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2002 | Buch

Cooperative Control and Optimization

herausgegeben von: Robert Murphey, Panos M. Pardalos

Verlag: Springer US

Buchreihe : Applied Optimization

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Über dieses Buch

A cooperative system is defined to be multiple dynamic entities that share information or tasks to accomplish a common, though perhaps not singular, objective. Examples of cooperative control systems might include: robots operating within a manufacturing cell, unmanned aircraft in search and rescue operations or military surveillance and attack missions, arrays of micro satellites that form a distributed large aperture radar, employees operating within an organization, and software agents. The term entity is most often associated with vehicles capable of physical motion such as robots, automobiles, ships, and aircraft, but the definition extends to any entity concept that exhibits a time dependent behavior. Critical to cooperation is communication, which may be accomplished through active message passing or by passive observation. It is assumed that cooperation is being used to accomplish some common purpose that is greater than the purpose of each individual, but we recognize that the individual may have other objectives as well, perhaps due to being a member of other caucuses. This implies that cooperation may assume hierarchical forms as well. The decision-making processes (control) are typically thought to be distributed or decentralized to some degree. For if not, a cooperative system could always be modeled as a single entity. The level of cooperation may be indicated by the amount of information exchanged between entities. Cooperative systems may involve task sharing and can consist of heterogeneous entities. Mixed initiative systems are particularly interesting heterogeneous systems since they are composed of humans and machines. Finally, one is often interested in how cooperative systems perform under noisy or adversary conditions.
In December 2000, the Air Force Research Laboratory and the University of Florida successfully hosted the first Workshop on Cooperative Control and Optimization in Gainesville, Florida. This book contains selected refereed papers summarizing the participants' research in control and optimization of cooperative systems.
Audience: Faculty, graduate students, and researchers in optimization and control, computer sciences and engineering.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Cooperative Control for Target Classification
Abstract
An overview is presented of ongoing work in cooperative control for unmanned air vehicles, specifically wide area search munitions, which perform search, target classification, attack, and damage assessment. The focus of this paper is the cooperative use of multiple vehicles to maximize the probability of correct target classification. Capacitated transhipment and market based bidding are presented as two approaches to team and vehicle assigment for cooperative classification. Templates are developed and views are combined to maximize the probability of correct target classification over various aspect angles. Optimal trajectories are developed to view the targets. A false classification matrix is used to represent the probability of incorrectly classifying nontargets as targets. A hierarchical distributed decision system is presented that has three levels of decomposition: The top level performs task assignment using a market based bidding scheme; the middle subteam level coordinates cooperative tasks; and the lower level executes the elementary tasks, eg path planning. Simulations are performed for a team of eight air vehicles that show superior classification performance over that achievable when the vehicles operate independently.
P. R. Chandler, M. Pachter, Kendall E. Nygard, Dharba Swaroop
Chapter 2. Guillotine Cut in Approximation Algorithms
Abstract
The guillotine cut is one of main techniques to design polynomial-time approximation schemes for geometric optimization problems. This article is a short survey on its history and current developments.
Xiuzhen Cheng, Ding-Zhu Du, Joon-Mo Kim, Hung Quang Ngo
Chapter 3. Unmanned Aerial Vehicles: Autonomous Control Challenges, A Researcher’s Perspective
Abstract
AFRL is pressing ahead with development of truly autonomous UAV control systems. As we go from systems where the human is the pilot, through systems where the human is the operator, to systems where the human is the supervisor; with the ultimate goal simply to have the human as customer of UAV ops, we are running into numerous challenges. Yes, we face the typical technological questions of “What types of human tasks can we replace with on-board algorithms?” and “How big of a processor is required on-board to do this?”. What are usually not asked are other questions, maybe not technically exciting, but with enormous practical impact: “How can we affordably add more code to already costly flight critical s oftware programs?” “How do I flight certify a system that has non-deterministic attributes?” “What is the impact of implementing distributed, coordinated, info-centric control systems that now have flight critical data links susceptible to electronic and information warfare?” “How do I convince the FAA, and foreign governments, that it’s safe to let autonomous vehicles roam the skies?” These, and other questions, have just as great, if not greater, impact on systems development as the raw autonomous technology itself. This paper examines some of these challenges, how current AFRL research is addressing them, and points the way to future research that will allow truly autonomous operations.
Bruce T. Clough
Chapter 4. Using Grasp for Choosing Best Periodic Observation Strategy in Stochastic Systems Filtering
Abstract
The problem of optimal periodic scheduling of single channel measures for the state estimation of a multi output discrete time stochastic system is considered. The optimality criterion chosen is the value of the trace of the error covariance matrix of Kalman filter in the periodic steady state, averaged over the observation period. Two interesting examples for practical applications, are studied. The first one considers the case of a number of independent single output subsystems observed by a single observation channel, while the second case deals with the optimization of measurement points and of the relative scanning sequence for the model of a parabolic distributed parameter system. Given the combinatorial nature of the resulting problem, an approximate global optimization method is used to solve it and heuristic rules are devised to overcome difficulties arising from possibly slow convergence in computation of objective function. Numerical examples are reported showing a great improvement with respect to the standard scanning policy.
Paola Festa, Giancarlo Raiconi
Chapter 5. Cooperative Control of Robot Formations
Abstract
We describe a framework for controlling and coordinating a group of nonholonomic mobile robots equipped with range sensors, with applications ranging from scouting and reconnaissance, to search and rescue and manipulation tasks. We derive control algorithms that allow the robots to control their position and orientation with respect to neighboring robots or obstacles in the environment. We then outline a coordination protocol that automatically switches between the control laws to maintain a specified formation. Two simple trajectory generators are derived from potential field theory. The first allows each robot to plan its reference trajectory based on the information available to it. The second scheme requires sharing of information and enables a rigid group formation. Numerical simulations illustrate the application of these ideas and demonstrate the scalability of the proposed framework for a large group of robots.
Rafael Fierro, Peng Song, Aveek Das, Vijay Kumar
Chapter 6. Cooperative Behavior Schemes for Improving The Effectiveness of Autonomous Wide Area Search Munitions
Abstract
The problem being addressed is how to best find and engage an unknown number of targets in unknown locations (some moving) using multiple autonomous wide area search munitions. In this research cooperative behavior is being investigated to improve the overall mission effectiveness. A computer simulation was used to emulate the behavior of autonomous wide area search munitions and measure their overall expected performance. This code was modified to incorporate the capability for cooperative engagement based on a parameterized decision rule. Using Design of Experiments (DOE) and Response Surface Methodologies (RSM), the simulation was run to achieve optimal decision rule parameters for given scenarios and to determine the sensitivities of those parameters to the precision of the Autonomous Target Recognition (ATR) algorithm, lethality and guidance precision of the warhead, and the characteristics of the battlefield.
Daniel P. Gillen, David R. Jacques
Chapter 7. On A General Framework To Study Cooperative Systems
Abstract
A collection of many systems that cooperatively solve an optimization problem is considered. The consideration aims to determine criteria such that the systems as a whole show their best performance for the problem. A general framework based on a concept of structural complexity is proposed to determine the criteria. The main merit of this framework is that it allows to set up computational experiments revealing the criteria. In particular, the experiments give evidence to suggest that criteria of best performance are realized when the structural complexity of cooperative systems equals the structural complexity of the optimization problem. The results of the paper could give a new perspective in the developing of optimization methods based on cooperative systems.
Victor Korotkich
Chapter 8. Cooperative Multi-agent Constellation Formation Under Sensing and Communication Constraints
Abstract
A group of cooperating vehicles (smart bombs, robots) moves toward a set of (possibly moving) prioritized destinations. During their journey towards the destinations, some of the vehicles may be damaged, but it is also possible that reinforcements may arrive. The objective is to maximize the number of encounters between the vehicles and the high-priority destinations. In this preliminary study, we explore how position sensors and (possibly fading) communication channels can assist the group in performing its task. We show how joint operation, and exchange of observations and estimates, improve convergence. On the other hand unfavorable cooperation attempts can sometimes lead to oscillations and confusion. In unfavorable circumstances our agents suspend cooperation and engage in “every agent for itself” mode. One of the interesting features of the proposed architecture is that individual team members can predict the success or failure of the cooperation mechanism by testing the consistency of assigned target destinations.
Lit-Hsin Loo, Erwei Lin, Moshe Kam, Pramod Varshney
Chapter 9. An Introduction to Collective and Cooperative Systems
Abstract
Cooperative systems are introduced to the reader as a part of a broader class of collective systems. A taxonomy of collective systems is defined such that each class within the taxonomy is rigorously defined based upon the mathematical constructs of team theory. It is shown that this taxonomy leads to a precise definition of cooperation and clearly separates intentional cooperation from serendipitous complementary behavior. Concepts of precedence, hierarchy, and supervision are made clear in the presence of information such that team theory and decentralized control theory are generalized into the single framework of collective systems. It is anticipated that this framework will lead to a consistent representation of cooperation in future research and new methods for solving the hard problem of non nested information structures in team theory.
Robert Murphey
Chapter 10. Cooperative Aircraft Control for Minimum Radar Exposure
Abstract
Two aircraft exposed to illumination by a tracking radar are considered and the optimization problem of cooperatively steering them to a prespecified rendezvous point is addressed. First, the problem of a single aircraft exposed to illumination by a tracking radar is considered and the problem of determining an optimal planar trajectory connecting two prespecified points is addressed. The solution is shown to exist only if the angle θf formed by the lines connecting the radar to the two prespecified trajectory points, is less than 60°. In addition, expressions are given for the optimal path length, l*, and optimal cost. When the angle θf≥60° an unconstrained optimal solution does not exist, and in order to render the optimization problem well posed, a path length constraint is imposed. Numerical optimization techniques are used to obtain optimal aircraft trajectories for the constrained case. Finally, the problem of isochronous rendezvous of the two aircraft is addressed using an optimization argument and the analytic results previously derived for a single aircraft trajectory.
Meir Pachter, Jeffrey Hebert
Chapter 11. Robust Recursive Bayesian Estimation and Quantum Minimax Strategies
Abstract
The problem of a recursive realization of Bayesian estimation for incomplete experimental data is considered. A differential-geometric structure of nonlinear estimation is studied. It is shown that the use of a rationally chosen description of the true posterior density produces a geometrical structure defined on the family of possible posteriors. Pythagorean-like relations valid for probability distributions are presented and their importance for estimation under reduced data is indicated. A robust algorithm for estimation of unknown parameters is proposed, which is based on a quantum implementation of the Bayesian estimation procedure.
P. Pardalos, V. Yatsenko, S. Butenko
Chapter 12. Cooperative Control for Autonomous Air Vehicles
Abstract
The main objective of this research is to develop and evaluate the performance of strategies for cooperative control of autonomous air vehicles that seek to gather information about a dynamic target environment, evade threats, and coordinate strikes against targets. The air vehicles are equipped with sensors to view a limited region of the environment they are visiting, and are able to communicate with one another to enable cooperation. They are assumed to have some “physical” limitations including possibly maneuverability limitations, fuel/time constraints and sensor range and accuracy. The developed cooperative search framework is based on two inter-dependent tasks: (i) on-line learning of the environment and storing of the information in the form of a “target search map”; and (ii) utilization of the target search map and other information to compute on-line a guidance trajectory for the vehicle to follow. We study the stability of vehicular swarms to try to understand what types of communications are needed to achieve cooperative search and engagement, and characteristics that affect swarm aggregation and disintegration. Finally, we explore the utility of using-biomimicry of social foraging strategies to develop coordination strategies.
Kevin Passino, Marios Polycarpou, David Jacques, Meir Pachter, Yang Liu, Yanli Yang, Matt Flint, Michael Baum
Chapter 13. Optimal Risk Path Algorithms
Abstract
Analytical and discrete optimization approaches for routing an aircraft in a threat environment have been developed. Using these approaches, an aircraft’s optimal risk trajectory with a constraint on the path length can be efficiently calculated. The analytical approach based on calculus of variations reduces the original risk optimization problem to the system of nonlinear differential equations. In the case of a single radarinstallation, the solution of such a system is expressed by the elliptic sine. The discrete optimization approach reformulates the problem as the Weight Constrained Shortest Path Problem (WCSPP) for a grid undirected graph. The WCSPP is efficiently solved by the Modified Label Setting Algorithm (MLSA). Both approaches have been tested with several numerical examples. Discrete nonsmooth solutions with high precision coincide with exact continuous solutions. For the same graph, time in which the discrete optimization algorithm computes the optimal trajectory is independent of the number of radars. The discrete approach is also efficient for solving the problem using different risk functions.
Michael Zabarankin, Stanislav Uryasev, Panos Pardalos
Backmatter
Metadaten
Titel
Cooperative Control and Optimization
herausgegeben von
Robert Murphey
Panos M. Pardalos
Copyright-Jahr
2002
Verlag
Springer US
Electronic ISBN
978-0-306-47536-8
Print ISBN
978-1-4020-0549-7
DOI
https://doi.org/10.1007/b130435