible functions, or its affordances. Therefore, we propose two approaches for learning affordances from local shape and geometry primitives: 1) superpixel based hierarchical matching pursuit (S-HMP); and 2) structured random forests (SRF). Moreover, since a part can be used in many ways, we introduce a large RGB-Depth dataset where tool parts are labeled with multiple affordances and their relative rankings. With ranked affordances, we evaluate the proposed methods on 3 cluttered scenes and over 105 kitchen, workshop and garden tools, using ranked correlation and a weighted F-measure score [26]. Experimental results over sequences containing clutter, occlusions, and viewpoint changes show that the approaches return precise predictions that could be used by a robot. S-HMP achieves high accuracy but at a significant computational cost, while SRF provides slightly less accurate predictions but in real-time. Finally, we validate the effectiveness of our approaches on the Cornell Grasping Dataset [25] for detecting graspable regions, and achieve state-of-the-art performance. We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots evolving in a discrete space with a finite number of locations (here, a ring). A large number of algorithms have been proposed working for rings whose size is not a priori fixed and can be hence considered as a parameter. Handmade correctness proofs of these algorithms have been shown to be error-prone, and recent attention had been given to the application of formal methods to automatically prove those. Our work is the first to study the verification problem of such algorithms in the parameterized case. We show that safety and reachability problems are undecidable for robots evolving asynchronously. On the positive side, we show that safety properties are decidable in the synchronous case, as well as in the asynchronous case for a particular class of algorithms. Several properties on the protocol can be decided as well. Decision procedures rely on an encoding in Presburger arithmetics formulae that can be verified by an SMT-solver. Feasibility of our approach is demonstrated by the encoding of several case studies. Swarms of mobile robots recently attracted the focus of the Distributed Computing community. One of the fundamental problems in this context is that of exploration: the robots must coordinate to visit all locations that are reachable from their initial positions. Despite its apparent simplicity, this problem proved quite hard to characterise fully, due to many model variants, leading to informal error-prone reasoning. Over the past few years, a significant effort permitted to set up a formal framework, relying on the Coq proof assistant, which was used to provide certified results when robots evolve in a continuous bi-dimensional Euclidean space. However, the most challenging issues with exploration arise in the discrete setting (a.k.a. graph), where locations are modeled as vertices and where edges between vertices denote the ability for a robot to move from one location to the next. We present a formal model to tackle problems and reason about robot algorithms arising in the discrete setting. Our approach extends and generalises previous research efforts focusing on the continuous model. As case studies, we consider fundamental impossibility results for exploration with stop in the discrete model. To our knowledge, those are the first certified results in this context. This framework paves the way for a general certification workflow dedicated to mobile robots on graphs.