Volume 2, Issue 4, July 2017, Page: 75-82
Biped Robot Modeling and Control Using Controlled Hybrid Automata
Ying Shang, Department of Electrical and Computer Engineering, Southern Illinois University Edwardsville, Edwardsville, USA
Received: May 18, 2017;       Accepted: May 27, 2017;       Published: Jul. 18, 2017
DOI: 10.11648/j.ijssam.20170204.11      View  1882      Downloads  80
Abstract
Hybrid systems are dynamical systems consisting of interacting discrete event and continuous state subsystems. A controlled hybrid automaton is a hybrid automaton whose continuous-state dynamics are described by inhomogeneous differential equations. This paper presents a sufficient condition for the existence of global non-terminating solutions in controlled hybrid automata. The condition is based on a recursive algorithm that can always terminate after a finite number of iterations to a limit set of states, i.e. the fixed point of the recursion. If the fixed point is non-empty, then there exists a measurable control under which the hybrid automaton generates a global non-terminating solution. The more important is that this result can also be used to infer the existence of global solutions to compositions of controlled hybrid automata, thereby providing a foundation for the analysis of large scale hybrid systems. The controlled hybrid automata model can be used for robotics system modeling and control. By solving the global non-terminating solution to controlled hybrid automata, the biped robots can be guaranteed to keep the walking gait without falling down.
Keywords
Hybrid Automata, Decidability Problem, Backward Reachability
To cite this article
Ying Shang, Biped Robot Modeling and Control Using Controlled Hybrid Automata, International Journal of Systems Science and Applied Mathematics. Vol. 2, No. 4, 2017, pp. 75-82. doi: 10.11648/j.ijssam.20170204.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
M. S. Branicky, Wivek S. Borkar, S. K. Mitter, “A unified framework for hybrid control,” IEEE Trans. on Automatic Control, Vol. 43, Issue 1, pp. 31-45, 1998.
[2]
R. W. Brockett, “Hybrid models for motion control systems,” Essays in Control, pp. 29-53, Birkhauser, Boston, 1993.
[3]
K. E. Colthier, Y. Shang, “ A geometric approach for robotic arm kinematics wit hardware design, electrical design, and implementation. Journal of Robotics, 2010.
[4]
S. Cubero, Editor, Industrial Robotics: Theory, Modeling and Control, Pro Literatur Verlag, Germany, 2016.
[5]
A. R. C. Donati, et. al. “Long-term training with a Brain-machine interface-based gait protocol induces partial neurological recovery in paraplegic patients,” Scientific Report, 6: 30383, 2016.
[6]
L. A. Fuente, M. A. Lones, A. P. Turner, L. S. Caves, S. Stepney, A. M. Tyrrell. “Adaptive robotic gait control using coupled artificial signaling networks, Hopf oscillators and inverse kinematics. IEEE Congress on Evolutionary Computation (CEC), June 20-23, 2013.
[7]
M. Garcia, A. Chattejee, A. Ruina, and M. Coleman, “The simplest walking model: stability, complexity, and scaling,” ASME J. Biomech. Eng. Vol. 120, pp. 281-288, 1998.
[8]
B. Goodwine, J. W. Burdick, “Controllability of kinematic control systems on stratified configuration spaces,” IEEE Trans. on Automatic Control, Vol. 46, No. 3, pp. 358-368, 2001.
[9]
K. Leibrandt, C. Bergeles, G-Z. Yang, “Concentric tube robots: rapid, stable path-planning and guidance for surgical use”, IEEE Robotics & Automation Magazine, Vol: PP, Issue: 99, May 2017, DOI: 10.1109/MRA.2017.2680546.
[10]
Y. K. Leow, Y. Shang, “Mobile robot tracking in wireless sensor networks”, Computer in Educaion Journal, Vol. 1, Issue 1, pp. 36-44, 2010.
[11]
Y. Shang, “The existence of non-terminating solutions to controlled hybrid automata,” master thesis, University of Notre Dame, 2002.
[12]
S. Tadokoro, “Robotics leads social innovation without boarders for the future of humanity,” IEEE Robotics &Automation Magazine, Vol. 24, Issue 1, 4-4, 2017.
[13]
A. Teel, J. Hespanha, “Stochastic hybrid systems: a modeling and stability theory tutorial” Proc. of the 54th Conference on Decision and Control, Dec. 15-18, 2015.
[14]
T. Umedachi, T. Kano, A Ishiguro, B. A. Trimmer, “Gait control in a soft robot by sensing interactions with the environment using self-deformation,” Royal Society Open Science, 3: 160766, 2016.
[15]
B. Vanderborght, “The impact of hardware and open-source initiatives on robotics,” IEEE Robotics &Automation Magazine, Vol. 24, Issue 1, 4-4, 2017.
[16]
H. S. Witsenhausen, “A class of hybrid-state continuous-time dynamic systems,” IEEE Trans. Automatic Control, Vol. 11, Issue 2, pp. 161-167, 1966.
Browse journals by subject