Stabilization of the spatial double inverted pendulum using stochastic programming seen as a model of standing postural control

The stabilization of a double inverted pendulum actuated at the hip only and moving in a three dimensional space may be considered to be a model of a human — and of other animals — postural control. Here, we show that postural control is possible by minimization of the system Lagrangian. A stochastic programming procedure proves to be able to find oscillatory inputs that bring the system close to the unstable upright equilibrium position. Our study shows that steering complex mechanical systems may in certain cases be actually be simpler than expected.

[1]  F Honegger,et al.  The influence of a bilateral peripheral vestibular deficit on postural synergies. , 1994, Journal of vestibular research : equilibrium & orientation.

[2]  Shuzhi Sam Ge,et al.  Feedback linearization and discontinuous control of second-order nonholonomic chained systems , 2001, Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204).

[3]  Jerrold E. Marsden,et al.  Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems , 1999 .

[4]  K. Y. Wichlund,et al.  Control of Vehicles with Second-Order , 1995 .

[5]  Arjan van der Schaft,et al.  Dynamics and control of a class of underactuated mechanical systems , 1999, IEEE Trans. Autom. Control..

[6]  Alessandro Astolfi,et al.  Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one , 2004, Proceedings of the 2004 American Control Conference.

[7]  Alan M. Wing,et al.  Light touch contribution to balance in normal bipedal stance , 1999, Experimental Brain Research.

[8]  H. Sussmann,et al.  Lie Bracket Extensions and Averaging: The Single-Bracket Case , 1993 .

[9]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

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

[11]  James R. Lackner,et al.  The role of haptic cues from rough and slippery surfaces in human postural control , 2004, Experimental Brain Research.

[12]  Weiliang Xu,et al.  Stabilization of second-order nonholonomic systems in canonical chained form , 2001, Robotics Auton. Syst..

[13]  Philippe Poignet,et al.  Artificial locomotion control: from human to robots , 2004, Robotics Auton. Syst..

[14]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[15]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem , 2000, IEEE Trans. Autom. Control..

[16]  Alan M. Wing,et al.  The dynamics of standing balance , 2002, Trends in Cognitive Sciences.

[17]  J P Roll,et al.  Foot sole and ankle muscle inputs contribute jointly to human erect posture regulation , 2001, The Journal of physiology.

[18]  Giuseppe Oriolo,et al.  Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[19]  Min Wu,et al.  Singularity avoidance for acrobots based on fuzzy-control strategy , 2009, Robotics Auton. Syst..

[20]  Kazuhito Yokoi,et al.  Resolved momentum control: humanoid motion planning based on the linear and angular momentum , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[21]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[22]  Alessandro Astolfi,et al.  Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes , 2007, IEEE Transactions on Automatic Control.

[23]  M. Yamakita,et al.  3D motion control of 2 links (5 D.O.F.) underactuated manipulator named AcroBOX , 2006, 2006 American Control Conference.

[24]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[25]  Naomi Ehrich Leonard,et al.  A normal form for energy shaping: application to the Furuta pendulum , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[26]  A. Berthoz,et al.  Visual contribution to rapid motor responses during postural control , 1978, Brain Research.

[27]  Hirochika Inoue,et al.  Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[28]  R. Bootsma,et al.  Dynamics of human postural transitions. , 2002, Journal of experimental psychology. Human perception and performance.

[29]  H. Benjamin Brown,et al.  Experiments in Balance with a 3D One-Legged Hopping Machine , 1984 .

[30]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[31]  J. F. Yang,et al.  Postural dynamics in the standing human , 1990, Biological Cybernetics.

[32]  Henk Nijmeijer,et al.  Trajectory tracking by cascaded backstepping control for a second-order nonholonomic mechanical system , 2001 .