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  • Jean-Paul Laumond • Nicolas Mansard Jean-Bernard Lasserre Editors

    Geometric and Numerical Foundations of Movements

    123

  • Editors Jean-Paul Laumond LAAS-CNRS Toulouse France

    Nicolas Mansard LAAS-CNRS Toulouse France

    Jean-Bernard Lasserre LAAS-CNRS Toulouse France

    ISSN 1610-7438 ISSN 1610-742X (electronic) Springer Tracts in Advanced Robotics ISBN 978-3-319-51546-5 ISBN 978-3-319-51547-2 (eBook) DOI 10.1007/978-3-319-51547-2

    Library of Congress Control Number: 2016963164

    © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part 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 dissimilar methodology now known or hereafter developed. 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 from the relevant protective laws and regulations and therefore free for general use. 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 authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

    Printed on acid-free paper

    This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

  • 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

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  • Part III Foundation of Human Movement

    Inverse Optimal Control as a Tool to Understand Human Movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Katja Mombaur and Debora Clever

    Versatile Interaction Control and Haptic Identification in Humans and Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Yanan Li, Nathanael Jarrassé and Etienne Burdet

    The Variational Principles of Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Karl Friston

    Modeling of Coordinated Human Body Motion by Learning of Structured Dynamic Representations. . . . . . . . . . . . . . . . 237 Albert Mukovskiy, Nick Taubert, Dominik Endres, Christian Vassallo, Maximilien Naveau, Olivier Stasse, Philippe Souères and Martin A. Giese

    Physical Interaction via Dynamic Primitives . . . . . . . . . . . . . . . . . . . . . . . 269 Neville Hogan

    Human Control of Interactions with Objects – Variability, Stability and Predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Dagmar Sternad

    Part IV Robot Motion Generation

    Momentum-Centered Control of Contact Interactions . . . . . . . . . . . . . . 339 Ludovic Righetti and Alexander Herzog

    A Tutorial on Newton Methods for Constrained Trajectory Optimization and Relations to SLAM, Gaussian Process Smoothing, Optimal Control, and Probabilistic Inference . . . . . . . . . . . . . . . . . . . . . . 361 Marc Toussaint

    Optimal Control of Variable Stiffness Policies: Dealing with Switching Dynamics and Model Mismatch . . . . . . . . . . . . . . . . . . . . 393 Andreea Radulescu, Jun Nakanishi, David J. Braun and Sethu Vijayakumar

    x Contents

  • Human Control of Interactions with Objects – Variability, Stability and Predictability

    Dagmar Sternad

    Abstract How do humans control their actions and interactions with the physical world? How do we learn to throw a ball or drink a glass of wine without spilling? Compared to robots human dexterity remains astonishing, especially as slow neural transmission and high levels of noise seem to plague the biological system. What are human control strategies that skillfully navigate, overcome, and even exploit these disadvantages? To gain insight we propose an approach that centers on how task dynamics constrain and enable (inter-)actions. Agnostic about details of the controller, we start with a physical model of the task that permits full understanding of the solution space. Rendering the task in a virtual environment, we examine how humans learn solutions that meet complex task demands. Central to numerous skills is redundancy that allows exploration and exploitation of subsets of solutions. We hypothesize that humans seek solutions that are stable to perturbations to make their intrinsic noise matter less. With fewer corrections necessary, the system is less afflicted by long delays in the feedback loop. Three experimental paradigms exemplify our approach: throwing a ball to a target, rhythmic bouncing of a ball, and carrying a complex object. For the throwing task, results show that actors are sensitive to the error-tolerance afforded by the task. In rhythmic ball bouncing, subjects exploit the dynamic stability of the paddle-ball system.Whenmanipulating a “glass ofwine”, subjects learn strategies that make the hand-object interactions more predictable. These findings set the stage for developing propositions about the controller: We posit that complex actions are generated with dynamic primitives, modules with attractor stability that are less sensitive to delays and noise in the neuro-mechanical system.

    Keywords Humanmotor control ·Motor learning ·Neuromotor noise ·Variability · Stability · Predictability · Tool use

    Submitted to: Laumond, J.-P. Geometric and Numerical Foundations of Movement.

    D. Sternad (B) Departments of Biology, Electrical and Computer Engineering, and Physics, Center for the Interdisciplinary Research on Complex Systems, Northeastern University, 134 Mugar Life Science Building, 360 Huntington Avenue, Boston, MA 02115, USA e-mail: [email protected]

    © Springer International Publishing AG 2017 J.-P. Laumond et al. (eds.), Geometric and Numerical Foundations of Movements, Springer Tracts in Advanced Robotics 117, DOI 10.1007/978-3-319-51547-2_13

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  • 302 D. Sternad

    1 Introduction

    Imagine a dancer, perhaps Rudolf Nureyev or Margaret Fonteyn, both legends in classical ballet: we can only marvel at how they are in complete control of their body, combining extraordinary flexibility and strength with technical difficulty and elegance. And yet, I submit that Evgenia Kanaeva, two-times all-around Olympic champion in rhythmic gymnastics, equals, if not surpasses their level of skill:Not only does shemove her lithe bodywith perfection and grace, she also plays with numerous objects: she throws, catches and bounces a ball, she rolls and swivels a hoop, and sets a 6m-long ribbon into smooth spirals with the most exquisite movements of her hands and fingers – and yes, sometimes also using her arms, shoulders, or her legs and feet. Her magical actions and interactions with objects arguably represent the pinnacle of human motor control.

    How do humans act and interact with objects and tools? After all, tool use is what gave humans their evolutionary advantage over other animals. In robotics, manipulation of tools has clearly been one of the primary motivations to develop robots, going back to the first industrial robots designed to automate repetitive tasks such as placing parts or tightening screws. However, these actions lack the dexterity that not only elite performers, but all healthy humans display. Opening a bottle of wine with a corkscrew or eating escargot with a fork and tongs are skills that require subtle interactions with complex tools and objects. How do humans control these actions and interactions?

    Research in motor neuroscience has only arrived at limited answers. To assure experimental control and rigor, computational research has confined itself to sim- ple laboratory tasks, most commonly reaching to a point target, while restricting arm movements to two joints moving in the horizontal plane [57, 58]. Research on sequence learning has typically been limited