Control of bimanual rhythmic movements: trading efficiency for robustness depending on the context

This paper investigates how the efficiency and robustness of a skilled rhythmic task compete against each other in the control of a bimanual movement. Human subjects juggled a puck in 2D through impacts with two metallic arms, requiring rhythmic bimanual actuation. The arms kinematics were only constrained by the position, velocity and time of impacts while the rest of the trajectory did not influence the movement of the puck. In order to expose the task robustness, we manipulated the task context in two distinct manners: the task tempo was assigned at four different values (hence manipulating the time available to plan and execute each impact movement individually); and vision was withdrawn during half of the trials (hence reducing the sensory inflows). We show that when the tempo was fast, the actuation was rhythmic (no pause in the trajectory) while at slow tempo, the actuation was discrete (with pause intervals between individual movements). Moreover, the withdrawal of visual information encouraged the rhythmic behavior at the four tested tempi. The discrete versus rhythmic behavior give different answers to the efficiency/robustness trade-off: discrete movements result in energy efficient movements, while rhythmic movements impact the puck with negative acceleration, a property preserving robustness. Moreover, we report that in all conditions the impact velocity of the arms was negatively correlated with the energy of the puck. This correlation tended to stabilize the task and was influenced by vision, revealing again different control strategies. In conclusion, this task involves different modes of control that balance efficiency and robustness, depending on the context.

[1]  S. Swinnen,et al.  Two hands, one brain: cognitive neuroscience of bimanual skill , 2004, Trends in Cognitive Sciences.

[2]  D Goodman,et al.  On the nature of human interlimb coordination. , 1979, Science.

[3]  A. H. Clarke,et al.  Using high frame rate CMOS sensors for three-dimensional eye tracking , 2002, Behavior research methods, instruments, & computers : a journal of the Psychonomic Society, Inc.

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

[5]  Philippe Lefèvre,et al.  Robotics and neuroscience: A rhythmic interaction , 2008, Neural Networks.

[6]  E. Bizzi,et al.  The Cognitive Neurosciences , 1996 .

[7]  A. Büschges Sensory control and organization of neural networks mediating coordination of multisegmental organs for locomotion. , 2005, Journal of neurophysiology.

[8]  Emanuel Todorov,et al.  Evidence for the Flexible Sensorimotor Strategies Predicted by Optimal Feedback Control , 2007, The Journal of Neuroscience.

[9]  Jun Nakanishi,et al.  Learning Attractor Landscapes for Learning Motor Primitives , 2002, NIPS.

[10]  S. Swinnen Intermanual coordination: From behavioural principles to neural-network interactions , 2002, Nature Reviews Neuroscience.

[11]  Martijn Wisse,et al.  A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees , 2001, Int. J. Robotics Res..

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

[13]  Tad McGeer,et al.  Passive Dynamic Walking , 1990, Int. J. Robotics Res..

[14]  Benoit Boulet,et al.  The fundamental tradeoff between performance and robusteness: A new perspective on loop shaping , 2007 .

[15]  D. Sternad,et al.  Juggling and bouncing balls: parallels and differences in dynamic concepts and tools. , 1999 .

[16]  S. Schaal,et al.  Computational motor control in humans and robots , 2005, Current Opinion in Neurobiology.

[17]  K. E. Novak,et al.  The use of overlapping submovements in the control of rapid hand movements , 2002, Experimental Brain Research.

[18]  Russ Tedrake,et al.  Efficient Bipedal Robots Based on Passive-Dynamic Walkers , 2005, Science.

[19]  Gideon F. Inbar,et al.  Human motor control: learning to control a time-varying, nonlinear, many-to-one system , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[20]  E. Todorov Optimality principles in sensorimotor control , 2004, Nature Neuroscience.

[21]  Michael F. Land,et al.  From eye movements to actions: how batsmen hit the ball , 2000, Nature Neuroscience.

[22]  S. Schaal,et al.  Bouncing a ball: tuning into dynamic stability. , 2001, Journal of experimental psychology. Human perception and performance.

[23]  Zoubin Ghahramani,et al.  Computational motor control , 2004 .

[24]  Zoubin Ghahramani,et al.  Computational principles of movement neuroscience , 2000, Nature Neuroscience.

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

[26]  Philippe Lefèvre,et al.  Rhythmic Feedback Control of a Blind Planar Juggler , 2007, IEEE Transactions on Robotics.

[27]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[28]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[29]  Michael I. Jordan,et al.  Optimal feedback control as a theory of motor coordination , 2002, Nature Neuroscience.

[30]  Daniel M Wolpert,et al.  Computational principles of sensorimotor control that minimize uncertainty and variability , 2007, The Journal of physiology.

[31]  Bernard Espiau,et al.  A Study of the Passive Gait of a Compass-Like Biped Robot , 1998, Int. J. Robotics Res..

[32]  A. Opstal Dynamic Patterns: The Self-Organization of Brain and Behavior , 1995 .

[33]  Scott T. Grafton,et al.  Forward modeling allows feedback control for fast reaching movements , 2000, Trends in Cognitive Sciences.

[34]  Dagmar Sternad,et al.  Passive stability and active control in a rhythmic task. , 2007, Journal of neurophysiology.

[35]  Daniel M. Wolpert,et al.  The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off , 2006, Biological Cybernetics.

[36]  P. Beek,et al.  The coupling between point-of-gaze and ballmovements in three-ball cascade juggling: the effects of expertise, pattern and tempo , 2002, Journal of sports sciences.

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

[38]  Philippe Lefèvre,et al.  Sensorless stabilization of bounce juggling , 2006, IEEE Transactions on Robotics.

[39]  Mitsuo Kawato,et al.  MOSAIC Model for Sensorimotor Learning and Control , 2001, Neural Computation.

[40]  Dagmar Sternad,et al.  The dialogue between data and model: passive stability and relaxation behavior in a ball bouncing task , 2004 .

[41]  Richard M. Murray,et al.  Feedback Systems An Introduction for Scientists and Engineers , 2007 .

[42]  G. Ermentrout Dynamic patterns: The self-organization of brain and behavior , 1997 .

[43]  Jose B. Cruz,et al.  Feedback systems , 1971 .

[44]  S. Scott Optimal feedback control and the neural basis of volitional motor control , 2004, Nature Reviews Neuroscience.

[45]  Emanuel Todorov,et al.  Optimal Control Theory , 2006 .

[46]  D M Wolpert,et al.  Multiple paired forward and inverse models for motor control , 1998, Neural Networks.

[47]  D. Sternad,et al.  Actively tracking ‘passive’ stability in a ball bouncing task , 2003, Brain Research.

[48]  Arthur D Kuo,et al.  The relative roles of feedforward and feedback in the control of rhythmic movements. , 2002, Motor control.

[49]  D. Sternad,et al.  Control of ball-racket interactions in rhythmic propulsion of elastic and non-elastic balls , 2003, Experimental Brain Research.

[50]  Y Uno,et al.  Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. , 1999, Journal of neurophysiology.

[51]  N. Hogan,et al.  On rhythmic and discrete movements: reflections, definitions and implications for motor control , 2007, Experimental Brain Research.

[52]  Yingxuan Duan,et al.  The fundamental tradeoff between performance and robustness - A new perspective on loop shaping - Classic control revisited part II , 2007, IEEE Control Systems.