Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints

Zeguo Wang; Leonid B. Freidovich; Honghua Zhang

doi:10.1109/JAS.2017.7510712

Volume 6 Issue 1

Jan. 2019

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2019 > 6(1): 291-298

Zeguo Wang, Leonid B. Freidovich and Honghua Zhang, "Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 291-298, Jan. 2019. doi: 10.1109/JAS.2017.7510712

Citation:

Zeguo Wang, Leonid B. Freidovich and Honghua Zhang, "Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 291-298, Jan. 2019. doi: 10.1109/JAS.2017.7510712

Citation:

PDF( 1537 KB)

Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints

doi: 10.1109/JAS.2017.7510712

1.
Beijing Institute of Control Engineering, Beijing 100190, China
2.
Robotics and Control Laboratory (www.control.tfe.umu.se), Department of Applied Physics and Electronics, Umeå University, SE-901 87 Umeå, Sweden

Funds: This work was supported by China Scholarship Council (201504980073) for Zeguo Wang to visit Umeå University

More Information

Author Bio:
Zeguo Wang received the B.Eng. degree in automation from Harbin Institute of Technology, Harbin, China, in 2010, and M.Eng. degree in control theory and control engineering from China Academy of Space Technology, Beijing, China, in 2013. He was a visiting Ph.D. student at Umeå University in 2015 and 2016.
He is an Engineer at Beijing Institute of Control Engineering, Beijing, China. His research interests include motion planning, spacecraft control and guidance. (email: wang.zeguo@qq.com)

Leonid B. Freidovich (M'06-SM'11) received the M.Sc. degree in mechanics and engineering and the Kandidat degree in physical and mathematical sciences from Saint-Petersburg State Technical University, St. Petersburg, Russia, in 1996 and 1999, respectively, and the Ph.D. degree in mathematics from Michigan State University, East Lansing, MI, USA, in 2005.
He has been with Umeå University, Umeå, Sweden, since 2005, where he is currently an Associate Professor of control systems with the Department of Applied Physics and Electronics leading the Robotics and Control Group, and has been a Docent since 2010. Leonid is a Co-Founder of RobotikUm AB. His current research interests include control systems engineering and nonlinear control systems with applications in robotics and automation. (email: leonid.freidovich@umu.se)

Honghua Zhang received the B.S. degree from Xidian University in 1983, M.S. degree from Beijing Institute of Control Engineering in 1985, and Ph.D. degree from Beijing University of Aeronautics and Astronautics in 1991, China, respectively.
He is currently a research fellow at Beijing Institute of Control Engineering. His research interests include control of flexible spacecraft, guidance, navigation and control of lander. (email: 13911653638@163.com)
Corresponding author: Zeguo Wang, e-mail: wang.zeguo@qq.com
Received Date: 2016-07-20
Accepted Date: 2016-11-01

Abstract

Abstract

Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint (VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.
- Double rotary pendulum,
- periodic motion planning,
- under-actuated mechanical systems,
- virtual holonomic constraint (VHC)

FullText(HTML)

References(24)

References

[1]	M. Yamakita, K. Nonaka, and K. Furuta, "Swing up control of a double pendulum, " in Proc. American Control Conf., San Francisco, USA, 1993, pp. 2229-2233.
[2]	M. W. Spong, "Partial feedback linearization of underactuated mechanical systems, " in Proc. IEEE/RSJ/GI Int. Conf. Intelligent Robots and Systems, Munich, Germany, 1994, pp. 314-321. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=407375
[3]	M. Reyhanoglu, A. van der Schaft, N. H. McClamroch, and I. Kolmanovsky, "Dynamics and control of a class of underactuated mechanical systems, " IEEE Trans. Automat. Control, vol. 44, no. 9, pp. 1663-1671, Sep. 1999. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=788533
[4]	R. Ortega, M. W. Spong, F. Gomez-Estern, and G. Blankenstein, "Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment, " IEEE Trans. Automat. Control, vol. 47, no. 8, pp. 1218-1233, Aug. 2002. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=1024334
[5]	N. Sun, Y. C. Fang, H. Chen, and B. Lu, "Amplitude-saturated nonlinear output feedback antiswing control for underactuated cranes with doublependulum cargo dynamics, " IEEE Trans. Ind. Electron., vol. 64, no. 3, pp. 2135-2146, Mar. 2017. http://ieeexplore.ieee.org/document/7725990/
[6]	N. Sun, Y. M. Wu, Y. C. Fang, H. Chen, and B. Lu, "Nonlinear continuous global stabilization control for underactuated RTAC systems: design, analysis, and experimentation, " IEEE/ASME Trans. Mechatronics, vol. 22, no. 3, pp. 1104-1115, Apr. 2017. http://ieeexplore.ieee.org/document/7752953/
[7]	Y. Liu and H. N. Yu, "A survey of underactuated mechanical systems, " IET Control Theory Appl., vol. 7, no. 7, pp. 921-935, May 2013. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6562926
[8]	L. T. Aguilar, I. Boiko, L. Fridman, and R. Iriarte, "Generating selfexcited oscillations via two-relay controller, " IEEE Trans. Automat. Control, vol. 54, no. 2, pp. 416-420, Feb. 2009. http://ieeexplore.ieee.org/document/4782016/
[9]	L. Freidovich, A. Shiriaev, F. Gordillo, F. Gomez-Estern, and J. Aracil, "Partial-energy-shaping control for orbital stabilization of highfrequency oscillations of the furuta pendulum, " IEEE Trans. Control Syst. Technol., vol. 17, no. 4, pp. 853-858, Jul. 2009. http://ieeexplore.ieee.org/document/4837870/
[10]	A. S. Shiriaev, L. B. Freidovich, A. Robertsson, R. Johansson, and A. Sandberg, "Virtual-holonomic-constraints-based design of stable oscillations of Furuta pendulum: theory and experiments, " IEEE Trans. Robot., vol. 23, no. 4, pp. 827-832, Aug. 2007. http://www.mendeley.com/research/virtualholonomicconstraintsbased-design-stable-oscillations-furuta-pendulum-theory-experiments/
[11]	L. Freidovich, A. Robertsson, A. Shiriaev, and R. Johansson, "Periodic motions of the pendubot via virtual holonomic constraints: theory and experiments, " Automatica, vol. 44, no. 3, pp. 785-791, Mar. 2008. http://www.sciencedirect.com/science/article/pii/S0005109807003676
[12]	A. S. Shiriaev, L. B. Freidovich, and S. V. Gusev, "Transverse linearization for controlled mechanical systems with several passive degrees of freedom, " IEEE Trans. Automat. Control, vol. 55, no. 4, pp. 893-906, Apr. 2010. http://ieeexplore.ieee.org/document/5404418/
[13]	P. X. M. La Hera, A. S. Shiriaev, L. B. Freidovich, U. Mettin, and S. V. Gusev, "Stable walking gaits for a three-link planar biped robot with one actuator, " IEEE Trans. Robot., vol. 29, no. 3, pp. 589-601, June. 2013. http://ieeexplore.ieee.org/document/6423288/
[14]	M. Maggiore and L. Consolini, "Virtual holonomic constraints for EulerLagrange systems, " IEEE Trans. Automat. Control, vol. 58, no. 4, pp. 1001-1008, Apr. 2013. http://ieeexplore.ieee.org/document/6286994/
[15]	J. W. Grizzle, G. Abba, and F. Plestan, "Asymptotically stable walking for biped robots: analysis via systems with impulse effects, " IEEE Trans. Automat. Control, vol. 46, no. 1, pp. 51-64, Jan. 2001. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=898695
[16]	E. R. Westervelt, J. W. Grizzle, C. Chevallereau, J. H. Choi, and B. Morris, Feedback Control of Dynamic Bipedal Robot Locomotion. Boca Raton: CRC Press, 2007.
[17]	L. Consolini and M. Maggiore, "Control of a bicycle using virtual holonomic constraints, " Automatica, vol. 49, no. 9, pp. 2831-2839, Sep. 2013. https://linkinghub.elsevier.com/retrieve/pii/S000510981300304X
[18]	A. P. Aguiar, J. P. Hespanha, and P. V. Kokotovic, "Path-following for nonminimum phase systems removes performance limitations, " IEEE Trans. Automat. Control, vol. 50, no. 2, pp. 234-239, Feb. 2005. http://ieeexplore.ieee.org/document/1393141
[19]	C. Nielsen, C. Fulford, and M. Maggiore, "Path following using transverse feedback linearization: application to a maglev positioning system, " Automatica, vol. 46, no. 3, pp. 585-590, Mar. 2010. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5159998
[20]	A. Shiriaev, J. W. Perram, and C. Canudas-de-Wit, "Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach, " IEEE Trans. Automat. Control, vol. 50, no. 8, pp. 1164-1176, Aug. 2005. http://ieeexplore.ieee.org/document/1492559/
[21]	S. V. Gusev, A. S. Shiriaev, and L. B. Freidovich, "SDP-based approximation of stabilising solutions for periodic matrix Riccati differential equations, " Int. J. Control, vol. 89, no. 7, pp. 1396-1405, Jul. 2016. doi: 10.1080/00207179.2015.1131850
[22]	A. S. Shiriaev, L. B. Freidovich, and M. W. Spong, "Controlled invariants and trajectory planning for underactuated mechanical systems, " IEEE Trans. Automat. Control, vol. 59, no. 9, pp. 2555-2561, Sep. 2014. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6760115
[23]	W. J. Rugh, Linear System Theory. 2nd ed. Upper Saddle River, USA:Prentice Hall, 1996.
[24]	H. K. Khalil, Nonlinear Systems. 3rd ed. Upper Saddle River, New Jersey, USA:Prentice Hall, 2002.

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(10) / Tables(2)

Get Citation

PDF

XML

Article Metrics

Article views (883) PDF downloads(31)

Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints

doi: 10.1109/JAS.2017.7510712

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content