arXiv subjects

Stacy Patterson

Publications and source records attributed to Stacy Patterson.

50 records · Page 3Linked to original sources

arXiv2017

A Resistance Distance-Based Approach for Optimal Leader Selection in Noisy Consensus Networks

We study the performance of leader-follower noisy consensus networks, and in particular, the relationship between this performance and the locations of the leader nodes. Two types of dynamics are considered (1) noise-free leaders, in which leaders dictate the trajectory exactly and followers are subject to external disturbances, and (2) noise-corrupted leaders, in which both leaders and followers are subject to external perturbations. We measure the performance of a network by its coherence, an $H_2$ norm that quantifies how closely the followers track the leaders' trajectory. For both dynamics, we show a relationship between the coherence and resistance distances in an a electrical network. Using this relationship, we derive closed-form expressions for coherence as a function of the locations of the leaders. Further, we give analytical solutions to the optimal leader selection problem for several special classes of graphs.

math.OC↗

arXiv2017

Compressed Sensing for Scalable Robotic Tactile Skins

The potential of large tactile arrays to improve robot perception for safe operation in human-dominated environments and of high-resolution tactile arrays to enable human-level dexterous manipulation is well accepted. However, the increase in the number of tactile sensing elements introduces challenges including wiring complexity, data acquisition, and data processing. To help address these challenges, we develop a tactile sensing technique based on compressed sensing. Compressed sensing simultaneously performs data sampling and compression with recovery guarantees and has been successfully applied in computer vision. We use compressed sensing techniques for tactile data acquisition to reduce hardware complexity and data transmission, while allowing fast, accurate reconstruction of the full-resolution signal. For our simulated test array of 4096 taxels, we achieve reconstruction quality equivalent to measuring all taxel signals independently (the full signal) from just 1024 measurements (the compressed signal) at a rate over 100Hz. We then apply tactile compressed sensing to the problem of object classification. Specifically, we perform object classification on the compressed tactile data based on a method called compressed learning. We obtain up to 98% classification accuracy, even with a compression ratio of 64:1.

cs.RO↗

arXiv2017

Optimizing the Coherence of Composite Networks

We consider how to connect a set of disjoint networks to optimize the performance of the resulting composite network. We quantify this performance by the coherence of the composite network, which is defined by an $H_2$ norm of the system. Two dynamics are considered: noisy consensus dynamics with and without stubborn agents. For noisy consensus dynamics without stubborn agents, we derive analytical expressions for the coherence of composite networks in terms of the coherence of the individual networks and the structure of their interconnections. We also identify optimal interconnection topologies and give bounds on coherence for general composite graphs. For noisy consensus dynamics with stubborn agents, we develop a non-combinatorial algorithm that identifies connecting edges such that the composite network coherence closely approximates the performance of the optimal composite graph.

math.OC↗

arXiv2016

Compressed Learning for Tactile Object Classification

The potential of large tactile arrays to improve robot perception for safe operation in human-dominated environments and of high-resolution tactile arrays to enable human-level dexterous manipulation is well accepted. However, the increase in the number of tactile sensing elements introduces challenges including wiring complexity, power consumption, and data processing. To help address these challenges, we previously developed a tactile sensing technique based compressed sensing that reduces hardware complexity and data transmission, while allowing accurate reconstruction of the full-resolution signal. In this paper, we apply tactile compressed sensing to the problem of object classification. Specifically, we perform object classification on the compressed tactile data. We evaluate our method using BubbleTouch, our tactile array simulator. Our results show our approach achieves high classification accuracy, even with compression factors up to 64.

cs.RO↗

arXiv2016

Optimal k-Leader Selection for Coherence and Convergence Rate in One-Dimensional Networks

We study the problem of optimal leader selection in consensus networks under two performance measures (1) formation coherence when subject to additive perturbations, as quantified by the steady-state variance of the deviation from the desired trajectory, and (2) convergence rate to a consensus value. The objective is to identify the set of $k$ leaders that optimizes the chosen performance measure. In both cases, an optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the $k$-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the $k$-leader selection problem can be solved in polynomial time (in both $k$ and the network size $n$). We give an $O(n^3)$ solution for optimal $k$-leader selection in path graphs and an $O(kn^3)$ solution for optimal $k$-leader selection in ring graphs.

math.OC↗

arXiv2016

Distributed Semi-Stochastic Optimization with Quantization Refinement

We consider the problem of regularized regression in a network of communication-constrained devices. Each node has local data and objectives, and the goal is for the nodes to optimize a global objective. We develop a distributed optimization algorithm that is based on recent work on semi-stochastic proximal gradient methods. Our algorithm employs iteratively refined quantization to limit message size. We present theoretical analysis and conditions for the algorithm to achieve a linear convergence rate. Finally, we demonstrate the performance of our algorithm through numerical simulations.

math.OC↗

arXiv2016

Compressed Sensing for Tactile Skins

Whole body tactile perception via tactile skins offers large benefits for robots in unstructured environments. To fully realize this benefit, tactile systems must support real-time data acquisition over a massive number of tactile sensor elements. We present a novel approach for scalable tactile data acquisition using compressed sensing. We first demonstrate that the tactile data is amenable to compressed sensing techniques. We then develop a solution for fast data sampling, compression, and reconstruction that is suited for tactile system hardware and has potential for reducing the wiring complexity. Finally, we evaluate the performance of our technique on simulated tactile sensor networks. Our evaluations show that compressed sensing, with a compression ratio of 3 to 1, can achieve higher signal acquisition accuracy than full data acquisition of noisy sensor data.

cs.RO↗

arXiv2014

Efficient, Optimal $k$-Leader Selection for Coherent, One-Dimensional Formations

We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of $k$ leaders that minimizes the formation's deviation from the desired trajectory established by the leaders. An optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the $k$-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the $k$-leader selection problem can be solved in polynomial time (in both $k$ and the network size $n$). We give an $O(n^3)$ solution for optimal $k$-leader selection in path graphs and an $O(kn^3)$ solution for optimal $k$-leader selection in ring graphs.

math.OC↗

arXiv2014

In-Network Leader Selection for Acyclic Graphs

We study the problem of leader selection in leader-follower multi-agent systems that are subject to stochastic disturbances. This problem arises in applications such as vehicle formation control, distributed clock synchronization, and distributed localization in sensor networks. We pose a new leader selection problem called the in-network leader selection problem. Initially, an arbitrary node is selected to be a leader, and in all consequent steps the network must have exactly one leader. The agents must collaborate to find the leader that minimizes the variance of the deviation from the desired trajectory, and they must do so within the network using only communication between neighbors. To develop a solution for this problem, we first show a connection between the leader selection problem and a class of discrete facility location problems. We then leverage a previously proposed self-stabilizing facility location algorithm to develop a self-stabilizing in-network leader selection algorithm for acyclic graphs.

math.OC↗

arXiv2014

Distributed Compressed Sensing For Static and Time-Varying Networks

We consider the problem of in-network compressed sensing from distributed measurements. Every agent has a set of measurements of a signal $x$, and the objective is for the agents to recover $x$ from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from distributed computing to execute in-network computations with minimized bandwidth consumption. Next, we address distributed signal recovery in networks with time-varying topologies. The network dynamics necessarily introduce inaccuracies to our in-network computations. To accommodate these inaccuracies, we show how centralized IHT can be extended to include inexact computations while still providing the same recovery guarantees as the original IHT algorithm. We then leverage these new theoretical results to develop a distributed version of IHT for time-varying networks. Evaluations show that our distributed algorithms for both static and time-varying networks outperform previously proposed solutions in time and bandwidth by several orders of magnitude.

cs.IT↗

arXiv2013

Consensus and Coherence in Fractal Networks

We consider first and second order consensus algorithms in networks with stochastic disturbances. We quantify the deviation from consensus using the notion of network coherence, which can be expressed as an $H_2$ norm of the stochastic system. We use the setting of fractal networks to investigate the question of whether a purely topological measure, such as the fractal dimension, can capture the asymptotics of coherence in the large system size limit. Our analysis for first-order systems is facilitated by connections between first-order stochastic consensus and the global mean first passage time of random walks. We then show how to apply similar techniques to analyze second-order stochastic consensus systems. Our analysis reveals that two networks with the same fractal dimension can exhibit different asymptotic scalings for network coherence. Thus, this topological characterization of the network does not uniquely determine coherence behavior. The question of whether the performance of stochastic consensus algorithms in large networks can be captured by purely topological measures, such as the spatial dimension, remains open.

eess.SY↗

arXiv2013

Distributed Sparse Signal Recovery For Sensor Networks

We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements at a minimal communication cost and with low computational complexity. A naive distributed implementation of IHT would require global communication of every agent's full state in each iteration. We find that we can dramatically reduce this communication cost by leveraging solutions to the distributed top-K problem in the database literature. Evaluations show that our algorithm requires up to three orders of magnitude less total bandwidth than the best-known distributed basis pursuit method.

cs.IT↗

arXiv2012

Serializability, not Serial: Concurrency Control and Availability in Multi-Datacenter Datastores

We present a framework for concurrency control and availability in multi-datacenter datastores. While we consider Google's Megastore as our motivating example, we define general abstractions for key components, making our solution extensible to any system that satisfies the abstraction properties. We first develop and analyze a transaction management and replication protocol based on a straightforward implementation of the Paxos algorithm. Our investigation reveals that this protocol acts as a concurrency prevention mechanism rather than a concurrency control mechanism. We then propose an enhanced protocol called Paxos with Combination and Promotion (Paxos-CP) that provides true transaction concurrency while requiring the same per instance message complexity as the basic Paxos protocol. Finally, we compare the performance of Paxos and Paxos-CP in a multi-datacenter experimental study, and we demonstrate that Paxos-CP results in significantly fewer aborted transactions than basic Paxos.

cs.DB↗

arXiv2011

Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

math.OC↗