Nearly optimal neural network stabilization of bipedal standing using genetic algorithm

In this work, stability control of bipedal standing is investigated. The biped is simplified as an inverted pendulum with a foot-link. The controller consists of a general regression neural network (GRNN) feedback control, which stabilizes the inverted pendulum in a region around the upright position, and a PID feedback control, which keeps the pendulum at the upright position. The GRNN controller is also designed to minimize an energy-related cost function while satisfying the constraints between the foot-link and the ground. The optimization has been carried out using the genetic algorithm (GA) and the GRNN is directly trained during optimization iteration process to provide the closed loop feedback optimal controller. The stability of the controlled system is analyzed using the concept of Lyapunov exponents, and a stability region is determined. Simulation results show that the controller can keep the inverted pendulum at the upright position while nearly minimizing an energy-related cost function and keeping the foot-link stationary on the ground. The work contributes to bipedal balancing control, which is important to the development of bipedal robots.

[1]  Brown,et al.  Computing the Lyapunov spectrum of a dynamical system from an observed time series. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[2]  Michael Kuperstein,et al.  Neural controller for adaptive movements with unforeseen payloads , 1990, IEEE Trans. Neural Networks.

[3]  L. Breiman,et al.  Variable Kernel Estimates of Multivariate Densities , 1977 .

[4]  A.D. Kuo,et al.  An optimal control model for analyzing human postural balance , 1995, IEEE Transactions on Biomedical Engineering.

[5]  M. Kuperstein,et al.  Implementation of an adaptive neural controller for sensory-motor coordination , 1989, International 1989 Joint Conference on Neural Networks.

[6]  Dean Pomerleau,et al.  Efficient Training of Artificial Neural Networks for Autonomous Navigation , 1991, Neural Computation.

[7]  Donald F. Specht,et al.  A general regression neural network , 1991, IEEE Trans. Neural Networks.

[8]  Q Wu,et al.  A Mathematical Model of the Stability Control of Human Thorax and Pelvis Movements During Walking , 2002, Computer methods in biomechanics and biomedical engineering.

[9]  G. Josin,et al.  Robot control using neural networks , 1988, IEEE 1988 International Conference on Neural Networks.

[10]  Hooshang Hemami,et al.  A Qualitative Discussion of Mechanisms of Feedback and Feedforward in the Control of Locomotion , 1983, IEEE Transactions on Biomedical Engineering.

[11]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[12]  Kazuhito Yokoi,et al.  Planning walking patterns for a biped robot , 2001, IEEE Trans. Robotics Autom..

[13]  Qiong Wu,et al.  On stabilization of bipedal robots during disturbed standing using the concept of Lyapunov exponents , 2006, 2006 American Control Conference.

[14]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[15]  Y. Pai,et al.  Center of mass velocity-position predictions for balance control. , 1997, Journal of biomechanics.

[16]  James A. Yorke,et al.  Dynamics: Numerical Explorations , 1994 .

[17]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..

[18]  Edward S. Plumer,et al.  Optimal control of terminal processes using neural networks , 1996, IEEE Trans. Neural Networks.

[19]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[20]  Yannick Aoustin,et al.  Optimal reference trajectories for walking and running of a biped robot , 2001, Robotica.

[21]  Roger A. Pielke,et al.  EXTRACTING LYAPUNOV EXPONENTS FROM SHORT TIME SERIES OF LOW PRECISION , 1992 .

[22]  Anton S. Shiriaev,et al.  Partial stabilization of underactuated Euler-Lagrange systems via a class of feedback transformations , 2002, Syst. Control. Lett..

[23]  N. Sepehri,et al.  Stability and Control of Human Trunk Movement During Walking. , 1998, Computer methods in biomechanics and biomedical engineering.

[24]  Leonard Barolli,et al.  Optimal trajectory generation for a prismatic joint biped robot using genetic algorithms , 2002, Robotics Auton. Syst..

[25]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[26]  H. Hemami,et al.  Constrained Inverted Pendulum Model For Evaluating Upright Postural Stability , 1982 .

[27]  Daniel E. Koditschek,et al.  Hybrid zero dynamics of planar biped walkers , 2003, IEEE Trans. Autom. Control..

[28]  Gabriel Abba,et al.  Quasi optimal gait for a biped robot using genetic algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[29]  N.V. Bhat,et al.  Modeling chemical process systems via neural computation , 1990, IEEE Control Systems Magazine.

[30]  Toshio Fukuda,et al.  Natural motion trajectory generation of biped locomotion robot using genetic algorithm through energy optimization , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[31]  Q. Wu,et al.  Effects of constraints on bipedal balance control , 2006, 2006 American Control Conference.