Advances in Robotics Research - media control€¦ · Robot Vision, Robot Programming, Humanoid...
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Advances in Robotics Research
Transcript of Advances in Robotics Research - media control€¦ · Robot Vision, Robot Programming, Humanoid...
Advances in Robotics Research
Torsten Kröger and Friedrich M. Wahl (Eds.)
Advances in RoboticsResearchTheory, Implementation, Application
ABC
Dr.-Ing. Torsten KrögerInstitut für Robotik und ProzessinformatikTechnische Universität BraunschweigMühlenpfordtstraße 2338106 BraunschweigGermanyE-mail: [email protected]
http://www.rob.cs.tu-bs.de
Prof. Dr.-Ing. Friedrich M. WahlInstitut für Robotik und ProzessinformatikTechnische Universität BraunschweigMühlenpfordtstraße 2338106 BraunschweigGermanyE-mail: [email protected]
http://www.rob.cs.tu-bs.de
ISBN 978-3-642-01212-9 e-ISBN 978-3-642-01213-6
DOI 10.1007/978-3-642-01213-6
Library of Congress Control Number: Applied for
c© 2009 Springer-Verlag Berlin Heidelberg
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Preface
This book is a collection of scientific papers presented at the German Workshopon Robotics — a convention of researchers from academia and industry workingon mathematical and algorithmic foundations of robotics, on the design and analy-sis of robotic systems as well as on robotic applications. As a new event of theDeutsche Gesellschaft fur Robotik (DGR, German Robotics Society), the workshoptook place at the Technische Universitat Carolo-Wilhelmina zu Braunschweig onJune 9-10, 2009.
Covering some of the most important ongoing robotics research topics, this vol-ume contains 31 carefully selected and discussed contributions. All of them werepresented at the workshop that was attended by 80 researchers representing a widerange of research areas within robotics. The papers are organized in ten scientifictracks: Kinematic and Dynamic Modeling, Motion Generation, Sensor Integration,Robot Vision, Robot Programming, Humanoid Robots, Grasping, Medical Robot-ics, Autonomous Helicopters, and Robot Applications. Two invited talks by AntonioBicchi and Atsuo Takanishi presented surveys of research activities in the fields ofhuman-robot interaction and humanoid robotics.
The Program Committee was comprised of Karsten Berns, Oliver Brock, Wol-fram Burgard, Martin Buss, Thomas Christaller, Rudiger Dillmann, Bernd Finke-meyer, Martin Hagele, Bodo Heimann, Dominik Henrich, Gerd Hirzinger, AloisKnoll, Helge-Bjorn Kuntze, Gisbert Lawitzky, Jurgen Roßmann, Roland Siegwart,Markus Vincze, and Heinz Worn. After an extensive review and discussion process,the committee met at February 17, 2009, and composed the scientific program froma pool of 49 submissions.
Organizing scientific conventions with a high level of originality cannot be per-formed by individuals alone. One always has to intercommunicate, to discuss, toexchange knowledge and experiences — to work together. Without the help of manypeople, the organization of the meeting would not have been possible. This includesall Program Committee members as well as all technical reviewers. A special wordof thanks goes to Ilona Engel for her great and diligent support during all stages ofthe organization and, in particular, for the work she did during the workshop. RalfWestphal organized the Web site in an excellent way, and he was responsible for theregistration procedure. Regarding design and layout of all handouts, Simon Winkel-bach was our design specialist for all issues concerning the workshop. The greatestword of thanks is — of course — due to all authors and participants of the GermanWorkshop on Robotics. Finally, we would like to acknowledge the financial supportof the Technische Universitat Carolo-Wilhelmina zu Braunschweig and the KUKARoboter GmbH.
Braunschweig Torsten KrogerJune 2009 Friedrich M. Wahl
Contents
Kinematic and Dynamic Modelling
Joint Dominance Coefficients: A Sensitivity-Based Measurefor Ranking Robotic Degrees of Freedom . . . . . . . . . . . . . . . . . . . . 1Klaas Klasing, Dirk Wollherr, Martin Buss
Learning Kinematics from Direct Self-Observation UsingNearest-Neighbor Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Hannes Schulz, Lionel Ott, Jurgen Sturm, Wolfram Burgard
Guidelines for Low Mass and Low Inertia DynamicBalancing of Mechanisms and Robotics . . . . . . . . . . . . . . . . . . . . . . 21Volkert van der Wijk, Just L. Herder
Motion Generation
Probability-Based Robot Search Paths . . . . . . . . . . . . . . . . . . . . . . . 31Jan Deiterding, Dominik Henrich
Mapping and Navigation of Mobile Robots in NaturalEnvironments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Jurgen Roßmann, Petra Krahwinkler, Arno Bucken
Sensor-Based Online Planning of Time-Optimized Paths inDynamic Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Thorsten Gecks, Dominik Henrich
Sensor Integration
Analysis of Strain Transfer to FBG’s for SensorizedTelerobotic End-Effector Applications . . . . . . . . . . . . . . . . . . . . . . . 65Dean J. Callaghan, Mark M. McGrath, Ginu Rajan, Eugene Coyle,Yuliya Semenova, Gerald Farrell
VIII Contents
Intuitive Collision Avoidance of Robots Using ChargeGenerated Virtual Force Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Alexander Winkler, Jozef Suchy
6D Pose Uncertainty in Robotic Perception . . . . . . . . . . . . . . . . . 89Wendelin Feiten, Pradeep Atwal, Robert Eidenberger,Thilo Grundmann
Robot Vision
3D Shape Detection for Mobile Robot Learning . . . . . . . . . . . . . 99Andreas Richtsfeld, Markus Vincze
3D Collision Detection for Industrial Robots and UnknownObstacles Using Multiple Depth Images . . . . . . . . . . . . . . . . . . . . . 111Markus Fischer, Dominik Henrich
Reducing Motion Artifacts in Mobile Vision Systems viaDynamic Filtering of Image Sequences . . . . . . . . . . . . . . . . . . . . . . . 123Christoph Walter, Felix Penzlin, Norbert Elkmann
Robot Programming
A Software Architecture for Model-Based Programming ofRobot Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Michael Geisinger, Simon Barner, Martin Wojtczyk, Alois Knoll
Intuitive Robot Programming of Spatial Control Loopswith Linear Movements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Katharina Soller, Dominik Henrich
Model-Based Programming “by Demonstration”–FastSetup of Robot Systems (ProDemo) . . . . . . . . . . . . . . . . . . . . . . . . . 159Jurgen Roßmann, Henning Ruf, Christian Schlette
Humanoid Robots
New Concept for Wrist Design of the Humanoid RobotARMAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169Albert Albers, Jens Ottnad, Christian Sander
Biological Motivated Control Architecture andMechatronics for a Human-Like Robot . . . . . . . . . . . . . . . . . . . . . . 179Thomas Wahl, Sebastian Blank, Tobias Luksch, Karsten Berns
Using the Torso to Compensate for Non-Minimum PhaseBehaviour in ZMP Bipedal Walking . . . . . . . . . . . . . . . . . . . . . . . . . 191Houman Dallali, Martin Brown, Bram Vanderborght
Contents IX
Grasping
Object-Specific Grasp Maps for Use in PlanningManipulation Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Franziska Zacharias, Christoph Borst, Gerd Hirzinger
Vision Controlled Grasping by Means of an IntelligentRobot Hand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215Giulio Milighetti, Moritz Ritter, Helge-Bjorn Kuntze
Learning an Object-Grasp Relation for Silhouette-BasedGrasp Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Nicolas Gorges, Heinz Worn
Efficient Parallel Random Sample Matching for PoseEstimation, Localization, and Related Problems . . . . . . . . . . . . . 239Daniel Kubus, Rene Iser, Simon Winkelbach, Friedrich M. Wahl
Medical Robotics
Automated Robot Assisted Fracture Reduction . . . . . . . . . . . . . . 251Ralf Westphal, Simon Winkelbach, Thomas Gosling,Markus Oszwald, Tobias Hufner, Christian Krettek,Friedrich M. Wahl
Path Planning for Robot-Guided Endoscopes in DeformableEnvironments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263Markus Rilk, Friedrich M. Wahl, Klaus W.G. Eichhorn,Ingo Wagner, Friedrich Bootz
Autonomous Helicopters
An Unmanned Helicopter for Autonomous Flights inUrban Terrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Florian Adolf, Franz Andert, Sven Lorenz, Lukas Goormann,Jorg Dittrich
Interaction of Altitude Control and Waypoint Navigationof a 4 Rotor Helicopter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287Tim Puls, Hannes Winkelmann, Sonke Eilers, Matthias Brucke,Andreas Hein
Cooperative Autonomous Helicopters for LoadTransportation and Environment Perception . . . . . . . . . . . . . . . . . 299Konstantin Kondak, Markus Bernard, Fernando Caballero,Ivan Maza, Anibal Ollero
X Contents
Applications
Robot on the Leash—An Intuitive Inexpensive Interfacefor Robots Using the Nintendo Wii Remote . . . . . . . . . . . . . . . . . 311Sven Olufs, Markus Vincze
Robot Basketball: Ball Dribbling—A Modified JugglingTask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323Georg Batz, Marion Sobotka, Dirk Wollherr, Martin Buss
Research on Exoskeletons at the TU Berlin . . . . . . . . . . . . . . . . . . 335Christian Fleischer, Konstantin Kondak, Andreas Wege,Ingo Kossyk
Hard- and Software Architecture of a Small AutonomousUnderwater Vehicle for Environmental Monitoring Tasks . . . . 347Christoph Osterloh, Marek Litza, Erik Maehle
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
List of Contributors
Florian AdolfGerman Aerospace Center (DLR), Institute of Flight Systems,Lilienthalplatz 7, 38108 Braunschweig, Germany,e-mail: [email protected]
Albert AlbersInstitute of Product Development Karlsruhe, University of Karlsruhe,Kaiserstraße 10, 76131 Karlsruhe, Germany,e-mail: [email protected]
Franz AndertGerman Aerospace Center (DLR), Institute of Flight Systems,Lilienthalplatz 7, 38108 Braunschweig, Germany,e-mail: [email protected]
Pradeep AtwalInstitute for Applied Mathematics, Bonn University,Regina-Pacis-Weg 3, 53115 Bonn, Germany,e-mail: [email protected]
Georg BatzInstitute of Automatic Control Engineering, Technische Universitat Munchen,Theresienstraße 90, 80290 Munich, Germany,e-mail: [email protected]
Simon BarnerInstitut fur Informatik VI, Technische Universitat Munchen,Boltzmannstraße 3, 85748 Garching bei Munchen, Germany,e-mail: [email protected]
XII List of Contributors
Markus BernardInstitut fur Technische Informatik und Mikroelektronik,Technische Universitat Berlin, Einsteinufer 17, 10587 Berlin, Germany,e-mail: [email protected]
Karsten BernsRobotics Research Lab at the Department of Computer Sciences,Kaiserslautern University of Technology,P.O. Box 3049, 67653 Kaiserslautern, Germany,e-mail: [email protected]
Sebastian BlankRobotics Research Lab at the Department of Computer Sciences,Kaiserslautern University of Technology,P.O. Box 3049, 67653 Kaiserslautern, Germany,e-mail: [email protected]
Friedrich BootzKlinik und Poliklinik fur Hals-Nasen-Ohrenheilkunde/Chirurgie,Universitatsklinikum Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany,e-mail: [email protected]
Christoph BorstGerman Aerospace Center (DLR), Institute of Robotics and Mechatronics,Munchner Straße 20, 82234 Weßling, Germany,e-mail: [email protected]
Martin BrownThe University of Manchester, Control Systems Centre,School of Electrical and Electronic Engineering, M60 1QD, United Kingdom,e-mail: [email protected]
Matthias BruckeOFFIS, University of Oldenburg, Escherweg 2,26121 Oldenburg, Germany,e-mail: [email protected]
Arno BuckenInstitute of Man-Machine-Interaction, RWTH Aachen,Ahornstraße 55, 52074 Aachen, Germany,e-mail: [email protected]
Wolfram BurgardDepartment of Computer Science, University of Freiburg,Georges-Kohler-Allee 79, 79110 Freiburg, Germany,e-mail: [email protected]
Contributors XIII
Martin BussInstitute of Automatic Control Engineering, Technische Universitat Munchen,Theresienstraße 90, 80290 Munich, Germany,e-mail: [email protected]
Fernando CaballeroRobotics, Vision and Control Group, University of Seville,Camino de los Descubrimientos, 41092 Seville, Spain,e-mail: [email protected]
Dean J. CallaghanSchool of Manufacturing and Design Engineering, Faculty of Engineering,Dublin Institute of Technology, Bolton Street, Dublin 1, Ireland,e-mail: [email protected]
Eugene CoyleSchool of Electrical Engineering Systems, Faculty of Engineering,Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland,e-mail: [email protected]
Houman DallaliThe University of Manchester, Control Systems Centre,School of Electrical and Electronic Engineering, M60 1QD, United Kingdom,e-mail: [email protected]
Jan DeiterdingLehrstuhl fur angewandte Informatik III, Universitat Bayreuth,Universitatsstraße 30, 95447 Bayreuth, Germany,e-mail: [email protected]
Jorg DittrichGerman Aerospace Center (DLR), Institute of Flight Systems,Lilienthalplatz 7, 38108 Braunschweig, Germany,e-mail: [email protected]
Klaus W.G. EichhornKlinik und Poliklinik fur Hals-Nasen-Ohrenheilkunde/Chirurgie,Universitatsklinikum Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany,e-mail: [email protected]
Robert EidenbergerDepartment of Computational Perception, Johannes Kepler University Linz,Altenbergerstraße 69, 4040 Linz, Austria,e-mail: [email protected]
Sonke EilersOFFIS, University of Oldenburg, Escherweg 2,26121 Oldenburg, Germany,e-mail: [email protected]
XIV List of Contributors
Norbert ElkmannFraunhofer Institute for Factory Operation and Automation,Sandtorstraße 22, 39106 Magdeburg, Germany,e-mail: [email protected]
Gerald FarrellSchool of Electronic and Communications Engineering, Faculty of Engineering,Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland,e-mail: [email protected]
Wendelin FeitenDepartment of Intelligent Autonomous Systems, Information and Communication,Siemens AG, Otto-Hahn-Ring 6, 81739 Munich, Germany,e-mail: [email protected]
Markus FischerLehrstuhl fur angewandte Informatik III, Universitat Bayreuth,Universitatsstraße 30, 95447 Bayreuth, Germany,e-mail: [email protected]
Christian FleischerInstitut fur Technische Informatik und Mikroelektronik,Technische Universitat Berlin, Einsteinufer 17, 10587 Berlin, Germany,e-mail: [email protected]
Thorsten GecksLehrstuhl fur angewandte Informatik III, Universitat Bayreuth,Universitatsstraße 30, 95447 Bayreuth, Germany,e-mail: [email protected]
Michael GeisingerInstitut fur Informatik VI, Technische Universitat Munchen,Boltzmannstraße 3, 85748 Garching bei Munchen, Germany,e-mail: [email protected]
Lukas GoormannGerman Aerospace Center (DLR), Institute of Flight Systems,Lilienthalplatz 7, 38108 Braunschweig, Germany,e-mail: [email protected]
Nicolas GorgesInstitute for Process Control and Robotics, University of Karlsruhe,Engler-Bunte-Ring 8, 76131 Karlsruhe, Germany,e-mail: [email protected]
Thomas GoslingUnfallchirurgische Klinik, Medizinische Hochschule Hannover,Carl-Neuberg-Straße 1, 30625 Hannover, Germany,e-mail: [email protected]
Contributors XV
Thilo GrundmannDepartment of Intelligent Autonomous Systems, Information and Communication,Siemens AG, Otto-Hahn-Ring 6, 81739 Munich, Germany,e-mail: [email protected]
Andreas HeinOFFIS, University of Oldenburg, Escherweg 2,26121 Oldenburg, Germany,e-mail: [email protected]
Dominik HenrichLehrstuhl fur angewandte Informatik III, Universitat Bayreuth,Universitatsstraße 30, 95447 Bayreuth, Germany,e-mail: [email protected]
Just L. HerderDepartment of Biomechanical Engineering, Faculty of Mechanical, Maritime andMaterials Engineering, Delft University of Technology,Mekelweg 2, 2628 CD Delft, The Netherlands,e-mail: [email protected]
Gerd HirzingerGerman Aerospace Center (DLR), Institute of Robotics and Mechatronics,Munchner Straße 20, 82234 Weßling, Germany,e-mail: [email protected]
Tobias HufnerUnfallchirurgische Klinik, Medizinische Hochschule Hannover,Carl-Neuberg-Straße 1, 30625 Hannover, Germany,e-mail: [email protected]
Rene IserInstitut fur Robotik und Prozessinformatik, Technische UniversitatCarolo-Wilhelmina zu Braunschweig, Muhlenpfordtstraße 23, 38106Braunschweig, Germany,e-mail: [email protected]
Klaas KlasingInstitute of Automatic Control Engineering, Technische Universitat Munchen,Theresienstraße 90, 80290 Munich, Germany,e-mail: [email protected]
Alois KnollInstitut fur Informatik VI, Technische Universitat Munchen, Boltzmannstraße 3,85748 Garching bei Munchen, Germany,e-mail: [email protected]
XVI List of Contributors
Konstantin KondakInstitut fur Technische Informatik und Mikroelektronik,Technische Universitat Berlin, Einsteinufer 17, 10587 Berlin, Germany,e-mail: [email protected]
Ingo KossykInstitut fur Technische Informatik und Mikroelektronik,Technische Universitat Berlin, Einsteinufer 17, 10587 Berlin, Germany,e-mail: [email protected]
Petra KrahwinklerInstitute of Man-Machine-Interaction, RWTH Aachen,Ahornstraße 55, 52074 Aachen, Germany,e-mail: [email protected]
Christian KrettekUnfallchirurgische Klinik, Medizinische Hochschule Hannover,Carl-Neuberg-Straße 1, 30625 Hannover, Germany,e-mail: [email protected]
Daniel KubusInstitut fur Robotik und Prozessinformatik,Technische Universitat Carolo-Wilhelmina zu Braunschweig,Muhlenpfordtstraße 23, 38106 Braunschweig, Germany,e-mail: [email protected]
Helge-Bjorn KuntzeFraunhofer-Institute for Information and Data Processing (IITB),Fraunhoferstraße 1, 76131 Karlsruhe, Germany,e-mail: [email protected]
Marek LitzaInstitute of Computer Engineering, University of Lubeck,Ratzeburger Allee 160, 23538 Lubeck, Germany,e-mail: [email protected]
Sven LorenzGerman Aerospace Center (DLR), Institute of Flight Systems,Lilienthalplatz 7, 38108 Braunschweig, Germany,e-mail: [email protected]
Tobias LukschRobotics Research Lab at the Department of Computer Sciences,Kaiserslautern University of Technology, P.O. Box 3049,67653 Kaiserslautern, Germany,e-mail: [email protected]
Contributors XVII
Erik MaehleInstitute of Computer Engineering, University of Lubeck,Ratzeburger Allee 160, 23538 Lubeck, Germany,e-mail: [email protected]
Ivan MazaRobotics, Vision and Control Group, University of Seville,Camino de los Descubrimientos, 41092 Seville, Spain,e-mail: [email protected]
Mark M. McGrathSchool of Manufacturing and Design Engineering, Faculty of Engineering,Dublin Institute of Technology, Bolton Street, Dublin 1, Ireland,e-mail: [email protected]
Giulio MilighettiFraunhofer-Institute for Information and Data Processing (IITB),Fraunhoferstraße 1, 76131 Karlsruhe, Germany,e-mail: [email protected]
Anibal OlleroRobotics, Vision and Control Group, University of Seville,Camino de los Descubrimientos, 41092 Seville, Spain,e-mail: [email protected]
Sven OlufsAutomation and Control Institute, Technische Universitat Wien,Gußhausstraße 27–29 / E376, 1040 Wien, Austria,e-mail: [email protected]
Christoph OsterlohInstitute of Computer Engineering, University of Lubeck,Ratzeburger Allee 160, 23538 Lubeck, Germany,e-mail: [email protected]
Markus OszwaldUnfallchirurgische Klinik, Medizinische Hochschule Hannover,Carl-Neuberg-Straße 1, 30625 Hannover, Germany,e-mail: [email protected]
Lionel OttDepartment of Computer Science, University of Freiburg,Georges-Kohler-Allee 79, 79110 Freiburg, Germany,e-mail: [email protected]
Jens OttnadInstitute of Product Development Karlsruhe, University of Karlsruhe,Kaiserstraße 10, 76131 Karlsruhe, Germany,e-mail: [email protected]
XVIII List of Contributors
Felix PenzlinFraunhofer Institute for Factory Operation and Automation,Sandtorstraße 22, 39106 Magdeburg, Germany,e-mail: [email protected]
Tim PulsOFFIS, University of Oldenburg,Escherweg 2, 26121 Oldenburg, Germany,e-mail: [email protected]
Ginu RajanPhotonics Research Centre, Faculty of Engineering,Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland,e-mail: [email protected]
Andreas RichtsfeldAutomation and Control Institute, Technische Universitat Wien,Gußhausstraße 27–29 / E376, 1040 Wien, Austria,e-mail: [email protected]
Markus RilkInstitut fur Robotik und Prozessinformatik,Technische Universitat Carolo-Wilhelmina zu Braunschweig,Muhlenpfordtstraße 23, 38106 Braunschweig, Germany,e-mail: [email protected]
Moritz RitterFraunhofer-Institute for Information and Data Processing (IITB),Fraunhoferstraße 1, 76131 Karlsruhe, Germany,e-mail: [email protected]
Jurgen RoßmannInstitute of Man-Machine-Interaction, RWTH Aachen,Ahornstraße 55, 52074 Aachen, Germany,e-mail: [email protected]
Henning RufInstitute of Man-Machine-Interaction, RWTH Aachen, Ahornstraße 55, 52074Aachen, Germany, e-mail: [email protected]
Christian SanderInstitute of Product Development Karlsruhe, University of Karlsruhe,Kaiserstraße 10, 76131 Karlsruhe, Germany,e-mail: [email protected]
Christian SchletteInstitute of Man-Machine-Interaction, RWTH Aachen, Ahornstraße 55,52074 Aachen, Germany,e-mail: [email protected]
Contributors XIX
Hannes SchulzDepartment of Computer Science, University of Freiburg,Georges-Kohler-Allee 79, 79110 Freiburg, Germany,e-mail: [email protected]
Yuliya SemenovaPhotonics Research Centre, Faculty of Engineering,Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland,e-mail: [email protected]
Marion SobotkaInstitute of Automatic Control Engineering,Technische Universitat Munchen,Theresienstraße 90, 80290 Munich, Germany,e-mail: [email protected]
Katharina SollerLehrstuhl fur angewandte Informatik III, Universitat Bayreuth,Universitatsstraße 30, 95447 Bayreuth, Germany,e-mail: [email protected]
Jurgen SturmDepartment of Computer Science, University of Freiburg,Georges-Kohler-Allee 79, 79110 Freiburg, Germany,e-mail: [email protected]
Jozef SuchyChemnitz University of Technology, Faculty of Electrical Engineering andInformation Technology, Robot Systems,Reichenhainer Straße 70, 09126 Chemnitz, Germany,e-mail: [email protected]
Bram VanderborghtItalian Institute of Technology, Robotics, Brain and Cognitive Sciences Department,Via Morego 30, 16163 Genova, Italy,e-mail: [email protected]
Markus VinczeAutomation and Control Institute, Technische Universitat Wien,Gußhausstraße 27–29 / E376, 1040 Wien, Austria,e-mail: [email protected]
Ingo WagnerKlinik und Poliklinik fur Hals-Nasen-Ohrenheilkunde/Chirurgie,Universitatsklinikum Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany,e-mail: [email protected]
XX List of Contributors
Friedrich M. WahlInstitut fur Robotik und Prozessinformatik,Technische Universitat Carolo-Wilhelmina zu Braunschweig,Muhlenpfordtstraße 23, 38106 Braunschweig, Germany,e-mail: [email protected]
Thomas WahlRobotics Research Lab at the Department of Computer Sciences,Kaiserslautern University of Technology, P.O. Box 3049,67653 Kaiserslautern, Germany,e-mail: t [email protected]
Christoph WalterFraunhofer Institute for Factory Operation and Automation,Sandtorstraße 22, 39106 Magdeburg, Germany,e-mail: [email protected]
Andreas WegeInstitut fur Technische Informatik und Mikroelektronik,Technische Universitat Berlin, Einsteinufer 17, 10587 Berlin, Germany,e-mail: [email protected]
Ralf WestphalInstitut fur Robotik und Prozessinformatik,Technische Universitat Carolo-Wilhelmina zu Braunschweig,Muhlenpfordtstraße 23, 38106 Braunschweig, Germany,e-mail: [email protected]
Volkert van der WijkDepartment of Biomechanical Engineering, Faculty of Mechanical,Maritime and Materials Engineering, Delft University of Technology,Mekelweg 2, 2628 CD Delft, The Netherlands,e-mail: [email protected]
Simon WinkelbachInstitut fur Robotik und Prozessinformatik,Technische Universitat Carolo-Wilhelmina zu Braunschweig,Muhlenpfordtstraße 23, 38106 Braunschweig, Germany,e-mail: [email protected]
Hannes WinkelmannOFFIS, University of Oldenburg,Escherweg 2, 26121 Oldenburg, Germany,e-mail: [email protected]
Contributors XXI
Alexander WinklerChemnitz University of Technology, Faculty of Electrical Engineering andInformation Technology, Robot Systems, Reichenhainer Straße 70,09126 Chemnitz, Germany,e-mail: [email protected]
Martin WojtczykInstitut fur Informatik VI, Technische Universitat Munchen,Boltzmannstraße 3, 85748 Garching bei Munchen, Germany,e-mail: [email protected]
Dirk WollherrInstitute of Automatic Control Engineering, Technische Universitat Munchen,Theresienstraße 90, 80290 Munich, Germany,e-mail: [email protected]
Heinz WornInstitute for Process Control and Robotics, University of Karlsruhe,Engler-Bunte-Ring 8, 76131 Karlsruhe, Germany,e-mail: [email protected]
Franziska ZachariasGerman Aerospace Center (DLR), Institute of Robotics and Mechatronics,Munchner Straße 20, 82234 Weßling, Germany,e-mail: [email protected]
Joint Dominance Coefficients:A Sensitivity-Based Measure for RankingRobotic Degrees of Freedom
Klaas Klasing, Dirk Wollherr, and Martin Buss
Abstract. Many robotics applications require a weighting scheme for individualdegrees of freedom in a kinematic linkage. Such schemes are used for example inpath and motion planning algorithms to penalize large end-effector movements orscale distance computations for the retrieval of nearest neighbors. Most often, theweights are manually picked and heuristically adjusted for specific linkages. In thispaper we propose joint dominance coefficients as a universal tool for estimating theinfluence of each degree of freedom of a robot on the overall robot displacement.The measure is easy to compute, converges quickly and can be applied to any kindof parameterized kinematic linkage, including tree-structured and closed kinematicchains. A mathematical derivation is provided along with application examples forvarious robotic linkages. The results show that the method accurately and reliablyyields the desired weights.
1 Introduction
Most robotics applications involve kinematic linkages with several degrees of free-dom (DoF). These DoF arise from revolute or prismatic joints that connect the robotlinks. The overall geometry of the robot is usually parameterized by the DoF ofthe base link (movement of the robot base) and the joint values (angles for revolutejoints, distances for prismatic joints), which describe the robot configuration. A cen-tral question for many applications is how the overall robot displacement dependson the degrees of freedom of the robot. Such a dependency measure is useful forexample in the context of path and motion planning applications, where DoF thatcause larger displacements must be penalized by corresponding weights.
While for prismatic DoF there is a linear relationship between parameter changeand robot displacement, for revolute DoF the overall displacement is a nonlinear
Klaas Klasing · Dirk Wollherr · Martin BussInstitute of Automatic Control Engineering, Technische Universitat Munchen,Theresienstraße 90, 80290 Munich, Germany,e-mail: kk,dw,[email protected]
2 K. Klasing et al.
function of the robot configuration. As an example, consider a 20-link serial kine-matic chain with equally long links connected by revolute joints. When the chain isfully extended, an angular change in the first joint has a much larger influence onoverall robot displacement than the same angular change applied to the 19th joint inthe chain. However, for a configuration in which the robot is ’folded’ to its minimalexpansion, for both the first and the 19th joint an angular change has the same effecton overall displacement. The influence of each DoF on robot displacement is there-fore configuration dependent. The question addressed in this paper is whether thereis a practically feasible way of assessing the influence of each DoF over all possiblerobot configurations.
The measure presented in the following provides an automated numeric proce-dure for assigning a weight to each degree of freedom that correctly captures theoverall influence of the respective DoF on the robot displacement. To the best ofour knowledge there exists no method that is able to generically derive meaningfulcoefficients similar to those obtained by our approach.
The remainder of this paper is structured as follows: Section 2 briefly reviewsexisting related methods. Section 3 presents prerequisites, a derivation of joint dom-inance coefficients as well as an efficient way to calculate the coefficients in practice.Section 4 demonstrates the application of the method to a number of different kine-matic linkages. A discussion of the results and the applicability of the method isgiven in Section 5.
2 Related Work
The problem of weighting the links in a kinematic linkage is equivalent to the prob-lem of scaling an underlying distance metric. In the field mechanism design find-ing suitable distance metrics for specific linkage topologies is an active researchtopic [1, 2]. In the context of sampling-based path planning suitable distance met-rics are relevant for effective sampling [3], nearest neighbor searching [4] and localplanning [5]. All of these works are related in that they try to provide a consistentand meaningful notion of distance within the topology defined by the linkage. Incontrast, this paper is not concerned with deriving new metrics for specific linkages.Instead it aims to provide a universal numeric measure for each DoF in a linkage,which can then be used to adjust a given metric.
The proposed coefficients can also be used for the analysis of kinematiclinkages. In this respect they are loosely related to swept volume [6, 7], whichrepresents a powerful tool for analyzing the reachable workspace of a kinematiclinkage. However, for the simple purpose of finding suitable weights for spec-ifying DoF displacement influence, swept volume methods are somewhat of anoverkill. While weights similar to the coefficients proposed in this paper could bederived from swept volume methods for many linkages, these methods are compu-tationally expensive and require detailed geometric considerations. In contrast, theproposed joint dominance coefficients only need a parametrization of the forwardkinematics as well as a number of representative points on the linkage. Although
Joint Dominance Coefficients 3
only moderately sized tree-structured linkages are examined in this paper, thesampling-based nature of joint dominance coefficients makes them perfectly suit-able for closed-loop parametrizations, such as [8], as well as systems with manyDoF. In both cases analytical derivation of similar coefficients from swept volumequickly becomes infeasible because of the complexity increase.
Joint dominance coefficients are also loosely related to the individual Lipschitzconstants that can be used to bound robot displacement for iterative collision check-ing [5]. While our approach provides an average value per DoF, the Lipschitzconstants represent an upper limit for displacement on a per-DoF basis. To ourknowledge there exists no automated generic procedure for deriving these constants;in fact in most path planning applications that utilize iterative collision checking, theDoF scaling is usually hand-tuned until certain displacement constants seem to bemet.
3 Methodology
In this section the concept of joint dominance coefficients is derived and a methodfor efficient calculation of the coefficients is presented.
3.1 Distance Metrics
In the following we will assume that a robot A (q) has n degrees of freedom that areparameterized by a vector q ∈ R
n, q = [q1 . . . qn]. The geometry of the robot A isdefined over either R
2 or R3. The set of all possible robot configurations makes up
the so-called configuration space C , or simply C-space [9, 5]. Each DoF is assumedto be bounded by joint limits [qi,min,qi,max].
A central prerequisite for all research methods that utilize the configuration spaceof a robot is a notion of the distance between two configurations q and q′. For manyapplications a simple Euclidean distance in joint space
ρE(q,q′) =∥∥q−q′
∥∥2 (1)
works sufficiently well for the purposes of nearest neighbor searching, uniform sam-pling of configurations etc. However, if the linkage contains many revolute joints,the metric does not respect the topology of the configuration space1 and for manypairs of configuration (q,q′) does not reflect the actual displacement of the robot inthe world.
A much better measure is provided by the so-called robot displacement metric [5]
ρD(q,q′) = maxa∈A
∥∥a(q)−a(q′)∥∥
(2)
1 For n+1 links attached by n revolute joints the configuration space has the topology of ann-dimensional torus.
4 K. Klasing et al.
that yields the maximum distance that any point on the robot A has been displaced.Unfortunately, ρD(q,q′) cannot be efficiently computed for generic kinematic link-ages in practice, however, as we shall see in the following, it is possible to findefficient approximations.
3.2 Derivation of the Joint Dominance Coefficient Vector
To distinguish between the ’importance’ of different degrees of freedom, a so-calledjoint dominance coefficient for each DoF/joint is proposed. This coefficient reflectshow much a given degree of freedom influences the overall average displacement ofthe robot.
Fig. 1 Several representa-tive points on a kinematiclinkage can be used toapproximate the robot dis-placement metric.
0T1
1T2
2T3
For simplicity of derivation consider the serial kinematic linkage depicted in Fig-ure 1. Let the position of the end effector (in orange) with respect to frame 3 bedenoted by 3 pe. The values of the rotational joints2 will be denoted by q1, q2, andq3 and the corresponding homogeneous transformation matrices T1(q1), T2(q3), andT3(q3). Then, the position of the end effector in world coordinates is given by
0 pe = 0T1 · 1T2 · 2T3 · 3 pe = f (q). (3)
The local sensitivity of the end effector position f (q) with respect to the value ofthe ith joint qi is – for a given configuration q∗ = [q∗1, . . . , q∗i−1, qi, q∗i+1, . . . , q∗n] –given by
∂ f (q)∂qi
∣∣∣∣q∗
:= f ′(qi)∣∣q∗ . (4)
Note that the sensitivity derivative is a vectorial function of qi. Taking the Euclideannorm of this vector to obtain its magnitude and integrating over the joint limits ofthe respective joint qi yields
σi(q∗) =∫ qi,max
qi,min
∥∥∥ f ′(qi)∣∣q∗
∥∥∥2
dqi, (5)
2 All derivation steps hold for prismatic joints as well as for more complicated tree-structured linkages, too.
Joint Dominance Coefficients 5
which is a scalar measure that indicates how much qi influences end effector dis-placement over its joint range. Two further adjustments are necessary to obtain ameaningful coefficient for the entire configuration space: Firstly, sensitivity is a lo-cal measure that may drastically differ for different configurations. Since the goal isto have one coefficient per joint for the entire configuration space, the overall mea-sure is aggregated by randomly sampling ns configurations q∗j , where j = 1, . . . ,ns.The average influence of joint qi on the end effector position is then given by
σi =1ns
ns
∑j=1
∫ qi,max
qi,min
∥∥∥∥ f ′(qi)∣∣q∗j
∥∥∥∥2
dqi. (6)
Secondly, a good displacement metric should not only take into account the endeffector, but essentially the movement of any link on the robot. The robot displace-ment metric from (2) would be an ideal measure for this but is hard to calculatein practice. We therefore propose to use a collection of np representative pointsp1, . . . , pnp on the robot for expressing the overall displacement. Obviously, the po-sition of each point is calculated from a sequence of transformation matrices andcan be represented by corresponding functions f1(q), . . . , fnp(q). Such points wouldusually be chosen at the robot base, at the origin of each coordinate frame and ateach end effector. For the simple robot from Figure 1 all highlighted points wouldbe chosen as representative points.
Then, the overall displacement between two configurations q and q′ is expressedby the new metric
ρP(q,q′) =np
∑i=1
∥∥ fi(q)− fi(q′)∥∥
2 . (7)
Therefore, the overall average influence of a given joint on the robot displacementfrom (7), which we call joint dominance coefficient, is given by
σi =1ns
np
∑j=1
ns
∑k=1
∫ qi,max
qi,min
∥∥∥ f ′(qi)∣∣q∗k
∥∥∥2
dqi. (8)
When calculated for each joint, the resulting vector σ = [σ1 · · ·σn] of joint domi-nance coefficients should be normalized to obtain
σ∗ =1
‖σ‖2σ =
1‖σ‖2
⎡⎢⎣σ1...σn
⎤⎥⎦ . (9)
This joint dominance coefficient vector indicates what percentage of the overall av-erage displacement of a robot is caused by each degree of freedom.
6 K. Klasing et al.
3.3 Calculation of the Joint Dominance Coefficient Vector
In a practical implementation, the calculation of the partial derivatives f ′(qi) as wellas the analytical evaluation of the integral would require a symbolic math engine.Although the derivatives exhibit a certain structure and can be broken down into afinite series of sin and cos expressions that stem from the transformation matrices,arbitrary kinematic linkages may still cause arbitrarily complex symbolic terms thatneed to be integrated. For efficient calculation of σ it is therefore desirable to havea numeric approximation of (8). Such an approximation can be achieved in twosteps: Firstly, the derivative is substituted by a difference quotient, and secondlythe integration is replaced by a summation. To this end each degree of freedomis gridded at a certain resolution and nr samples qi,1, . . . ,qi,nr are placed evenlybetween qi,min and qi,max, i.e. qi,1 = qi,min and qi,nr = qi,max. For notational feasibility,let q(i,k, l) denote the kth randomly generated configuration vector for which the ithentry (corresponding to the ith DoF) has been set to qi,l . Then the resulting term forthe approximated joint dominance coefficient is
σi =1ns
np
∑j=1
ns
∑k=1
nr−1
∑l=1
∥∥ f j(q(i,k, l))− f j(q(i,k, l + 1))∥∥
2 . (10)
Since the vector is normalized in the end and ns is the same for all degrees offreedom the factor 1
nscan be dropped. After rearranging the order of summation,
one obtains
σi =ns
∑j=1
nr−1
∑k=1
ρP (q(i, j,k),q(i, j,k + 1)) , (11)
where ρ is the displacement metric from (7).To summarize, σ∗ is calculated by generating ns random configurations, comput-
ing – for each configuration – the displacement ρD between each two consecutiveconfigurations spaced at nr even steps in [qi,min,qi,max] for the ith degree of freedom,adding all displacements for each i and finally normalizing the vector. Note that theestimation has a runtime complexity of O(n ·ns ·nr) and thus is linear in the numberof DoF.
3.4 Remarks
Several remarks are in order for the chosen way of calculating the coefficients.Firstly, the algorithm relies on random sampling to aggregate the local sensitivity-based measures to an overall measure for the entire configuration space. Randomsampling was preferred over sampling on a grid, because the number of sampleson a grid increases exponentially with the number of DoF. In fact this is the sameproblem that led researchers to turn to sampling-based path planning as a meansfor solving high-dimensional planning problems. Consequently, much the same
Joint Dominance Coefficients 7
requirements apply for the sampling sequence. Since we try to achieve a fairly uni-form covering of the configuration space with a finite number of ns samples, thesampling sequence should be dense [5]. For our purposes we used uniform randomsampling in the hypercube bounded by the individual [qi,min,qi,max]. A deterministic(quasi-random) alternative would be the use of Halton points [10]. Since the numberof samples is known beforehand it is also possible to use Hammersley points [11] orlattice sampling [12].
A second remark concerns the convergence of the computation. A detailed proofis omitted due to space constraints but can be constructed along the following lines:The integral in the inner term of (8),∫ qi,max
qi,min
∥∥∥ f ′(qi)∣∣q∗k
∥∥∥2
dqi, (12)
has been replaced by its Riemann sum in (10), which implies asymptotic conver-gence as nr grows. The convergence of the overall coefficient with growing ns thendepends on the continuous differentiability of the configuration space manifold, andthe denseness of the sampling sequence. An empirical study of the convergence ispresented in the following section, which allows for specifying recommended valuesfor nr and ns.
4 Application to Kinematic Linkages
To evaluate the meaningfulness of the proposed coefficients, the method was appliedto the four kinematic linkages depicted in Figure 2. All of them represent robots in a
Table 1 Admissable DoF ranges for each robot.
Robot DoF qi,min qi,max
simple3 1 -15 m 15 m
2 -100 100
3 -90 90
snake6 1,2 -21.5 m 21.5 m
3 -180 180
4,5,6 -90 90
crab11 1,2 -25 m 25 m
3 -180 180
4,6,8,10 -55 55
5,7,9,11 -20 20
tree11 1,3,4,5,6,8,9,10,11 -20 20
2,7 -45 45
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3
3
3 34
4
4
5 55
6
6
67 78
8
9
9
1010
11 11
2
2 2
21
1
1
1
(a) simple3 (b) snake6 (c) crab11 (d) tree11
Fig. 2 Four robots used for evaluation: (a) A simple robot with 3 DoF (b) A snake robot with6 DoF (c) A crab-like robot with 11 DoF (d) A tree-like robot with 11 DoF.
1 2 3 4 5 60
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 2 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 1100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 2 3 4 5 6 7 8 9 10 11
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Join
tDom
inan
ceσ∗ i
Join
tDom
inan
ceσ∗ i
Join
tDom
inan
ceσ∗ i
Join
tDom
inan
ceσ∗ i
DoF Index i
DoF Index i DoF Index i
DoF Index i
(a) (b)
(c) (d)
simple3 robot snake6 robot
crab11 robot tree11 robot
Fig. 3 Joint dominance coefficients of the four robots. Translational and rotational DoF ofthe base link have the strongest influence (a), (b), and (c). For each DoF the coefficient nicelyreflects the position in the kinematic tree and the available joint range.
Joint Dominance Coefficients 9
0204060800 20 40 60 80 100
0.424
0.425
0.426
0.427
0.428
0.429
0.43
0.431
0.432
nsnr
σ∗ 1
Fig. 4 Convergence of the first joint dominance coefficient of the crab11 robot.
2D world3. Their respective degrees of freedom are marked by the numbered circles.The simple3 robot in Figure 2(a) can move in the horizontal direction and actuateits rotational joints. Both the snake6 robot and the crab11 robot can translate androtate freely in the plane and actuate all indicated degrees of freedom. The tree11robot has a fixed base, but can actuate any of its revolute joints.
Table 1 lists the admissable range of each DoF for all four robots. The transla-tional DoF were constrained to the ranges usually used in planning scenarios, i.e.the size of the workcell the robot would move in.
The joint dominance coefficient vectors of the four robots are shown inFigures 3(a)-(d). The coefficients were calculated with nr = 20 and ns = 100. Quiteclearly, the values nicely reflect the overall influence of each DoF. The translationalDoF of the base dominate because they cause the largest displacement, regardlessof the remaining configuration. After that, the rotation of the base has the great-est influence, followed by the hierarchy of the individual DoF in the kinematictree.
Figure 4 shows the value of the first joint dominance coefficient σ∗1 of the crab11
robot plotted over different values of nr and ns4. It can be seen that the value con-
verges quite quickly in nr and decently fast in ns. For nr ≥ 10 and ns ≥ 50 the valueremains invariant in the first three significant digits. Individual simulations over nr
and ns for the other robots showed the exact same convergence behavior.
3 Equivalent results would be obtained for a 3D world, as the displacement is measured bythe sum of Euclidean distances and the joints are assumed to have only one revolute orprismatic DoF each.
4 Since the algorithm uses random sampling, each value was averaged over 20 runs. Thevariance was observed to converge proportionally with the mean.
10 K. Klasing et al.
5 Conclusion
In this paper we have presented Joint Dominance Coefficients, a novel numeric pro-cedure for estimating the influence of each DoF in a kinematic linkage on the over-all displacement. The algorithm makes use of random sampling in the configurationspace to assess the displacement caused by a change in each DoF over its range. Themethod was observed to converge quickly and yield meaningful weights for varioustree-structured kinematic linkages.
The presented applications mainly stem from our involvement with sampling-based path planning. In fact the proposed method was developed to overcome therepeatedly encountered problem of manually having to pick suitable weights fora given linkage; however, we expect that it can be useful far beyond the domainin which we have examined it. Future research could aim at extending the methodto the mentioned Lipschitz constants or to providing coefficients for dynamic con-straints, i.e. maximum joint velocities.
Acknowledgements. This work is supported in part within the DFG excellence initiativeresearch cluster Cognition for Technical Systems – CoTeSys, see also www.cotesys.org.
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Learning Kinematics from DirectSelf-Observation Using Nearest-NeighborMethods
Hannes Schulz, Lionel Ott, Jurgen Sturm, and Wolfram Burgard
Abstract. Commonly, the inverse kinematic function of robotic manipulators is de-rived analytically from the robot model. However, there are cases in which a modelis not a priori available. In this paper, we propose an approach that enables an au-tonomous robot to estimate the inverse kinematic function on-the-fly directly fromself-observation and without a given kinematic model. The robot executes randomlysampled joint configurations and observes the resulting world positions. To approx-imate the inverse kinematic function, we propose to use instance-based learningtechniques such as Nearest Neighbor and Linear Weighted Regression. After learn-ing, the robot can take advantage of the learned model to build roadmaps for motionplanning. A further advantage of our approach is that the environment can implic-itly be represented by the sample configurations. We analyze properties of this ap-proach and present results obtained from experiments on a real 6-DOF robot andfrom simulation. We show that our approach allows us to accurately control robotswith unknown kinematic models of various complexity and joint types.
1 Introduction
Robotic manipulators typically require a Cartesian controller that maps the three-dimensional world space coordinates to joint configurations. The equations for theinverse kinematics can analytically be derived in advance when a robot model isavailable. Careful parameter calibration then ensures high accuracy in positioningtasks.
In the emerging field of home robotics, robots are likely to be assembled withoutsurveillance of an engineer, meaning that no accurate construction model is avail-able at design time. Further, home robots need to operate for extended periods of
Hannes Schulz · Lionel Ott · Jurgen Sturm · Wolfram BurgardDepartment of Computer Science, University of Freiburg,Georges-Kohler-Allee 79, 79110 Freiburg, Germany,e-mail:schulzha,ottli,sturm,[email protected]
