Abbreviated Title for the Running Head: Haptic Feedback Reduces Rhythmic Variability 2

Title: Haptic Feedback Enhances Rhythmic Motor Control By Reducing Variability, Not Convergence Rate 1 Abbreviated Title for the Running Head: Haptic Feedback Reduces Rhythmic Variability 2 Authors: M. Mert Ankaralı1•, H. Tutkun Şen2, Avik De3, Allison M. Okamura4, Noah J. Cowan1. 3 1Dept. of Mechanical Eng., Johns Hopkins Univ., Baltimore, MD, USA, 21218 4 2Dept. of Computer Science, Johns Hopkins Univ., Baltimore, MD, USA, 21218 5 3Dept. of Electrical and Systems Eng., Uni. of Pennsylvania, Philadelphia, PA, USA, 19104 6 4Dept. of Mechanical Eng., Stanford Univ., Stanford, CA, USA, 94305 7 Corresponding Author. E-mail: mertankarali@jhu.edu. Address: 136 Hackerman Hall, 3400 N Charles Street, 8 Baltimore, MD 21218 9 Author Contributions: 10 M. Mert Ankaralı designed and performed experiments, developed analytical tools, analyzed data and wrote the 11 paper. H. Tutkun Şen designed and performed experiments. Avik De performed preliminary experiments and 12 analysis that gave direction to the research. Allison M. Okamura designed experiments and wrote the paper. Noah J. 13 Cowan designed experiments, developed analytical tools, analyzed data and wrote the paper. 14

[1]  Daniel M. Wolpert,et al.  Signal-dependent noise determines motor planning , 1998, Nature.

[2]  Richard M. Everson,et al.  Chaotic dynamics of a bouncing ball , 1986 .

[3]  P. Hänggi,et al.  Discrete dynamics and metastability: Mean first passage times and escape rates , 1987 .

[4]  P. Holmes,et al.  Spikes alone do not behavior make: why neuroscience needs biomechanics , 2011, Current Opinion in Neurobiology.

[5]  Katie Byl,et al.  Metastable Walking Machines , 2009, Int. J. Robotics Res..

[6]  Uluc Saranli,et al.  Model-Based Proprioceptive State Estimation for Spring-Mass Running , 2011, Robotics: Science and Systems.

[7]  R J Full,et al.  Templates and anchors: neuromechanical hypotheses of legged locomotion on land. , 1999, The Journal of experimental biology.

[8]  R. Harris-Warrick,et al.  Serotonin modulates the central pattern generator for locomotion in the isolated lamprey spinal cord. , 1985, The Journal of experimental biology.

[9]  S. Schaal,et al.  Rhythmic arm movement is not discrete , 2004, Nature Neuroscience.

[10]  John Guckenheimer,et al.  The Dynamics of Legged Locomotion: Models, Analyses, and Challenges , 2006, SIAM Rev..

[11]  Noah J. Cowan,et al.  State-estimation and cooperative control with uncertain time , 2013, 2013 American Control Conference.

[12]  Magnus Egerstedt,et al.  On time: Clocks, chronometers, and open-loop control , 2007, 2007 46th IEEE Conference on Decision and Control.

[13]  Dagmar Sternad,et al.  Optimal control of a hybrid rhythmic-discrete task: the bouncing ball revisited. , 2010, Journal of neurophysiology.

[14]  Felix C Huang,et al.  Visual and Haptic Feedback Contribute to Tuning and Online Control During Object Manipulation , 2007, Journal of motor behavior.

[15]  J. Krakauer,et al.  A computational neuroanatomy for motor control , 2008, Experimental Brain Research.

[16]  Benoît G. Bardy,et al.  Learning new perception–action solutions in virtual ball bouncing , 2007, Experimental Brain Research.

[17]  John G. Milton,et al.  Balancing with Vibration: A Prelude for “Drift and Act” Balance Control , 2009, PloS one.

[18]  Andy Ruina,et al.  Energetic Consequences of Walking Like an Inverted Pendulum: Step-to-Step Transitions , 2005, Exercise and sport sciences reviews.

[19]  T. McGeer,et al.  Passive bipedal running , 1990, Proceedings of the Royal Society of London. B. Biological Sciences.

[20]  Shawn M O'Connor,et al.  Fast visual prediction and slow optimization of preferred walking speed. , 2012, Journal of neurophysiology.

[21]  Tyson L Hedrick,et al.  Within-wingbeat damping: dynamics of continuous free-flight yaw turns in Manduca sexta , 2010, Biology Letters.

[22]  Stefan Schaal,et al.  Dynamics systems vs. optimal control--a unifying view. , 2007, Progress in brain research.

[23]  J. Guckenheimer,et al.  Estimating the phase of synchronized oscillators. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Hillel J. Chiel,et al.  The Brain in Its Body: Motor Control and Sensing in a Biomechanical Context , 2009, The Journal of Neuroscience.

[25]  Daniel E. Koditschek,et al.  Approximating the Stance Map of a 2-DOF Monoped Runner , 2000, J. Nonlinear Sci..

[26]  C. Bazile,et al.  Mixed control for perception and action: timing and error correction in rhythmic ball-bouncing , 2013, Experimental Brain Research.

[27]  H. Oster,et al.  Interaction of central and peripheral clocks in physiological regulation. , 2012, Progress in brain research.

[28]  R. Shadmehr,et al.  Temporal Discounting of Reward and the Cost of Time in Motor Control , 2010, The Journal of Neuroscience.

[29]  P. Holmes,et al.  The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model , 1982, Journal of mathematical biology.

[30]  John Guckenheimer,et al.  Planar Hybrid Systems , 1994, Hybrid Systems.

[31]  D Sternad,et al.  Dynamics of a bouncing ball in human performance. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[33]  Noah J Cowan,et al.  The Critical Role of Locomotion Mechanics in Decoding Sensory Systems , 2007, The Journal of Neuroscience.

[34]  Tim Kiemel,et al.  Optimal motor control may mask sensory dynamics , 2009, Biological Cybernetics.

[35]  Breanna E. Studenka,et al.  The Distinction between Tapping and Circle Drawing with and without Tactile Feedback: An Examination of the Sources of Timing Variance , 2012, Quarterly journal of experimental psychology.

[36]  William H Warren,et al.  Passive vs. active control of rhythmic ball bouncing: the role of visual information. , 2010, Journal of experimental psychology. Human perception and performance.

[37]  S. Schaal,et al.  One-Handed Juggling: A Dynamical Approach to a Rhythmic Movement Task. , 1996, Journal of motor behavior.

[38]  J. Guckenheimer,et al.  Finding the dimension of slow dynamics in a rhythmic system , 2012, Journal of The Royal Society Interface.

[39]  R J Full,et al.  How animals move: an integrative view. , 2000, Science.

[40]  D. Eagleman.  Human time perception and its illusions , 2008, Current Opinion in Neurobiology.

[41]  Noah J. Cowan,et al.  Time-changed linear quadratic regulators , 2013, 2013 European Control Conference (ECC).