Table Of ContentSpringer 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
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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
