Nonuniform Coverage Control on the Line

This paper investigates control laws allowing mobile, autonomous agents to optimally position themselves on the line for distributed sensing in a nonuniform field. We show that a simple static control law, based only on local measurements of the field by each agent, drives the agents close to the optimal positions after the agents execute in parallel a number of sensing/movement/computation rounds that is essentially quadratic in the number of agents. Further, we exhibit a dynamic control law which, under slightly stronger assumptions on the capabilities and knowledge of each agent, drives the agents close to the optimal positions after the agents execute in parallel a number of sensing/communication/computation/movement rounds that is essentially linear in the number of agents. Crucially, both algorithms are fully distributed and robust to unpredictable loss and addition of agents

Multi-Agent Coverage Control with Energy Depletion and Repletion

We develop a hybrid system model to describe the behavior of multiple agents cooperatively solving an optimal coverage problem under energy depletion and repletion constraints. The model captures the controlled switching of agents between coverage (when energy is depleted) and battery charging (when energy is replenished) modes. It guarantees the feasibility of the coverage problem by defining a guard function on each agent's battery level to prevent it from dying on its way to a charging station. The charging station plays the role of a centralized scheduler to solve the contention problem of agents competing for the only charging resource in the mission space. The optimal coverage problem is transformed into a parametric optimization problem to determine an optimal recharging policy. This problem is solved through the use of Infinitesimal Perturbation Analysis (IPA), with simulation results showing that a full recharging policy is optimal

Coverage and Field Estimation on Bounded Domains by Diffusive Swarms

In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusion-based control strategy using standard operator semigroup-theoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016

Optimal one-dimensional coverage by unreliable sensors

This paper regards the problem of optimally placing unreliable sensors in a one-dimensional environment. We assume that sensors can fail with a certain probability and we minimize the expected maximum distance from any point in the environment to the closest active sensor. We provide a computational method to find the optimal placement and we estimate the relative quality of equispaced and random placements. We prove that the former is asymptotically equivalent to the optimal placement when the number of sensors goes to infinity, with a cost ratio converging to 1, while the cost of the latter remains strictly larger.Comment: 21 pages 2 figure

Implementation of distributed partitioning algorithms using mobile Wheelphones

This thesis presents the implementation process of partitioning algorithms from the theorical ideas to sperimental result

EFFICIENT PARAMETRIC AND NON-PARAMETRICLOCALIZATION AND MAPPING IN ROBOTIC NETWORKS

Since the eighties localization and mapping problems have attracted the efforts of robotics researchers. However in the last decade, thanks to the increasing capabilities of the new electronic devices, many new related challenges have been posed, such as swarm robotics, aerial vehicles, autonomous cars and robotics networks. Efficiency, robustness and scalability play a key role in these scenarios. Efficiency is intended as an ability for an application to minimize the resources usage, in particular CPU time and memory space. In the aforementioned applications an underlying communication network is required so, for robustness we mean asynchronous algorithms resilient to delays and packet-losses. Finally scalability is the ability of an application to continue functioning without any dramatic performance degradation even if the number of devices involved keep increasing. In this thesis the interest is focused on parametric and non-parametric estimation algorithms ap- plied to localization and mapping in robotics. The main contribution can be summarized in the following four arguments: (i) Consensus-based localization We address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors by means of only local communication and bounded complexity, independent of network size and topology. In particular we propose a consensus-based algorithm with the use of local memory variables which allows asynchronous implementation, has guaranteed exponential convergence to the optimal solution under simple deterministic and randomized communication protocols, and requires minimal packet transmission. In the randomized scenario, we then study the rate of convergence in expectation of the estimation error and we argue that it can be used to obtain upper and lower bound for the rate of converge in mean square. In particular, we show that for regular graphs, such as Cayley, Ramanujan, and complete graphs, the convergence rate in expectation has the same asymptotic degradation of memoryless asynchronous consensus algorithms in terms of network size. In addition, we show that the asynchronous implementation is also robust to delays and communication failures. We finally complement the analytical results with some numerical simulations, comparing the proposed strategy with other algorithms which have been recently proposed in the literature. (ii) Aerial Vehicles distributed localization: We study the problem of distributed multi- agent localization in presence of heterogeneous measurements and wireless communication. The proposed algorithm integrates low precision global sensors, like GPS and compasses, with more precise relative position (i.e., range plus bearing) sensors. Global sensors are used to reconstruct the absolute position and orientation, while relative sensors are used to retrieve the shape of the formation. A fast distributed and asynchronous linear least-squares algorithm is proposed to solve an approximated version of the non-linear Maximum Likelihood problem. The algorithm is provably shown to be robust to communication losses and random delays. The use of ACK-less broadcast-based communication protocols ensures an efficient and easy implementation in real world scenarios. If the relative measurement errors are sufficiently small, we show that the algorithm attains a solution which is very close to the maximum likelihood solution. The theoretical findings and the algorithm performances are extensively tested by means of Monte-Carlo simulations. (iii) Estimation and Coverage: We address the problem of optimal coverage of a region via multiple robots when the sensory field used to approximate the density of event appearance is not known in advance. We address this problem in the context of a client-server architecture in which the mobile robots can communicate with a base station via a possibly unreliable wireless network subject to packet losses. Based on Gaussian regression which allows to estimate the true sensory field with any arbitrary accuracy, we propose a randomised strategy in which the robots and the base station simultaneously estimate the true sensory distribution by collecting measurements and compute the corresponding optimal Voronoi partitions. This strategy is designed to promote exploration at the beginning and then smoothly transition to station the robots at the centroid of the estimated optimal Voronoi partitions. Under mild assumptions on the transmission failure probability, we prove that the proposed strategy guarantees the convergence of the estimated sensory field to the true field and that the corresponding Voronoi partitions asymptotically becomes arbitrarily close to an optimal Voronoi partition. Additionally, we also provide numerically efficient approximation that trade-off accuracy of the estimated map for reduced memory and CPU complexity. Finally, we provide a set of extensive simulations which confirm the effectiveness of the proposed approach. (iv) Non-parametric estimation of spatio-temporal fields: We address the problem of efficiently and optimally estimating an unknown time-varying function through the collection of noisy measurements. We cast our problem in the framework of non-parametric estimation and we assume that the unknown function is generated by a Gaussian process with a known covariance. Under mild assumptions on the kernel function, we propose a solution which links the standard Gaussian regression to the Kalman filtering thanks to the exploitation of a grid where measurements collection and estimation take place. This work show an efficient in time and space method to estimate time-varying function, which combine the advantages of the Gaussian regression, e.g. model-less, and of the Kalman filter, e.g. efficiency

Nonuniform coverage control on the line

This paper investigates control laws allowing mobile, autonomous agents to optimally position themselves on the line for distributed sensing in a nonuniform field. We show that a simple static control law, based only on local measurements of the field by each agent, drives the agents to the optimal positions in time that is quadratic in the number of agents. Further, we exhibit a dynamic control law which, under slightly stronger assumptions on the capabilities and knowledge of each agent, drives the agents to the optimal positions an order of magnitude faster, namely in time that is linear in the number of agents. Both algorithms are fully distributed and robust to unpredictable loss and addition of agents. © 2011 IEEE