Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior

A detailed mathematical analysis of the two-dimensional hybrid model for the lateral dynamics of walking-like mechanical systems (the so-called hybrid inverted pendulum) is presented in this articl...

[2]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[3]  Nikolay V. Kuznetsov,et al.  Hidden attractors in Dynamical Systems. From Hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits , 2013, Int. J. Bifurc. Chaos.

[4]  M. Kunze.  On Lyapunov Exponents for Non-Smooth Dynamical Systems with an Application to a Pendulum with Dry Friction , 2000 .

[5]  Milos Zefran,et al.  Underactuated dynamic three-dimensional bipedal walking , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[6]  Leonid B. Freidovich,et al.  A Passive 2-DOF Walker: Hunting for Gaits Using Virtual Holonomic Constraints , 2009, IEEE Transactions on Robotics.

[7]  Tomasz Kapitaniak,et al.  Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization , 2003 .

[8]  Leonid B. Freidovich,et al.  Controlled Invariants and Trajectory Planning for Underactuated Mechanical Systems , 2014, IEEE Trans. Autom. Control..

[9]  Yuri A. Kuznetsov,et al.  One-Parameter bifurcations in Planar Filippov Systems , 2003, Int. J. Bifurc. Chaos.

[10]  Wei Zhang,et al.  Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems , 2016, Int. J. Bifurc. Chaos.

[11]  Sergej Celikovský,et al.  On the anti-synchronization detection for the generalized Lorenz system and its applications to secure encryption , 2010, Kybernetika.

[12]  A. Shiriaev,et al.  Periodic motion planning for virtually constrained Euler-Lagrange systems , 2006, Syst. Control. Lett..

[13]  Arthur D. Kuo,et al.  Stabilization of Lateral Motion in Passive Dynamic Walking , 1999, Int. J. Robotics Res..

[14]  I. VagaitsevV.,et al.  Localization of hidden Chua ’ s attractors , 2022 .

[15]  Sergej Celikovsky,et al.  ADAPTIVE NONLINEAR TRACKING FOR ROBOTIC WALKING , 2012 .

[16]  Carlos Canudas-de-Wit,et al.  Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach , 2005, IEEE Transactions on Automatic Control.

[17]  Gábor Csernák,et al.  On the chaotic behaviour of a simple dry-friction oscillator , 2014, Math. Comput. Simul..

[18]  G. Leonov,et al.  Localization of hidden Chuaʼs attractors , 2011 .

[19]  T. Küpper,et al.  Melnikov method and detection of chaos for non-smooth systems , 2013 .

[20]  Wei Zhang,et al.  The Melnikov method of heteroclinic orbits for a class of planar hybrid piecewise-smooth systems and application , 2016 .

[21]  Sergej Celikovský,et al.  Desynchronization Chaos Shift Keying Method Based on the Error Second derivative and its Security Analysis , 2012, Int. J. Bifurc. Chaos.

[22]  R. Leine,et al.  Bifurcations in Nonlinear Discontinuous Systems , 2000 .

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

[24]  M. Coleman,et al.  The simplest walking model: stability, complexity, and scaling. , 1998, Journal of biomechanical engineering.

[26]  Francesco Bullo,et al.  Controlled symmetries and passive walking , 2005, IEEE Transactions on Automatic Control.

[27]  R. Leine,et al.  Synchronization-based Estimation of the Maximal Lyapunov Exponent of Nonsmooth Systems☆ , 2017 .

[28]  Sergej Čelikovský,et al.  Application of the Method of Maximum Likelihood to Identification of Bipedal Walking Robots , 2018, IEEE Transactions on Control Systems Technology.

[29]  Andrzej Stefański,et al.  Estimation of the largest Lyapunov exponent in systems with impacts , 2000 .

[30]  Sergej Celikovský,et al.  Collocated virtual holonomic constraints in hamiltonian formalism and their application in the underactuated walking , 2017, 2017 11th Asian Control Conference (ASCC).

[31]  Tomasz Kapitaniak,et al.  Using Chaos Synchronization to Estimate the Largest Lyapunov Exponent of Nonsmooth Systems , 2000 .

[32]  Shihui Fu,et al.  Estimating the Largest Lyapunov Exponent in a Multibody System with Dry Friction by using Chaos Synchronization , 2006 .

[33]  Leonid B. Freidovich,et al.  Stable Walking Gaits for a Three-Link Planar Biped Robot With One Actuator , 2013, IEEE Transactions on Robotics.

[34]  Leonid B. Freidovich,et al.  A dynamic human motion: coordination analysis , 2015, Biological Cybernetics.

[35]  Amir Ali Ahmadi,et al.  Control design along trajectories with sums of squares programming , 2012, 2013 IEEE International Conference on Robotics and Automation.

[36]  Nikolay V. Kuznetsov,et al.  Hidden Attractors on One Path: Glukhovsky-Dolzhansky, Lorenz, and Rabinovich Systems , 2017, Int. J. Bifurc. Chaos.

[37]  Christine Chevallereau,et al.  RABBIT: a testbed for advanced control theory , 2003 .

[38]  Christine Chevallereau,et al.  Models, feedback control, and open problems of 3D bipedal robotic walking , 2014, Autom..

[39]  M. Žefran,et al.  Stabilization of hybrid periodic orbits with application to bipedal walking , 2006, 2006 American Control Conference.