Centroidal area-constrained partitioning for robotic networks

We consider the problem of optimal coverage with area constraints in a mobile multi-agent system. For a planar environment with an associated density function, this problem is equivalent to dividing the environment into optimal subregions such that each agent is responsible for the coverage of its own region. In this paper, we design a continuous-time distributed policy which allows a team of agents to achieve a convex area-constrained partition of a convex workspace. Our work is related to the classic Lloyd algorithm, and makes use of generalized Voronoi diagrams. We also discuss practical implementation for real mobile networks. Simulation methods are presented and discussed

Cooperative Search by Multiple Unmanned Aerial Vehicles in a Nonconvex Environment

This paper presents a distributed cooperative search algorithm for multiple unmanned aerial vehicles (UAVs) with limited sensing and communication capabilities in a nonconvex environment. The objective is to control multiple UAVs to find several unknown targets deployed in a given region, while minimizing the expected search time and avoiding obstacles. First, an asynchronous distributed cooperative search framework is proposed by integrating the information update into the coverage control scheme. And an adaptive density function is designed based on the real-time updated probability map and uncertainty map, which can balance target detection and environment exploration. Second, in order to handle nonconvex environment with arbitrary obstacles, a new transformation method is proposed to transform the cooperative search problem in the nonconvex region into an equivalent one in the convex region. Furthermore, a control strategy for cooperative search is proposed to plan feasible trajectories for UAVs under the kinematic constraints, and the convergence is proved by LaSalle’s invariance principle. Finally, by simulation results, it can be seen that our proposed algorithm is effective to handle the search problem in the nonconvex environment and efficient to find targets in shorter time compared with other algorithms

Multi-Robot Persistent Coverage in Complex Environments

Los recientes avances en robótica móvil y un creciente desarrollo de robots móviles asequibles han impulsado numerosas investigaciones en sistemas multi-robot. La complejidad de estos sistemas reside en el diseño de estrategias de comunicación, coordinación y controlpara llevar a cabo tareas complejas que un único robot no puede realizar. Una tarea particularmente interesante es la cobertura persistente, que pretende mantener cubierto en el tiempo un entorno con un equipo de robots moviles. Este problema tiene muchas aplicaciones como aspiración o limpieza de lugares en los que la suciedad se acumula constantemente, corte de césped o monitorización ambiental. Además, la aparición de vehículos aéreos no tripulados amplía estas aplicaciones con otras como la vigilancia o el rescate.Esta tesis se centra en el problema de cubrir persistentemente entornos progresivamente mas complejos. En primer lugar, proponemos una solución óptima para un entorno convexo con un sistema centralizado, utilizando programación dinámica en un horizonte temporalnito. Posteriormente nos centramos en soluciones distribuidas, que son más robustas, escalables y eficientes. Para solventar la falta de información global, presentamos un algoritmo de estimación distribuido con comunicaciones reducidas. Éste permite a los robots teneruna estimación precisa de la cobertura incluso cuando no intercambian información con todos los miembros del equipo. Usando esta estimación, proponemos dos soluciones diferentes basadas en objetivos de cobertura, que son los puntos del entorno en los que más se puedemejorar dicha cobertura. El primer método es un controlador del movimiento que combina un término de gradiente con un término que dirige a los robots hacia sus objetivos. Este método funciona bien en entornos convexos. Para entornos con algunos obstáculos, el segundométodo planifica trayectorias abiertas hasta los objetivos, que son óptimas en términos de cobertura. Finalmente, para entornos complejos no convexos, presentamos un algoritmo capaz de encontrar particiones equitativas para los robots. En dichas regiones, cada robotplanifica trayectorias de longitud finita a través de un grafo de caminos de tipo barrido.La parte final de la tesis se centra en entornos discretos, en los que únicamente un conjunto finito de puntos debe que ser cubierto. Proponemos una estrategia que reduce la complejidad del problema separándolo en tres subproblemas: planificación de trayectoriascerradas, cálculo de tiempos y acciones de cobertura y generación de un plan de equipo sin colisiones. Estos subproblemas más pequeños se resuelven de manera óptima. Esta solución se utiliza en último lugar para una novedosa aplicación como es el calentamiento por inducción doméstico con inductores móviles. En concreto, la adaptamos a las particularidades de una cocina de inducción y mostramos su buen funcionamiento en un prototipo real.Recent advances in mobile robotics and an increasing development of aordable autonomous mobile robots have motivated an extensive research in multi-robot systems. The complexity of these systems resides in the design of communication, coordination and control strategies to perform complex tasks that a single robot can not. A particularly interesting task is that of persistent coverage, that aims to maintain covered over time a given environment with a team of robotic agents. This problem is of interest in many applications such as vacuuming, cleaning a place where dust is continuously settling, lawn mowing or environmental monitoring. More recently, the apparition of useful unmanned aerial vehicles (UAVs) has encouraged the application of the coverage problem to surveillance and monitoring. This thesis focuses on the problem of persistently covering a continuous environment in increasingly more dicult settings. At rst, we propose a receding-horizon optimal solution for a centralized system in a convex environment using dynamic programming. Then we look for distributed solutions, which are more robust, scalable and ecient. To deal with the lack of global information, we present a communication-eective distributed estimation algorithm that allows the robots to have an accurate estimate of the coverage of the environment even when they can not exchange information with all the members of the team. Using this estimation, we propose two dierent solutions based on coverage goals, which are the points of the environment in which the coverage can be improved the most. The rst method is a motion controller, that combines a gradient term with a term that drives the robots to the goals, and which performs well in convex environments. For environments with some obstacles, the second method plans open paths to the goals that are optimal in terms of coverage. Finally, for complex, non-convex environments we propose a distributed algorithm to nd equitable partitions for the robots, i.e., with an amount of work proportional to their capabilities. To cover this region, each robot plans optimal, nite-horizon paths through a graph of sweep-like paths. The nal part of the thesis is devoted to discrete environment, in which only a nite set of points has to be covered. We propose a divide-and-conquer strategy to separate the problem to reduce its complexity into three smaller subproblem, which can be optimally solved. We rst plan closed paths through the points, then calculate the optimal coverage times and actions to periodically satisfy the coverage required by the points, and nally join together the individual plans of the robots into a collision-free team plan that minimizes simultaneous motions. This solution is eventually used for a novel application that is domestic induction heating with mobile inductors. We adapt it to the particular setting of a domestic hob and demonstrate that it performs really well in a real prototype.<br /

Geometric partitioning algorithms for fair division of geographic resources

University of Minnesota Ph.D. dissertation. July 2014. Major: Industrial and Systems Engineering. Advisor: John Gunnar Carlsson. 1 computer file (PDF): vi, 140 pages, appendices p. 129-140.This dissertation focuses on a fundamental but under-researched problem: how does one divide a piece of territory into smaller pieces in an efficient way? In particular, we are interested in \emph{map segmentation problem} of partitioning a geographic region into smaller subregions for allocating resources or distributing a workload among multiple agents. This work would result in useful solutions for a variety of fundamental problems, ranging from congressional districting, facility location, and supply chain management to air traffic control and vehicle routing. In a typical map segmentation problem, we are given a geographic region $R$, a probability density function defined on $R$ (representing, say population density, distribution of a natural resource, or locations of clients) and a set of points in $R$ (representing, say service facilities or vehicle depots). We seek a \emph{partition} of $R$ that is a collection of disjoint sub-regions $\{R_1, . . . , R_n\}$ such that $\bigcup_i R_i = R$, that optimizes some objective function while satisfying a shape condition. As examples of shape conditions, we may require that all sub-regions be compact, convex, star convex, simply connected (not having holes), connected, or merely measurable.Such problems are difficult because the search space is infinite-dimensional (since we are designing boundaries between sub-regions) and because the shape conditions are generally difficult to enforce using standard optimization methods. There are also many interesting variants and extensions to this problem. It is often the case that the optimal partition for a problem changes over time as new information about the region is collected. In that case, we have an \emph{online} problem and we must re-draw the sub-region boundaries as time progresses. In addition, we often prefer to construct these sub-regions in a \emph{decentralized} fashion: that is, the sub-region assigned to agent $i$ should be computable using only local information to agent $i$ (such as nearby neighbors or information about its surroundings), and the optimal boundary between two sub-regions should be computable using only knowledge available to those two agents.This dissertation is an attempt to design geometric algorithms aiming to solve the above mentioned problems keeping in view the various design constraints. We describe the drawbacks of the current approach to solving map segmentation problems, its ineffectiveness to impose geometric shape conditions and its limited utility in solving the online version of the problem. Using an intrinsically interdisciplinary approach, combining elements from variational calculus, computational geometry, geometric probability theory, and vector space optimization, we present an approach where we formulate the problems geometrically and then use a fast geometric algorithm to solve them. We demonstrate our success by solving problems having a particular choice of objective function and enforcing certain shape conditions. In fact, it turns out that such methods actually give useful insights and algorithms into classical location problems such as the continuous $k$-medians problem, where the aim is to find optimal locations for facilities. We use a map segmentation technique to present a constant factor approximation algorithm to solve the continuous $k$-medians problem in a convex polygon. We conclude this thesis by describing how we intend to build on this success and develop algorithms to solve larger classes of these problems

Multi-robot Coverage and Redeployment Algorithms

In this thesis, we focus on two classes of multi-robot task allocation and deployment problems motivated by applications in ride-sourcing transportation networks and service robots: 1) coverage control with multiple robots, and 2) robots servicing tasks arriving sequentially over time. The first problem considers the deployment of multiple robots to cover a domain. The multi-robot problem consists of multiple robots with sensors on-board observing the spatially distributed events in an environment. The objective is to maximize the sensing quality of the events via optimally distributing the robots in the environment. This problem has been studied extensively in the literature and several algorithms have been proposed for different variants of this problem. However, there has been a lack of theoretical results on the quality of the solutions provided by these algorithms. In this thesis, we provide a new distributed multi-robot coverage algorithm with theoretical guarantees on the solution quality, run-time complexity, and communication complexity. The theoretical bound on the solution quality holds for on-board sensors where the sensing quality of the sensors is a sub-additive function of the distance to the event location in convex and non-convex environments. A natural extension of the multi-robot coverage control problem is considered in this thesis where each robot is equipped with a set of different sensors and observes different event types in the environment. Servicing a task in this problem corresponds to sensing an event occurring at a particular location and does not involve visiting the task location. Each event type has a different distribution over the domain. The robots are heterogeneous in that each robot is capable of sensing a subset of the event types. The objective is to deploy the robots into the domain to maximize the total coverage of the multiple event types. We propose a new formulation for the heterogeneous coverage problem. We provide a simple distributed algorithm to maximize the coverage. Then, we extend the result to the case where the event distribution is unknown before the deployment and provide a distributed algorithm and prove the convergence of the approach to a locally optimal solution. The third problem considers the deployment of a set of autonomous robots to efficiently service tasks that arrive sequentially in an environment over time. Each task is serviced when a robot visits the corresponding task location. Robots can then redeploy while waiting for the next task to arrive. The objective is to redeploy the robots taking into account the next N task arrivals. We seek to minimize a linear combination of the expected cost to service tasks and the redeployment cost between task arrivals. In the single robot case, we propose a one-stage greedy algorithm and prove its optimality. For multiple robots, the problem is NP-hard, and we propose two constant-factor approximation algorithms, one for the problem with a horizon of two task arrivals and the other for the infinite horizon when the redeployment cost is weighted more heavily than the service cost. Finally, we extend the second problem to scenarios where the robots are self-interested service units maximizing their payoff. The payoff of a robot is a linear combination of its relocation cost and its expected revenue from servicing the tasks in its vicinity. In this extension, the global objective is either to minimize the expected time or minimize the maximum time to respond to the tasks. We introduce two indirect control methods to relocate the self-interested service units: 1) an information sharing method, and 2) a method that incentivizes relocation with payments. We prove NP-hardness of finding the optimal controls and provide algorithms to find the near-optimal control. We quantify the performance of the proposed algorithms with analytical upper-bounds and real-world data from ride-sourcing applications

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

Robotic Surveillance and Deployment Strategies

Autonomous mobile systems are becoming more common place, and have the opportunity to revolutionize many modern application areas. They include, but are not limited to, tasks such as search and rescue operations, ad-hoc mobile wireless networks and warehouse management; each application having its own complexities and challenging problems that need addressing. In this thesis, we explore and characterize two application areas in particular. First, we explore the problem of autonomous stochastic surveillance. In particular, we study random walks on a finite graph that are described by a Markov chain. We present strategies that minimize the first hitting time of the Markov chain, and look at both the single agent and multi-agent cases. In the single agent case, we provide a formulation and convex optimization scheme for the hitting time on graphs with travel distances. In addition, we provide detailed simulation results showing the effectiveness of our strategy versus other well-known Markov chain design strategies. In the multi-agent case, we provide the first characterization of the hitting time for multiple random walkers, which we denote the "group hitting time". We also provide a closed form solution for calculating the hitting time between specified nodes for both the single and multiple random walker cases. Our results allow for the multiple random walks to be different and, moreover, for the random walks to operate on different subgraphs. Finally, we use sequential quadratic programming to find the transition matrices that generate minimal "group hitting time".Second, we consider the problem of optimal coverage with a group of mobile agents. For a planar environment with an associated density function, this problem is equivalent to dividing the environment into optimal subregions such that each agent is responsible for the coverage of its own region. We study this problem for the discrete time and space case and the continuous time and space case. For the discrete time and space case, we present algorithms that provide optimal coverage control in a non-convex environment when each robot has only asynchronous and sporadic communication with a base station. We introduce the notion of coverings, a generalization of partitions, to do this. For the continuous time and space case, we present a continuous-time distributed policy which allows a team of agents to achieve a convex area-constrained partition in a convex workspace. This work is related to the classic Lloyd algorithm, and makes use of generalized Voronoi diagrams. For both cases we provide detailed simulation results and discuss practical implementation issues