Workspaces of continuous robotic manipulators [Elektronische Ressource] / Boris Thomaschewski

Workspaces of continuous roboticmanipulatorsD i s s e r t a t i o nzur Erlangung des akademischen GradesDr. rer. nat.eingereicht bei der Fakult˜at fur˜ Mathematik und Naturwissenschaftender Technischen Universit˜at Ilmenauvorgelegt von Dipl.-Math. Boris ThomaschewskiGutachter: Privatdozent Dr. H. Abe…er, TU IlmenauProf. Dr. A. Hofmann, TU IlmenauProf. Dr. Ch. Gro…mann, TU Dresdeneingereicht am 13. September 2001verteidigt am 12. August 2002Preface1This thesis was the result of a 4 year stay with the Analysis Group at the In-2stitute for Mathematics of the Technische Universit˜at Ilmenau.The motivation to this subject is due to Professor J. Steigenberger and Dozent H.Abe…er, who patiently supervised and enriched my work throughout the years.Very useful hints also came from Dr. H. Huijberts, in particular during my oneweek stay with him in London. Thank you very much!In this context I also wish to thank all my colleagues of the Analysis Group whoalways helped my ideas with encouraging discussions and precious comments.And, last but not least, they made my stay in Ilmenau a great experience also inprivate life.iiiContentsPreface i1 Introduction 11.1 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . 41.2 Mathematical preliminaries . . . . . . . . . . . . . . . . . . . . . 51.2.1 Optimal control . . . . . . . . . . . . . . . . . . . . . . . . 51.2.2 Difierential geometry . . . . . . . . . . . . . . . . . . . . . 71.