Rhythmic Feedback Control of a Blind Planar Juggler

The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is "blind," i.e, he has no other sensing capabilities than the detection of impact times. The robustness analysis of the proposed control suggests that the arms acceleration at impact is a crucial design parameter even though it plays no role in the stability analysis. Analytical results and convergence proofs are provided for a simplified model of the juggler. The control law is then adapted to a more accurate model and validated in an experimental setup.

[1]  P. J. Holmes.  The dynamics of repeated impacts with a sinusoidally vibrating table , 1982 .

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

[3]  H. Lehtihet,et al.  Numerical study of a billiard in a gravitational field , 1986 .

[4]  S. Sankar,et al.  Repeated impacts on a sinusoidally vibrating table reappraised , 1986 .

[5]  S. Rossignol,et al.  Neural Control of Rhythmic Movements in Vertebrates , 1988 .

[6]  Daniel E. Koditschek,et al.  A One Degree of Freedom Juggler in a Two Degree of Freedom Environment , 1988, IEEE International Workshop on Intelligent Robots.

[7]  Daniel E. Koditschek,et al.  A family of robot control strategies for intermittent dynamical environments , 1990, IEEE Control Systems Magazine.

[8]  Daniel E. Koditschek,et al.  A family of robot control strategies for intermittent dynamical environments , 1990 .

[9]  N. Sloane,et al.  Scientific Aspects of Juggling , 1993 .

[10]  Daniel E. Koditschek,et al.  Planning and Control of Robotic Juggling and Catching Tasks , 1994, Int. J. Robotics Res..

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

[12]  E. Bizzi,et al.  Motor systems , 1997, Current Opinion in Neurobiology.

[13]  Eric L. Amazeen,et al.  Timing the Selection of Information During Rhythmic Catching. , 1999, Journal of motor behavior.

[14]  Antonio Tornambè,et al.  Modeling and control of impact in mechanical systems: theory and experimental results , 1999, IEEE Trans. Autom. Control..

[15]  Arturo Zavala-Río,et al.  On the control of complementary-slackness juggling mechanical systems , 2000, IEEE Trans. Autom. Control..

[16]  Thomas L. Vincent,et al.  Controlling a Bouncing ball , 2000, Int. J. Bifurc. Chaos.

[17]  Kevin M. Lynch,et al.  Recurrence, controllability, and stabilization of juggling , 2001, IEEE Trans. Robotics Autom..

[18]  Daniel E. Koditschek,et al.  RHex: A Simple and Highly Mobile Hexapod Robot , 2001, Int. J. Robotics Res..

[19]  Arturo Zavala-Río,et al.  Direct adaptive control design for one-degree-of-freedom complementary-slackness jugglers , 2001, Autom..

[20]  Mark W. Spong.  Impact controllability of an air hockey puck , 2001 .

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

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

[23]  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.

[24]  Rodolphe Sepulchre,et al.  Stabilization of periodic orbits in a wedge billiard , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[25]  Laura Menini,et al.  Control of (otherwise) uncontrollable linear mechanical systems through non-smooth impacts , 2003, Syst. Control. Lett..

[26]  Jessy W. Grizzle,et al.  Experimental Validation of a Framework for the Design of Controllers that Induce Stable Walking in Planar Bipeds , 2004, Int. J. Robotics Res..

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

[28]  R. Sepulchre,et al.  STABILIZATION THROUGH WEAK AND OCCASIONAL INTERACTIONS : A BILLIARD BENCHMARK , 2004 .

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

[30]  R. Ronsse,et al.  Timing Feedback Control of a Rhythmic System , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[31]  R. Sepulchre,et al.  RHYTHMIC STABILIZATION OF PERIODIC ORBITS IN A WEDGE , 2005 .

[32]  H. Hirai,et al.  Dynamic coordination between robots: self-organized timing selection in a juggling-like ball-passing task , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  Bernard Brogliato,et al.  On the controllability of linear juggling mechanical systems , 2006, Syst. Control. Lett..

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

[35]  R. Sepulchre,et al.  Feedback Control of Impact Dynamics: the Bouncing Ball Revisited , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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