Robust Environmental Mapping by Mobile Sensor Networks

Constructing a spatial map of environmental parameters is a crucial step to preventing hazardous chemical leakages, forest fires, or while estimating a spatially distributed physical quantities such as terrain elevation. Although prior methods can do such mapping tasks efficiently via dispatching a group of autonomous agents, they are unable to ensure satisfactory convergence to the underlying ground truth distribution in a decentralized manner when any of the agents fail. Since the types of agents utilized to perform such mapping are typically inexpensive and prone to failure, this results in poor overall mapping performance in real-world applications, which can in certain cases endanger human safety. This paper presents a Bayesian approach for robust spatial mapping of environmental parameters by deploying a group of mobile robots capable of ad-hoc communication equipped with short-range sensors in the presence of hardware failures. Our approach first utilizes a variant of the Voronoi diagram to partition the region to be mapped into disjoint regions that are each associated with at least one robot. These robots are then deployed in a decentralized manner to maximize the likelihood that at least one robot detects every target in their associated region despite a non-zero probability of failure. A suite of simulation results is presented to demonstrate the effectiveness and robustness of the proposed method when compared to existing techniques.Comment: accepted to icra 201

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations

Distributing the Kalman Filter for Large-Scale Systems

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional, where $n_l\ll n$) sub-systems that are obtained after spatially decomposing the large-scale system. The resulting sub-systems overlap, which along with an assimilation procedure on the local Kalman filters, preserve an $L$th order Gauss-Markovian structure of the centralized error processes. The information loss due to the $L$th order Gauss-Markovian approximation is controllable as it can be characterized by a divergence that decreases as $L\uparrow$. The order of the approximation, $L$, leads to a lower bound on the dimension of the sub-systems, hence, providing a criterion for sub-system selection. The assimilation procedure is carried out on the local error covariances with a distributed iterate collapse inversion (DICI) algorithm that we introduce. The DICI algorithm computes the (approximated) centralized Riccati and Lyapunov equations iteratively with only local communication and low-order computation. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter that is coherent with the centralized Kalman filter with an $L$th order Gaussian-Markovian structure on the centralized error processes. Nowhere storage, communication, or computation of $n-$dimensional vectors and matrices is needed; only $n_l \ll n$ dimensional vectors and matrices are communicated or used in the computation at the sensors

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Consensus-based control for a network of diffusion PDEs with boundary local interaction

In this paper the problem of driving the state of a network of identical agents, modeled by boundary-controlled heat equations, towards a common steady-state profile is addressed. Decentralized consensus protocols are proposed to address two distinct problems. The first problem is that of steering the states of all agents towards the same constant steady-state profile which corresponds to the spatial average of the agents initial condition. A linear local interaction rule addressing this requirement is given. The second problem deals with the case where the controlled boundaries of the agents dynamics are corrupted by additive persistent disturbances. To achieve synchronization between agents, while completely rejecting the effect of the boundary disturbances, a nonlinear sliding-mode based consensus protocol is proposed. Performance of the proposed local interaction rules are analyzed by applying a Lyapunov-based approach. Simulation results are presented to support the effectiveness of the proposed algorithms

Distributed Adaptive Learning of Graph Signals

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201

A Scalable Information Theoretic Approach to Distributed Robot Coordination

This paper presents a scalable information theoretic approach to infer the state of an environment by distributively controlling robots equipped with sensors. The robots iteratively estimate the environment state using a recursive Bayesian filter, while continuously moving to improve the quality of the estimate by following the gradient of mutual information. Both the filter and the controller use a novel algorithm for approximating the robots' joint measurement probabilities, which combines consensus (for decentralization) and sampling (for scalability). The approximations are shown to approach the true joint measurement probabilities as the size of the consensus rounds grows or as the network becomes complete. The resulting gradient controller runs in constant time with respect to the number of robots, and linear time with respect to the number of sensor measurements and environment discretization cells, while traditional mutual information methods are exponential in all of these quantities. Furthermore, the controller is proven to be convergent between consensus rounds and, under certain conditions, is locally optimal. The complete distributed inference and coordination algorithm is demonstrated in experiments with five quad-rotor flying robots and simulations with 100 robots.This work is sponsored by the Department of the Air Force under Air Force contract number FA8721-05-C-0002. The opinions, interpretations, recommendations, and conclusions are those of the authors and are not necessarily endorsed by the United States Government. This work is also supported in part by ARO grant number W911NF-05-1-0219, ONR grant number N00014-09-1-1051, NSF grant number EFRI-0735953, ARL grant number W911NF-08-2-0004, MIT Lincoln Laboratory, the European Commission, and the Boeing Company