There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.

/pdf/information-flow-and-cooperative-control-of-vehicle-4ws61wioze.pdf

Information flow and cooperative control of vehicle formations

An Introduction to MultiAgent Systems.

This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

/pdf/coverage-control-for-mobile-sensing-networks-3gs75qafnm.pdf

Coverage control for mobile sensing networks

Formations of multi-agent systems, such as satellites and aircraft, require that individual agents satisfy their kinematic equations while constantly maintaining inter-agent constraints. In this paper, we develop a systematic framework for studying formations of multiagent systems. In particular, we consider undirected formations for centralized formations and directed formations for decentralized formations. In each case, we determine differential geometric conditions that guarantee formation feasibility given the individual agent kinematics. Our framework also enables us to extract a smaller control system that describes the formation kinematics while maintaining,all formation constraints.

/pdf/feasible-formations-of-multi-agent-systems-55ybn6x4t1.pdf

Feasible formations of multi-agent systems

Programming the behavior of multi-robot systems is a challenging task which has a key role in developing effective systems in many application domains. In this paper, we present Petri Net Plans (PNPs), a language based on Petri Nets (PNs), which allows for intuitive and effective robot and multi-robot behavior design. PNPs are very expressive and support a rich set of features that are critical to develop robotic applications, including sensing, interrupts and concurrency. As a central feature, PNPs allow for a formal analysis of plans based on standard PN tools. Moreover, PNPs are suitable for modeling multi-robot systems and the developed behaviors can be executed in a distributed setting, while preserving the properties of the modeled system. PNPs have been deployed in several robotic platforms in different application domains. In this paper, we report three case studies, which address complex single robot plans, coordination and collaboration.

https://www.dis.uniroma1.it/~iocchi/publications/iocchi-moca06.pdf

Petri Net Plans

Formations of multi-agent systems, such as mobile robots, satellites and aircraft, require individual agents to satisfy their kinematic equations while constantly maintaining interagent constraints. In this paper, we develop a systematic framework for studying formation motion feasibility of multi-agent systems. In particular, we consider formations wherein all the agents cooperate to enforce the formation. We determine algebraic conditions that guarantee formation feasibility given the individual agent kinematics. Our framework also enables us to obtain lower dimensional control systems describing the group kinematics while maintaining all formation constraints.

/pdf/motion-feasibility-of-multi-agent-formations-3hg2umpzai.pdf

Motion feasibility of multi-agent formations

Multi-Robot Systems.

This paper describes an approach to the modeling and control of multiagent populations composed of a large number of agents. The complexity of population modeling is avoided by assuming a stochastic approach, under which the agent distribution over the state space is modeled. The dynamics of the state probability density functions is determined, and a control problem of maximizing the probability of robotic presence in a given region is introduced. The Minimum Principle for the optimal control of partial differential equations is exploited to solve this problem, and it is applied to the mission control of a simulated large robotic population

/pdf/modeling-and-optimal-centralized-control-of-a-large-size-4mnpkssfk1.pdf

Pedro U. Lima

Papers

Feasible formations of multi-agent systems

Petri Net Plans

Motion feasibility of multi-agent formations

Multi-Robot Systems.

Modeling and Optimal Centralized Control of a Large-Size Robotic Population