Distributed Online Optimization for Multi-Agent Optimal Transport

In this work, we propose and investigate a scalable, distributed iterative algorithm for large-scale optimal transport of collectives of autonomous agents. We formulate the problem as one of steering the collective towards a target probability measure while minimizing the total cost of transport, with the additional constraint of distributed implementation imposed by a range-limited network topology. Working within the framework of optimal transport theory, we realize the solution as an iterative transport based on a proximal point algorithm. At each stage of the transport, the agents implement an online, distributed primal-dual algorithm to obtain local estimates of the Kantorovich potential for optimal transport from the current distribution of the collective to the target distribution. Using these estimates as their local objective functions, the agents then implement the transport by a proximal point algorithm. This two-step process is carried out recursively by the collective to converge asymptotically to the target distribution. We analyze the behavior of the algorithm via a candidate system of feedback interconnected PDEs for the continuous time and $N \rightarrow \infty$ limit, and establish the asymptotic stability of this system of PDEs. We then test the behavior of the algorithm in simulation

Analysis and design of Multi-Agent Coverage and Transport algorithms

Els sistemes robòtics multi-agents són sistemes que presenten moltes aplicacions en ciència i enginyeria. En aquest treball estudiarem el control de la cobertura, que es centra en col·locar un grup de sensors per optimitzar la cobertura d’una densitat. Ens centrarem en el cas en què la densitat evoluciona en el temps i estudiarem l’ús de la teoría de perturbacions singulars per resoldre el problema. També considerarem grans eixams de robots, on podem fer servir models continus per analitzar el comportament dels agents. Recentment s'ha proposat models continus que incorporen idees de transport òptim en el problema de transport multi-agent. Presentarem aquests treballs i proveirem algunes modificacions.Los sistemas robóticos multi-agentes son sistemas que presentan muchas aplicaciones en ciencia y ingeniería. En este trabajo vamos a estudiar el control de la cobertura, que se centra en colocar un grupo de sensores para optimizar la cobertura de una densidad. Nos vamos a centrar en el casos en que la densidad evoluciona con el tiempo y estudiaremos el uso de la teoría de perturbaciones singulares para resolver el problema. También consideraremos grandes enjambres de robots, donde podemos utilizar modelos continuos para analizar el comportamiento del enjambre. Recientemente se ha propuesto el uso de modelos continuos que incorporan ideas de transporte òptimo para el problema de transporte multi-agente. Vamos a presentar dichos trabajos y proveeremos algunas modificaciones.Multi-agent robotic systems have shown to be useful and reliable solutions to many problems that arise in science and engineering. In this work we will study Coverage Control, that aims to achieve optimal coverage of a density. We will focus on the case when the density has a time dependence and we will study a Singular Perturbation Theory approach to solve the problem. We will also consider large swarms of agents, where we can develop continuous models to analyze the behaviour of the swarm. Recent work has focused on applying ideas from the theory of Optimal Transport to the Multi-Agent Transport problem. We will review the work and provide some modifications.Outgoin

Large-Scale Multi-Agent Transport: Theory, Algorithms and Analysis

The problem of transport of multi-agent systems has received much attention in a wide range of engineering and biological contexts, such as spatial coverage optimization, collective migration, estimation and mapping of unknown environments. In particular, the emphasis has been on the search for scalable decentralized algorithms that are applicable to large-scale multi-agent systems.For large multi-agent collectives, it is appropriate to describe the configuration of the collective and its evolution using macroscopic quantities, while actuation rests at the microscopic scale at the level of individual agents. Moreover, the control problem faces a multitude of information constraints imposed by the multi-agent setting, such as limitations in sensing, communication and localization. Viewed in this way, the problem naturally extends across scales and this motivates a search for algorithms that respect information constraints at the microscopic level while guaranteeing performance at the macroscopic level.We address the above concerns in this dissertation on three fronts: theory, algorithms and analysis. We begin with the development of a multiscale theory of gradient descent-based multi-agent transport that bridges the microscopic and macroscopic perspectives and sets out a general framework for the design and analysis of decentralized algorithms for transport. We then consider the problem of optimal transport of multi-agent systems, wherein the objective is the minimization of the net cost of transport under constraints of distributed computation. This is followed by a treatment of multi-agent transport under constraints on sensing and communication, in the absence of location information, where we study the problem of self-organization in swarms of agents. Motivated by the problem of multi-agent navigation and tracking of moving targets, we then present a study of moving-horizon estimation of nonlinear systems viewed as a transport of probability measures. Finally, we investigate the robustness of multi-agent networks to agent failure, via the problem of identifying critical nodes in large-scale networks

Planning Algorithms for Multi-Robot Active Perception

A fundamental task of robotic systems is to use on-board sensors and perception algorithms to understand high-level semantic properties of an environment. These semantic properties may include a map of the environment, the presence of objects, or the parameters of a dynamic field. Observations are highly viewpoint dependent and, thus, the performance of perception algorithms can be improved by planning the motion of the robots to obtain high-value observations. This motivates the problem of active perception, where the goal is to plan the motion of robots to improve perception performance. This fundamental problem is central to many robotics applications, including environmental monitoring, planetary exploration, and precision agriculture. The core contribution of this thesis is a suite of planning algorithms for multi-robot active perception. These algorithms are designed to improve system-level performance on many fronts: online and anytime planning, addressing uncertainty, optimising over a long time horizon, decentralised coordination, robustness to unreliable communication, predicting plans of other agents, and exploiting characteristics of perception models. We first propose the decentralised Monte Carlo tree search algorithm as a generally-applicable, decentralised algorithm for multi-robot planning. We then present a self-organising map algorithm designed to find paths that maximally observe points of interest. Finally, we consider the problem of mission monitoring, where a team of robots monitor the progress of a robotic mission. A spatiotemporal optimal stopping algorithm is proposed and a generalisation for decentralised monitoring. Experimental results are presented for a range of scenarios, such as marine operations and object recognition. Our analytical and empirical results demonstrate theoretically-interesting and practically-relevant properties that support the use of the approaches in practice