Applied Interval Analysis

Vision-based control in robotics based on considering a vision system as a specific sensor dedicated to a task and included in a control servo loop is described. Once the necessary modeling stage is performed, the framework becomes one of automatic control, and stability and robustness questions arise. State-of-the-art visual servoing is reviewed, and the basic concepts for modeling the concerned interactions are given. The interaction screw is thus defined in a general way, and the application to images follows. Starting from the concept of task function, the general framework of the control is described, and stability results are recalled. The concept of the hybrid task is presented and then applied to visual sensors. Simulation and experimental results are presented, and guidelines for future work are drawn in the conclusion. >

A new approach to visual servoing in robotics

Algebraically Closed Fields- Real Closed Fields- Semi-Algebraic Sets- Algebra- Decomposition of Semi-Algebraic Sets- Elements of Topology- Quantitative Semi-algebraic Geometry- Complexity of Basic Algorithms- Cauchy Index and Applications- Real Roots- Cylindrical Decomposition Algorithm- Polynomial System Solving- Existential Theory of the Reals- Quantifier Elimination- Computing Roadmaps and Connected Components of Algebraic Sets- Computing Roadmaps and Connected Components of Semi-algebraic Sets

Algorithms in real algebraic geometry

From exploring planets to cleaning homes, the reach and versatility of robotics is vast. The integration of actuation, sensing and control makes robotics systems powerful, but complicates their simulation. This paper introduces a versatile, scalable, yet powerful general-purpose robot simulation framework called V-REP. The paper discusses the utility of a portable and flexible simulation framework that allows for direct incorporation of various control techniques. This renders simulations and simulation models more accessible to a general-public, by reducing the simulation model deployment complexity. It also increases productivity by offering built-in and ready-to-use functionalities, as well as a multitude of programming approaches. This allows for a multitude of applications including rapid algorithm development, system verification, rapid prototyping, and deployment for cases such as safety/remote monitoring, training and education, hardware control, and factory automation simulation.

V-REP: A versatile and scalable robot simulation framework

http://inis.jinr.ru/sl/m_mathematics/mn_numerical methods/mnd_numerical calculus/allgower e.l., georg k. introduction to numerical continuation methods (colorado, 1990)(397s).pdf

Numerical Continuation Methods

Background: Polynomial Systems Homotopy Continuation Projective Spaces Probability One Polynomials of One Variable Other Methods Isolated Solutions: Coefficient-Parameter Homotopy Polynomial Structures Case Studies Endpoint Estimation Checking Positive Dimensional Solution Sets: Some Concepts from Algebraic Geometry Basic Numerical Algebraic Geometry Cascading Through Embedded Systems The Numerical Irreducible Decomposition Intersection of Algebraic Sets.

The numerical solution of systems of polynomials arising in engineering and science

Inverse kinematic solutions are used in manipulator controllers to determine corrective joint motions for errors in end-effector position and orientation. Previous formulations of these solutions, based on the Jacobian matrix, are inefficient and fail near kinematic singularities. Vector formulations of inverse kinematic problems are developed that lead to efficient computer algorithms. To overcome the difficulties encountered near kinematic singularities, the exact inverse problem is reformulated as a damped least-squares problem, which balances the error in the solution against the size of the solution. This yields useful results for all manipulator configurations.

Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods

This book is a guide to concepts and practice in numerical algebraic geometry - the solution of systems of polynomial equations by numerical methods. The authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary webpage where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry. Audience: The book is designed to serve the following audiences: scientists and engineers needing to quickly solve systems of polynomial equations to find all the isolated roots or, if desired, to find all the solution components of any dimension; engineers or scientists and senior undergraduate or beginning graduate students with a computational focus who have a knowledge of calculus, linear algebra, and undergraduate-level ODEs; and those with a more mathematical bent who wish to explore the underpinnings of the methods, delve into more technical details, and read descriptions of the latest developments. Contents: List of Figures; Conventions; Preface; Part I: Isolated Systems; Chapter 1: Polynomial Systems; Chapter 2: Basic Polynomial Continuation; Chapter 3: Adaptive Precision and Endgames; Chapter 4: Projective Space; Chapter 5: Types of Homotopies; Chapter 6: Parameter Homotopies; Chapter 7: Advanced Topics about Isolated Solutions; Part II: Positive-Dimensional Solution Sets; Chapter 8: Positive-Dimensional Components; Chapter 9: Computing Witness Supersets; Chapter 10: The Numerical Irreducible Decomposition; Chapter 11: Advanced Topics about Positive-Dimensional Solution Sets; Part III: Further Algorithms and Applications; Chapter 12: Intersection; Chapter 13: Singular Sets; Chapter 14: Real Solutions; Chapter 15: Applications to Algebraic Geometry; Chapter 16: Projections of Algebraic Sets; Chapter 17: Big Polynomial Systems Arising from Differential Equations; Part IV: Bertini Users Manual; Appendix A: Bertini Quick Start Guide; Appendix B: Input Format; Appendix C: Calling Options; Appendix D: Output Files; Appendix E: Configuration Settings; Appendix F: Tips and Tricks; Appendix G: Parallel Computing; Appendix H: Related Software; Bibliography; Software Index; Subject Index.

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Numerically Solving Polynomial Systems with Bertini

Basic Algebraic Geometry

The major approaches toward kinematic calibration are unified by considering an end-point measurement system as forming a joint and closing the kinematic loop. A calibration index is in troduced, b...

Charles W. Wampler

Papers

The numerical solution of systems of polynomials arising in engineering and science

Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods

Numerically Solving Polynomial Systems with Bertini

Basic Algebraic Geometry

The calibration index and taxonomy for robot kinematic calibration methods