Geometric and Numerical Foundations of Movements PDF
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Springer Tracts in Advanced Robotics 117 Jean-Paul Laumond Nicolas Mansard Jean-Bernard Lasserre Editors Geometric and Numerical Foundations of Movements Springer Tracts in Advanced Robotics 117 Editors Prof. Bruno Siciliano Prof. Oussama Khatib Dipartimento di Ingegneria Elettrica Artificial Intelligence Laboratory e Tecnologie dell’Informazione Department of Computer Science Università degli Studi di Napoli Stanford University Federico II Stanford, CA 94305-9010 Via Claudio 21, 80125 Napoli USA Italy E-mail: [email protected] E-mail: [email protected] Editorial Advisory Board Nancy Amato, Texas A & M, USA Oliver Brock, TU Berlin, Germany Herman Bruyninckx, KU Leuven, Belgium Wolfram Burgard, Univ. Freiburg, Germany Raja Chatila, ISIR - UPMC & CNRS, France Francois Chaumette, INRIA Rennes - Bretagne Atlantique, France Wan Kyun Chung, POSTECH, Korea Peter Corke, Queensland Univ. Technology, Australia Paolo Dario, Scuola S. Anna Pisa, Italy Alessandro De Luca, Sapienza Univ. Rome, Italy Rüdiger Dillmann, Univ. Karlsruhe, Germany Ken Goldberg, UC Berkeley, USA John Hollerbach, Univ. Utah, USA Lydia Kavraki, Rice Univ., USA Vijay Kumar, Univ. Pennsylvania, USA Bradley Nelson, ETH Zürich, Switzerland Frank Park, Seoul National Univ., Korea Tim Salcudean, Univ. British Columbia, Canada Roland Siegwart, ETH Zurich, Switzerland Gaurav Sukhatme, Univ. Southern California, USA More information about this series at http://www.springer.com/series/5208 Jean-Paul Laumond Nicolas Mansard (cid:129) Jean-Bernard Lasserre Editors Geometric and Numerical Foundations of Movements 123 Editors Jean-Paul Laumond Jean-Bernard Lasserre LAAS-CNRS LAAS-CNRS Toulouse Toulouse France France NicolasMansard LAAS-CNRS Toulouse France ISSN 1610-7438 ISSN 1610-742X (electronic) SpringerTracts inAdvanced Robotics ISBN978-3-319-51546-5 ISBN978-3-319-51547-2 (eBook) DOI 10.1007/978-3-319-51547-2 LibraryofCongressControlNumber:2016963164 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Series Foreword Robotics is undergoing a major transformation in scope and dimension. From a largely dominant industrial focus, robotics is rapidly expanding into human envi- ronmentsandvigorouslyengagedinitsnewchallenges.Interactingwith,assisting, serving, and exploring with humans, the emerging robots will increasingly touch people and their lives. Beyond its impact on physical robots, the body of knowledge robotics has produced is revealing a much wider range of applications reaching across diverse research areas and scientific disciplines: biomechanics, haptics, neurosciences, virtualsimulation,animation,surgery,andsensornetworksamongothers.Inreturn, the challenges of the new emerging areas are proving an abundant source of stimulation and insights for the field of robotics. It is indeed at the intersection of disciplines that the most striking advances happen. TheSpringer TractsinAdvancedRobotics(STAR)isdevotedtobringingtothe research community the latest advances in the robotics field on the basis of their significance and quality. Through a wide and timely dissemination of critical researchdevelopmentsinrobotics,ourobjectivewiththisseriesistopromotemore exchanges and collaborations among the researchers in the community and con- tribute to further advancements in this rapidly growing field. The volume by J.P. Laumond, N. Mansard and J. Lasserre provides a broad edited collection on movement analysis, which is the outcome of the workshop “Geometric and Numerical Foundations of Movements” held at LAAS-CNRS in Toulouse in November 2015. Following a tutorial presentation of the problem, the contents are effectively organized into four main sections: geometry, action and movement; numerical analysis and optimization; foundation of human movement; robot motion generation. The unique feature of the volume stands in its inherent multidisciplinary character spanning robotics, control theory, neurosciences and v vi SeriesForeword mathematics. New optimization techniques are presented, based on recent results from real algebraic geometry, which shed new light for advancements on motion research. Rich of results by the most active teams in the field, this volume constitutes a very fine addition to STAR! Naples, Italy Bruno Siciliano November 2016 STAR Editor Preface This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “Geometric and Numerical Foundations of Movements”heldatLAAS-CNRSinToulouseinNovember2015.1Itsobjectiveis to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics—and control in general—of new optimization techniques based on recent results from real algebraic geometry. Starting from a robotics perspective, the generation of goal oriented motion for robotsobeysclassicallytoatwo-stepparadigm.Thefirststepistheplanning,where the typical problem is to find a geometric path that allows the robot to reach the desired configuration starting from the current position while ensuring obstacle avoidanceandenforcingthesatisfaction ofkinematic constraints.Motionplanning laysitsgroundingonthedecidabilitypropertiesofthisclassicgeometricalproblem. Moreover, the traditional approaches that are used to find solutions rely on the globalprobabilisticcertaintyoftheconvergenceofpathconstructionstochastically sampled in the configuration space. The second step of motion generation is the control, where the robot has to perform the planned motion while ensuring the respect of dynamical constraints. Motion control seeks primarily for local controllability or at least the stability of the motion. The basic instances of these problems have long been tackled using local state-space control. However, the typical nonlinearity of the dynamics, together with the non-controllability of its linearization, leads more and more solutions to resort to model preview control. Thesemethodsallowtopredicttheoutcomeofacontrolstrategyinafuturehorizon andtoimproveitaccordingly,usuallybyusingnumericaloptimizationswhichtake 1TheworkshoptookplaceintheframeworkoftheAnthropomorphicMotionFactorylaunchedby the European project ERC-ADG 340050 Actanthrope (2014–2018) devoted to exploring the computationalfoundationsofanthropomorphicaction.Theworkshopwasalsosupportedbythe EuropeanprojectERC-ADV666981Taming(2015–2019)andtheFrenchANRprojectEntracte (2014–2017). vii viii Preface intoaccountthesafetyconstraintsandefficiencyintents.However,sincefewyears, the improvement of computational capabilities and numerical algorithms allows more and more to deal with complex dynamical systems and for longer horizons. Thisallowstheseapproachestountightenthelocalnatureoftheirapplicationsand progressively start wider explorations of their reachable space. This evolution bringsustothequestionoftherisingoverlapbetweenplanningandcontrol.Today, most planning problems would take too much time to be solved online with numerical approaches. Does that imply that the generation of motion will theo- retically never be free of the necessity of a prior planning? Or on the contrary, is planning only a numerical issue? All these questions are also addressed in Life Sciences. Indeed, movement is a fundamental characteristic of living systems. How roboticists may benefit from neurophysiologist know-how and vice versa? System modelling is one way to gather both communities. While actions operate in a physical space, motions begin in a motor control space. For robots and living beings, the link between actions expressed in the physical space and motions originated in the motor space, turns to geometry in generaland,inparticular,tolinearalgebra.Geometriccontroltheoryandnumerical analysis highlight two complementary perspectives on optimal human and huma- noid motion. Among all possible motions performing a given action, optimization algorithms tend to choose the best motion according to a given performance criterion. Optimal motions then appear as plausible action signatures. How to express actions in terms of motions? How to face the computational complexity of bridging the 3D physical space with the high-dimension control space?Howtorevealmovementsynergies?Howtoaccountfortheunderactuation of the locomotion? What optimality criterion underlies a given action? All these questionsopenchallengingissuestodirectandinverseoptimalcontrol,withrecent developments in polynomial optimization and real algebraic geometry. Themultidisciplinaryperspectiveonmovementanalysisisreflectedinthebook by its table of content. After a specific chapter introducing the rational above, the chapters are gathered within four main parts addressing respectively mathematics (Part Geometry, Action and Movement), applied mathematics (Part Numerical Analysis and Optimization), life science (Part Foundations of Human Movement), and robotics (Part Robot Motion Generation). Editingabookwithamultidisciplinaryperspectiveisnotaneasytask.Wethank alltheauthorsfortheireffortinmakingtheirownresearchfieldaccessibletoothers and all the reviewers who helped us in reaching this objective. Toulouse, France Jean-Paul Laumond August 2016 Nicolas Mansard Jean-Bernard Lasserre Contents Robot Motion Planning and Control: Is It More than a Technological Problem?.... ..... .... .... .... .... .... ..... .... 1 Mehdi Benallegue, Jean-Paul Laumond and Nicolas Mansard Part I Geometry, Action and Movement Several Geometries for Movements Generations... .... .... ..... .... 13 Daniel Bennequin and Alain Berthoz On the Duration of Human Movement: From Self-paced to Slow/Fast Reaches up to Fitts’s Law.. .... .... .... .... ..... .... 43 Frédéric Jean and Bastien Berret Geometric and Numerical Aspects of Redundancy. .... .... ..... .... 67 Pierre-Brice Wieber, Adrien Escande, Dimitar Dimitrov and Alexander Sherikov Part II Numerical Analyzis and Optimization Some Recent Directions in Algebraic Methods for Optimization and Lyapunov Analysis .... .... .... .... ..... .... 89 Amir Ali Ahmadi and Pablo A. Parrilo Positivity Certificates in Optimal Control.... .... .... .... ..... .... 113 Edouard Pauwels, Didier Henrion and Jean-Bernard Lasserre The Interplay Between Big Data and Sparsity in Systems Identification. .... ..... .... .... .... .... .... ..... .... 133 O. Camps and M. Sznaier ix
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