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

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

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Consensus and Cooperation in Networked Multi-Agent Systems

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

The purpose of this article is to provide a tutorial overview of information consensus in multivehicle cooperative control. Theoretical results regarding consensus-seeking under both time invariant and dynamically changing communication topologies are summarized. Several specific applications of consensus algorithms to multivehicle coordination are described

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Information consensus in multivehicle cooperative control

We would like to give robots the ability to position and orient parts in the plane by pushing, particularly when the parts are too large or heavy to be grasped and lifted. Unfortunately, the motion of a pushed object is generally unpredictable due to unknown support friction forces. With multiple pushing contact points, however, it is possible to find pushing directions that cause the object to remain fixed to the manipulator. These are called stable pushing directions. In this article we consider the problem of planning pushing paths using stable pushes. Pushing imposes a set of nonholonomic velocity constraints on the motion of the object, and we study the issues of local and global controllability during pushing with point contact or stable line contact. We describe a planner for finding stable pushing paths among obstacles, and the planner is demon strated on several manipulation tasks.

Stable pushing: mechanics, controllability, and planning

We analyze two different estimation algorithms for dynamic average consensus in sensing and communication networks, a proportional algorithm and a proportional-integral algorithm. We investigate the stability properties of these estimators under changing inputs and network topologies as well as their convergence properties under constant or slowly-varying inputs. In doing so, we discover that the more complex proportional-integral algorithm has performance benefits over the simpler proportional algorithm

Stability and Convergence Properties of Dynamic Average Consensus Estimators

The bodies and brains of fish have evolved to achieve control objectives beyond the capabilities of current underwater vehicles. One route toward designing underwater vehicles with similar capabilities is to better understand fish physiological design and control strategies. This paper has two objectives: 1) to review clues to artificial swimmer design taken from fish physiology and 2) to formalize and review the control problems that must be solved by a robot fish. The goal is to exploit fish locomotion principles to address the truly difficult control challenges of station keeping under large perturbations, rapid maneuvering, power-efficient endurance swimming, and trajectory planning and tracking. The design and control of biomimetic swimming machines meeting these challenges will require state-of-the-art engineering and biology.

Mechanics and control of swimming: a review

Brief paper: Decentralized estimation and control of graph connectivity for mobile sensor networks

We describe a framework for the design of collective behaviors for groups of identical mobile agents. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm needed to make a local control decision. Challenges of the approach include designing a control law with desired convergence properties, assuming each agent has perfect global knowledge; designing an estimator that allows each agent to make correct estimates of the global properties needed to implement the controller; and possibly modifying the controller to recover desired convergence properties when using the estimates of global performance. We apply this framework to the problem of controlling the moment statistics describing the location and shape of a swarm. We derive conditions which guarantee that the formation statistics are driven to desired values, even in the presence of a changing network topology.

Kevin M. Lynch

Papers

Stable pushing: mechanics, controllability, and planning

Stability and Convergence Properties of Dynamic Average Consensus Estimators

Mechanics and control of swimming: a review

Brief paper: Decentralized estimation and control of graph connectivity for mobile sensor networks

Multi-Agent Coordination by Decentralized Estimation and Control