Approximation algorithms for mobile multi-agent sensing problem

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2020. 8. 문일경.Multi-agent systems are generally applicable in a wide diversity of domains, such as robot engineering, computer science, the military, and smart cities. In particular, the mobile multi-agent sensing problem can be defined as a problem of detecting events occurring in a large number of nodes using moving agents. In this thesis, we introduce a mobile multi-agent sensing problem and present a mathematical formulation. The model can be represented as a submodular maximization problem under a partition matroid constraint, which is NP-hard in general. The optimal solution of the model can be considered computationally intractable. Therefore, we propose two approximation algorithms based on the greedy approach, which are global greedy and sequential greedy algorithms, respectively. We present new approximation ratios of the sequential greedy algorithm and prove tightness of the ratios. Moreover, we show that the sequential greedy algorithm is competitive with the global greedy algorithm and has advantages of computation times. Finally, we demonstrate the performances of our results through numerical experiments.다중 에이전트 시스템은 일반적으로 로봇 공학, 컴퓨터 과학, 군사 및 스마트 도시와 같은 다양한 분야에 적용할 수 있다. 특히, 모바일 다중 에이전트 감지 문제는 움직이는 에이전트를 이용해 많은 수의 노드에서 발생하는 이벤트를 감지하는 문제로 정의할 수 있다. 본 논문에서는 모바일 다중 에이전트 감지 문제의 수학적 공식을 제안한다. 이 문제는 일반적으로 NP-난해 문제인 분할 매트로이드 제약 하에서 하위 모듈 함수의 최대화 문제로 표현할 수 있다. 문제의 최적해는 입력 데이터의 크기가 커질수록 보통 합리적인 시간 이내에 계산하기 어렵다. 따라서 본 논문에서는 탐욕적 접근 방식에 기초한 두 가지 근사 알고리즘 (전역 탐욕 알고리즘, 순차 탐욕 알고리즘)을 제안한다. 또한, 순차 탐욕 알고리즘의 새로운 근사 비율을 증명하고 근사 비율에 정확하게 일치하는 인스턴스를 제시한다. 또한, 수치 실험 결과로 순차 탐욕 알고리즘은 효과적인 해를 찾아줄 뿐 아니라, 전역 탐욕 알고리즘과 비교해 계산 시간의 이점을 가지고 있음을 확인한다.Chapter 1 Introduction 1 Chapter 2 Literature Review 4 Chapter 3 Problem statement 7 Chapter 4 Algorithms and approximation ratios 11 Chapter 5 Computational Experiments 22 Chapter 6 Conclusions 30 Bibliography 31 국문초록 40Maste

The Impact of Message Passing in Agent-Based Submodular Maximization

Submodular maximization problems are a relevant model set for many real-world applications. Since these problems are generally NP-Hard, many methods have been developed to approximate the optimal solution in polynomial time. One such approach uses an agent-based greedy algorithm, where the goal is for each agent to choose an action from its action set such that the union of all actions chosen is as high-valued as possible. Recent work has shown how the performance of the greedy algorithm degrades as the amount of information shared among the agents decreases, whereas this work addresses the scenario where agents are capable of sharing more information than allowed in the greedy algorithm. Specifically, we show how performance guarantees increase as agents are capable of passing messages, which can augment the allowable decision set for each agent. Under these circumstances, we show a near-optimal method for message passing, and how much such an algorithm could increase performance for any given problem instance

OASIS: Optimal Arrangements for Sensing in SLAM

The number and arrangement of sensors on an autonomous mobile robot dramatically influence its perception capabilities. Ensuring that sensors are mounted in a manner that enables accurate detection, localization, and mapping is essential for the success of downstream control tasks. However, when designing a new robotic platform, researchers and practitioners alike usually mimic standard configurations or maximize simple heuristics like field-of-view (FOV) coverage to decide where to place exteroceptive sensors. In this work, we conduct an information-theoretic investigation of this overlooked element of mobile robotic perception in the context of simultaneous localization and mapping (SLAM). We show how to formalize the sensor arrangement problem as a form of subset selection under the E-optimality performance criterion. While this formulation is NP-hard in general, we further show that a combination of greedy sensor selection and fast convex relaxation-based post-hoc verification enables the efficient recovery of certifiably optimal sensor designs in practice. Results from synthetic experiments reveal that sensors placed with OASIS outperform benchmarks in terms of mean squared error of visual SLAM estimates

Resilient Submodular Maximization For Control And Sensing

Fundamental applications in control, sensing, and robotics, motivate the design of systems by selecting system elements, such as actuators or sensors, subject to constraints that require the elements not only to be a few in number, but also, to satisfy heterogeneity or interdependency constraints (called matroid constraints). For example, consider the scenarios: - (Control) Actuator placement: In a power grid, how should we place a few generators both to guarantee its stabilization with minimal control effort, and to satisfy interdependency constraints where the power grid must be controllable from the generators? - (Sensing) Sensor placement: In medical brain-wearable devices, how should we place a few sensors to ensure smoothing estimation capabilities? - (Robotics) Sensor scheduling: At a team of mobile robots, which few on-board sensors should we activate at each robot ---subject to heterogeneity constraints on the number of sensors that each robot can activate at each time--- so both to maximize the robots\u27 battery life, and to ensure the robots\u27 capability to complete a formation control task? In the first part of this thesis we motivate the above design problems, and propose the first algorithms to address them. In particular, although traditional approaches to matroid-constrained maximization have met great success in machine learning and facility location, they are unable to meet the aforementioned problem of actuator placement. In addition, although traditional approaches to sensor selection enable Kalman filtering capabilities, they do not enable smoothing or formation control capabilities, as required in the above problems of sensor placement and scheduling. Therefore, in the first part of the thesis we provide the first algorithms, and prove they achieve the following characteristics: provable approximation performance: the algorithms guarantee a solution close to the optimal; minimal running time: the algorithms terminate with the same running time as state-of-the-art algorithms for matroid-constrained maximization; adaptiveness: where applicable, at each time step the algorithms select system elements based on both the history of selections. We achieve the above ends by taking advantage of a submodular structure of in all aforementioned problems ---submodularity is a diminishing property for set functions, parallel to convexity for continuous functions. But in failure-prone and adversarial environments, sensors and actuators can fail; sensors and actuators can get attacked. Thence, the traditional design paradigms over matroid-constraints become insufficient, and in contrast, resilient designs against attacks or failures become important. However, no approximation algorithms are known for their solution; relevantly, the problem of resilient maximization over matroid constraints is NP-hard. In the second part of this thesis we motivate the general problem of resilient maximization over matroid constraints, and propose the first algorithms to address it, to protect that way any design over matroid constraints, not only within the boundaries of control, sensing, and robotics, but also within machine learning, facility location, and matroid-constrained optimization in general. In particular, in the second part of this thesis we provide the first algorithms, and prove they achieve the following characteristics: resiliency: the algorithms are valid for any number of attacks or failures; adaptiveness: where applicable, at each time step the algorithms select system elements based on both the history of selections, and on the history of attacks or failures; provable approximation guarantees: the algorithms guarantee for any submodular or merely monotone function a solution close to the optimal; minimal running time: the algorithms terminate with the same running time as state-of-the-art algorithms for matroid-constrained maximization. We bound the performance of our algorithms by using notions of curvature for monotone (not necessarily submodular) set functions, which are established in the literature of submodular maximization. In the third and final part of this thesis we apply our tools for resilient maximization in robotics, and in particular, to the problem of active information gathering with mobile robots. This problem calls for the motion-design of a team of mobile robots so to enable the effective information gathering about a process of interest, to support, e.g., critical missions such as hazardous environmental monitoring, and search and rescue. Therefore, in the third part of this thesis we aim to protect such multi-robot information gathering tasks against attacks or failures that can result to the withdrawal of robots from the task. We conduct both numerical and hardware experiments in multi-robot multi-target tracking scenarios, and exemplify the benefits, as well as, the performance of our approach

Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio

Optimization and Communication in UAV Networks

UAVs are becoming a reality and attract increasing attention. They can be remotely controlled or completely autonomous and be used alone or as a fleet and in a large set of applications. They are constrained by hardware since they cannot be too heavy and rely on batteries. Their use still raises a large set of exciting new challenges in terms of trajectory optimization and positioning when they are used alone or in cooperation, and communication when they evolve in swarm, to name but a few examples. This book presents some new original contributions regarding UAV or UAV swarm optimization and communication aspects

Multi-agent persistent surveillance under temporal logic constraints

This thesis proposes algorithms for the deployment of multiple autonomous agents for persistent surveillance missions requiring repeated, periodic visits to regions of interest. Such problems arise in a variety of domains, such as monitoring ocean conditions like temperature and algae content, performing crowd security during public events, tracking wildlife in remote or dangerous areas, or watching traffic patterns and road conditions. Using robots for surveillance is an attractive solution to scenarios in which fixed sensors are not sufficient to maintain situational awareness. Multi-agent solutions are particularly promising, because they allow for improved spatial and temporal resolution of sensor information. In this work, we consider persistent monitoring by teams of agents that are tasked with satisfying missions specified using temporal logic formulas. Such formulas allow rich, complex tasks to be specified, such as "visit regions A and B infinitely often, and if region C is visited then go to region D, and always avoid obstacles." The agents must determine how to satisfy such missions according to fuel, communication, and other constraints. Such problems are inherently difficult due to the typically infinite horizon, state space explosion from planning for multiple agents, communication constraints, and other issues. Therefore, computing an optimal solution to these problems is often infeasible. Instead, a balance must be struck between computational complexity and optimality. This thesis describes solution methods for two main classes of multi-agent persistent surveillance problems. First, it considers the class of problems in which persistent surveillance goals are captured entirely by TL constraints. Such problems require agents to repeatedly visit a set of surveillance regions in order to satisfy their mission. We present results for agents solving such missions with charging constraints, with noisy observations, and in the presence of adversaries. The second class of problems include an additional optimality criterion, such as minimizing uncertainty about the location of a target or maximizing sensor information among the team of agents. We present solution methods and results for such missions with a variety of optimality criteria based on information metrics. For both classes of problems, the proposed algorithms are implemented and evaluated via simulation, experiments with robots in a motion capture environment, or both

SPINS: Structure Priors aided Inertial Navigation System

Although Simultaneous Localization and Mapping (SLAM) has been an active research topic for decades, current state-of-the-art methods still suffer from instability or inaccuracy due to feature insufficiency or its inherent estimation drift, in many civilian environments. To resolve these issues, we propose a navigation system combing the SLAM and prior-map-based localization. Specifically, we consider additional integration of line and plane features, which are ubiquitous and more structurally salient in civilian environments, into the SLAM to ensure feature sufficiency and localization robustness. More importantly, we incorporate general prior map information into the SLAM to restrain its drift and improve the accuracy. To avoid rigorous association between prior information and local observations, we parameterize the prior knowledge as low dimensional structural priors defined as relative distances/angles between different geometric primitives. The localization is formulated as a graph-based optimization problem that contains sliding-window-based variables and factors, including IMU, heterogeneous features, and structure priors. We also derive the analytical expressions of Jacobians of different factors to avoid the automatic differentiation overhead. To further alleviate the computation burden of incorporating structural prior factors, a selection mechanism is adopted based on the so-called information gain to incorporate only the most effective structure priors in the graph optimization. Finally, the proposed framework is extensively tested on synthetic data, public datasets, and, more importantly, on the real UAV flight data obtained from a building inspection task. The results show that the proposed scheme can effectively improve the accuracy and robustness of localization for autonomous robots in civilian applications.Comment: 14 pages, 14 figure

Distributed, Scalable And Resilient Information Acquisition For Multi-Robot Teams

Advances in robotic mobility and sensing technology have the potential to provide newcapabilities in a wide variety of information acquisition problems including environmental monitoring, structure inspection, localization and mapping of unknown environments, and search and rescue, amongst many others. In particular, teams composed of multiple robots have shown great potential in solving these problems, though it is challenging to design efficient algorithms that are distributed and scale well, and even more complex in hazardous or challenging environments. The purpose of this dissertation is to provide novel algorithms to the capabilities of multi-robot teams to gather information which are distributed, scalable, and resilient. The first part of the dissertation introduces the single-robot information acquisition problem, and focuses on algorithms that may be used for individual robots to plan their own trajectories. The methods presented here are search-based, meaning that an individual robot has a finite set of actions and is seeking to efficiently build a search tree over a known planning horizon. The first method presented details how to use the concept of algebraic redundancy and closeness to achieve a smooth trade-off of completeness in the exploration process, as an anytime planning algorithm. Next we show how a single robot can compute an admissible and consistent heuristic which guides the search towards the most informative regions of the state space, using the classic A* planning algorithm, drastically improving the search efficiency. The next chapter of the dissertation focuses on how to build on the single robot planning algorithms to create efficient algorithms for multi-robot teams, which operate in a distributed manner and scalable manner. The first method presented is coordinate descent, 5 otherwise known in the literature as sequential greedy assignment. This algorithm is implemented in a multi-robot target tracking hardware experiment. Next, we formulate an energy-aware multi-robot information acquisition problem, which allows for heterogeneity and captures trade-offs between information and energy expenditure. However, this results in a non-monotone objective function. Therefore we propose a new algorithm based on distributed local search, which achieves performance guarantees through a diminishing returns property known as submodularity. The final chapter focuses on hazardous or failure prone environments that necessitate resilience to a fixed number of failures in the multi-robot team. We provide a definition of resilience, and formulate a resilient information acquisition problem. We then propose the first algorithm that solves this problem through an online application of robust trajectory planning, and provide theoretical guarantees on its performance. We then present three unique applications of the resilient multi-robot information acquisition framework, including target tracking, occupancy grid mapping, and persistent surveillance which demonstrate the efficacy of our approach