Singularities of Robot Mechanisms: Numerical Computation and Avoidance Path Planning

by Oriol Bohigas, Montserrat Manubens, Lluïs Ros

Overview

This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves. The theory can be put into practice as well: a companion web page gives open access to implementations of the algorithms and the corresponding input files. Using them, the reader can gain hands-on experience on the topic, or analyse new mechanisms beyond those examined in the text. Overall, the book contributes new tools for robot design, and constitutes a single reference source of knowledge that is otherwise dispersed in the literature.

Product Details

ISBN-13:	9783319813998
Publisher:	Springer International Publishing
Publication date:	06/13/2018
Series:	Mechanisms and Machine Science , #41
Edition description:	Softcover reprint of the original 1st ed. 2017
Pages:	184
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

Preface.- Notation.- List of Figures.- 1 Introduction.- 1.1 Historical Context.- 1.2 Assumptions and Scope.- 1.3 Reader’s Guide.- 2 Singularity Types.- 2.1 Forward and Inverse Singularities.- 2.2 A Geometric Interpretation of Singularities.- 2.3 Lower-level Singularity Types.- 2.4 A Simple Mechanism with All Singularities.- 3 Numerical Computation of Singularity Sets.- 3.1 A Suitable Approach.- 3.2 Formulating the Equations of the Singularity Set.- 3.3 Isolating the Singularity Set.- 3.4 Visualising the Singularity Sets.- 3.5 Case Studies.- 4 Workspace Determination.- 4.1 The Need of a General Method.- 4.2 The Workspace and its Boundaries.- 4.3 Issues of Continuation Methods.- 4.4 Exploiting the Branch-and-Prune Machinery.- 4.5 Case Studies.- 5 Singularity-free Path Planning.- 5.1 Related Work.- 5.2 Formulating the Singularity-free C-space.- 5.3 Exploring the Singularity-free C-space.- 5.4 Case Studies.- 6 Planning with Further Constraints.- 6.1 Wrench-Feasibility Constraints.- 6.2 The Planning Problem.- 6.3 Proofs of the Properties.- 6.4 Case Studies.- 6.5 Details about the Wrench Ellipsoid.- 6.6 Extensions.- 7 Conclusions.- 7.1 Summary of Results.- 7.2 Future Research Directions.- References.- Index.- Author Index.

Editorial Reviews

The book is valuable from many points of view. One of them is the clear, systematic and synthetic characterization of singularities as an algebraic problem. Another is the abundant use of real-case examples and the care in the graphical display. Moreover, the authors' proposals for a novel numerical computation scheme of singularities and a singularity-free path planning scheme are worth noting.” (Gianni Ferretti, Mathematical Reviews, May 2017)

From the Publisher