Motion Planning in Environments with Low Obstacle Density

Motion Planning in Environments with Low Obstacle Density
Author: A. Frank van der Stappen
Publisher:
Total Pages: 40
Release: 1995
Genre: Computational complexity
ISBN:
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Abstract: "We present a simple and efficient paradigm for computing the exact solution of the motion planning problem in environments with a low obstacle density. Such environments frequently occur in practical instances of the motion planning problem. The complexity of the free space for such environments is known to be linear in the number of obstacles. Our paradigm is a new cell decomposition approach to motion planning and exploits properties that follow from the low density of the obstacles in the robot's workspace. These properties allow us to decompose the workspace, subject to some constraints, rather than to decompose the higher-dimensional free configuration space directly. A sequence of uniform steps transforms the workspace decomposition into a free space decomposition of asympototically the same size. The approach applies to robots with any fixed number of degrees of freedom and turns out to be eifficient in many cases: it leads to nearly optimal O(n log n) algorithms for motion planning in 2D, for motion planning in 3D amidst obstacles of comparable size, and for motion planning on a planar workfloor in 3D. In addition, we obtain algorithms for planning 3D motions among polyhedral obstacles, running in O(n2 log n) time, and among arbitrary obstacles, running in time O(n3). Several other interesting instances of the motion planning seem adequately solvable by the paradigm as well."

Motion Planning in Dynamic Environments

Motion Planning in Dynamic Environments
Author: Kikuo Fujimura
Publisher: Springer Science & Business Media
Total Pages: 190
Release: 2012-12-06
Genre: Computers
ISBN: 4431681655
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Computer Science Workbench is a monograph series which will provide you with an in-depth working knowledge of current developments in computer technology. Every volume in this series will deal with a topic of importance in computer science and elaborate on how you yourself can build systems related to the main theme. You will be able to develop a variety of systems, including computer software tools, computer graphics, computer animation, database management systems, and computer-aided design and manufacturing systems. Computer Science Workbench represents an important new contribution in the field of practical computer technology. TOSIYASU L. KUNII To my parents Kenjiro and Nori Fujimura Preface Motion planning is an area in robotics that has received much attention recently. Much of the past research focuses on static environments - various methods have been developed and their characteristics have been well investigated. Although it is essential for autonomous intelligent robots to be able to navigate within dynamic worlds, the problem of motion planning in dynamic domains is relatively little understood compared with static problems.

Sensor Based Intelligent Robots

Sensor Based Intelligent Robots
Author: Henrik I Christensen
Publisher: Springer
Total Pages: 334
Release: 2007-01-01
Genre: Computers
ISBN: 3540466193
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This book constitutes the thorougly refereed post-proceedings of an international workshop on sensor based Intelligent Robot held in Dagstuhl Castle, Germany in September/October 1998. The 17 revised full papers presented were carefully reviewed for inclusion in the book. Among the topics addressed are robot navigation, motion planning, autonomous mobile robots, wheelchair robots, interactive robots, car navigation systems, visual tracking, sensor based navigation, distributed algorithms, computer vision, intelligent agents, robot control, and computational geometry.

Algorithms and Data Structures

Algorithms and Data Structures
Author: Frank Dehne
Publisher: Springer Science & Business Media
Total Pages: 492
Release: 1997-07-23
Genre: Computers
ISBN: 9783540633075
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The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.

Handbook of Discrete and Computational Geometry

Handbook of Discrete and Computational Geometry
Author: Csaba D. Toth
Publisher: CRC Press
Total Pages: 1928
Release: 2017-11-22
Genre: Computers
ISBN: 1498711421
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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Handbook of Discrete and Computational Geometry, Second Edition

Handbook of Discrete and Computational Geometry, Second Edition
Author: Csaba D. Toth
Publisher: CRC Press
Total Pages: 1557
Release: 2004-04-13
Genre: Mathematics
ISBN: 1420035312
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While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies

The Complexity of Robot Motion Planning

The Complexity of Robot Motion Planning
Author: John Canny
Publisher: MIT Press
Total Pages: 220
Release: 1988
Genre: Computers
ISBN: 9780262031363
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The Complexity of Robot Motion Planning makes original contributions both to roboticsand to the analysis of algorithms. In this groundbreaking monograph John Canny resolveslong-standing problems concerning the complexity of motion planning and, for the central problem offinding a collision free path for a jointed robot in the presence of obstacles, obtains exponentialspeedups over existing algorithms by applying high-powered new mathematical techniques.Canny's newalgorithm for this "generalized movers' problem," the most-studied and basic robot motion planningproblem, has a single exponential running time, and is polynomial for any given robot. The algorithmhas an optimal running time exponent and is based on the notion of roadmaps - one-dimensionalsubsets of the robot's configuration space. In deriving the single exponential bound, Cannyintroduces and reveals the power of two tools that have not been previously used in geometricalgorithms: the generalized (multivariable) resultant for a system of polynomials and Whitney'snotion of stratified sets. He has also developed a novel representation of object orientation basedon unnormalized quaternions which reduces the complexity of the algorithms and enhances theirpractical applicability.After dealing with the movers' problem, the book next attacks and derivesseveral lower bounds on extensions of the problem: finding the shortest path among polyhedralobstacles, planning with velocity limits, and compliant motion planning with uncertainty. Itintroduces a clever technique, "path encoding," that allows a proof of NP-hardness for the first twoproblems and then shows that the general form of compliant motion planning, a problem that is thefocus of a great deal of recent work in robotics, is non-deterministic exponential time hard. Cannyproves this result using a highly original construction.John Canny received his doctorate from MITAnd is an assistant professor in the Computer Science Division at the University of California,Berkeley. The Complexity of Robot Motion Planning is the winner of the 1987 ACM DoctoralDissertation Award.

Computational Geometry

Computational Geometry
Author: Mark de Berg
Publisher: Springer Science & Business Media
Total Pages: 388
Release: 2008-03-07
Genre: Computers
ISBN: 3540779736
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This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.