Distributed Algorithms for Stochastic Source Seeking With Mobile Robot Networks

Autonomous robot networks are an effective tool for monitoring large-scale environmental fields. This paper proposes distributed control strategies for localizing the source of a noisy signal, which could represent a physical quantity of interest such as magnetic force, heat, radio signal, or chemical concentration. We develop algorithms specific to two scenarios: one in which the sensors have a precise model of the signal formation process and one in which a signal model is not available. In the model-free scenario, a team of sensors is used to follow a stochastic gradient of the signal field. Our approach is distributed, robust to deformations in the group geometry, does not necessitate global localization, and is guaranteed to lead the sensors to a neighborhood of a local maximum of the field. In the model-based scenario, the sensors follow a stochastic gradient of the mutual information (MI) between their expected measurements and the expected source location in a distributed manner. The performance is demonstrated in simulation using a robot sensor network to localize the source of a wireless radio signal

Distributed multi-agent Gaussian regression via finite-dimensional approximations

We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with limited computational and communication capabilities and to gather $M$ noisy measurements in total on input locations independently drawn from a known common probability density. The optimal solution would require agents to exchange all the $M$ input locations and measurements and then invert an $M \times M$ matrix, a non-scalable task. Differently, we propose two suboptimal approaches using the first $E$ orthonormal eigenfunctions obtained from the \ac{KL} expansion of the chosen kernel, where typically $E \ll M$. The benefits are that the computation and communication complexities scale with $E$ and not with $M$, and computing the required statistics can be performed via standard average consensus algorithms. We obtain probabilistic non-asymptotic bounds that determine a priori the desired level of estimation accuracy, and new distributed strategies relying on Stein's unbiased risk estimate (SURE) paradigms for tuning the regularization parameters and applicable to generic basis functions (thus not necessarily kernel eigenfunctions) and that can again be implemented via average consensus. The proposed estimators and bounds are finally tested on both synthetic and real field data

Adaptive Sampling for Learning Gaussian Processes Using Mobile Sensor Networks

This paper presents a novel class of self-organizing sensing agents that adaptively learn an anisotropic, spatio-temporal Gaussian process using noisy measurements and move in order to improve the quality of the estimated covariance function. This approach is based on a class of anisotropic covariance functions of Gaussian processes introduced to model a broad range of spatio-temporal physical phenomena. The covariance function is assumed to be unknown a priori. Hence, it is estimated by the maximum a posteriori probability (MAP) estimator. The prediction of the field of interest is then obtained based on the MAP estimate of the covariance function. An optimal sampling strategy is proposed to minimize the information-theoretic cost function of the Fisher Information Matrix. Simulation results demonstrate the effectiveness and the adaptability of the proposed scheme

Fault-tolerant Cooperative Tasking for Multi-agent Systems

A natural way for cooperative tasking in multi-agent systems is through a top-down design by decomposing a global task into sub-tasks for each individual agent such that the accomplishments of these sub-tasks will guarantee the achievement of the global task. In our previous works [1], [2] we presented necessary and sufficient conditions on the decomposability of a global task automaton between cooperative agents. As a follow-up work, this paper deals with the robustness issues of the proposed top-down design approach with respect to event failures in the multi-agent systems. The main concern under event failure is whether a previously decomposable task can still be achieved collectively by the agents, and if not, we would like to investigate that under what conditions the global task could be robustly accomplished. This is actually the fault-tolerance issue of the top-down design, and the results provide designers with hints on which events are fragile with respect to failures, and whether redundancies are needed. The main objective of this paper is to identify necessary and sufficient conditions on failed events under which a decomposable global task can still be achieved successfully. For such a purpose, a notion called passivity is introduced to characterize the type of event failures. The passivity is found to reflect the redundancy of communication links over shared events, based on which necessary and sufficient conditions for the reliability of cooperative tasking under event failures are derived, followed by illustrative examples and remarks for the derived conditions.Comment: Preprint, Submitted for publicatio

Estimation for decentralized safety control under communication delay and measurement uncertainty

This paper addresses the design of a decentralized safety controller for two agents, subject to communication delay and imperfect measurements. The control objective is to ensure safety, meaning that the state of the two-agent system does not enter an undesired set in the state space. Assuming that we know a feedback map designed for the delay free-case, we propose a state estimation strategy which guarantees control agreement between the two agents. We present an estimation technique for bounded communication delays, assuming that the agents share the same internal clock, and extend it for infinitely-distributed communication delays by determining a lower bound for the probability of safety. We also explain how the proposed approach can be extended to a general system of N agents and discuss efficient computation of our estimation strategy. Performance of the controller and relevance of the proposed approach are discussed in light of simulations performed for a collision avoidance problem between two semi-autonomous vehicles at an intersection. Keywords: Multi-agent systems; Communication delay; Estimation/prediction approaches; Safety contro

Chemical source localization fusing concentration information in the presence of chemical background noise

We present the estimation of a likelihood map for the location of the source of a chemical plume dispersed under atmospheric turbulence under uniform wind conditions. The main contribution of this work is to extend previous proposals based on Bayesian inference with binary detections to the use of concentration information while at the same time being robust against the presence of background chemical noise. For that, the algorithm builds a background model with robust statistics measurements to assess the posterior probability that a given chemical concentration reading comes from the background or from a source emitting at a distance with a specific release rate. In addition, our algorithm allows multiple mobile gas sensors to be used. Ten realistic simulations and ten real data experiments are used for evaluation purposes. For the simulations, we have supposed that sensors are mounted on cars which do not have among its main tasks navigating toward the source. To collect the real dataset, a special arena with induced wind is built, and an autonomous vehicle equipped with several sensors, including a photo ionization detector (PID) for sensing chemical concentration, is used. Simulation results show that our algorithm, provides a better estimation of the source location even for a low background level that benefits the performance of binary version. The improvement is clear for the synthetic data while for real data the estimation is only slightly better, probably because our exploration arena is not able to provide uniform wind conditions. Finally, an estimation of the computational cost of the algorithmic proposal is presente