Control of acrobot based on non-smooth Lyapunov function and comprehensive stability analysis
Control of acrobot based on non-smooth Lyapunov function and comprehensive stability analysis
- Author(s): X.-Z. Lai ; J.-H. She ; S.X. Yang ; M. Wu
- DOI: 10.1049/iet-cta:20060414
For access to this article, please select a purchase option:
Buy article PDF
Buy Knowledge Pack
IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.
Thank you
Your recommendation has been sent to your librarian.
- Author(s): X.-Z. Lai 1 ; J.-H. She 2 ; S.X. Yang 3 ; M. Wu 1
-
-
View affiliations
-
Affiliations:
1: School of Information Science and Engineering, Central South University, Changsha, People's Republic of China
2: School of Bionics, Tokyo University of Technology, Hachioji, Tokyo, Japan
3: School of Engineering, Advanced Robotics and Intelligent Systems (ARIS) Laboratory, University of Guelph, Guelph, Canada
-
Affiliations:
1: School of Information Science and Engineering, Central South University, Changsha, People's Republic of China
- Source:
Volume 2, Issue 3,
March 2008,
p.
181 – 191
DOI: 10.1049/iet-cta:20060414 , Print ISSN 1751-8644, Online ISSN 1751-8652
- « Previous Article
- Table of contents
- Next Article »
A new control strategy for an acrobot based on a non-smooth Lyapunov function to guarantee the stability of the system in the whole motion space is presented. Three control laws are derived based on three Lyapunov functions and are applied successively in three stages of motion control to achieve a suitable posture and to increase the energy so as to make the acrobot move into the area around the unstable upright equilibrium position and to stabilise it at that position. These three Lyapunov functions are combined into one non-smooth function, which theoretically guarantees the stability of the acrobot in the whole motion space.
Inspec keywords: manipulators; Lyapunov methods; motion control; position control; stability
Other keywords:
Subjects: Manipulators; Spatial variables control; Stability in control theory
References
-
-
1)
- Zergeroglu, E., Dixon, W.E., Dawson, D.M.: `Lyapunov-based set-point control of the acrobot', Proc. 1998 Int. Conf. Control Applications, September 1998, Trieste, Italy, p. 887–891.
-
2)
- Xin, X., Kaneda, M.: `A new solution to the swing up control problem for the acrobot', Proc. 40th SICE Annual Conf., July 2001, Nagoya, Japan, p. 124–129.
-
3)
- Kawada, K., Fujisawa, S., Obika, M.: `Creating swing-up patterns of an acrobot using evolutionary computation', Proc. IEEE Int. Symp. on Computational Intelligence in Robotics and Automation, June 2005, Espoo, Finland, p. 261–266.
-
4)
- Hauser, J., Murray, R.M.: `Nonlinear controllers for non-integrable systems: the acrobot example', Proc. American Control Conf., May 1990, San Diego, California, p. 669–671.
-
5)
- Xin, X., Kaneda, M.: `A robust control approach to the swing up control problem for the acrobot', Proc. 2001 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, November 2001, Hawaii, USA, p. 1650–1655.
-
6)
- Araki, N., Okada, M., Konishi, Y.: `Parameter identification and swing-up control of an acrobot system', Proc. IEEE Int. Conf. Industrial Technology, December 2005, Hong Kong, China, p. 1040–1045.
-
7)
- D.G. Schultz , J.L. Melsa . (1967) State functions and linear control systems.
-
8)
- Yonemura, T., Yamakita, A.: `Swing up control of acrobot based on switched output functions', Proc. SICE Annual Conf., August 2004, Sapporo, Japan, p. 1909–1914.
-
9)
- S. Brown , K. Passino . Intelligent control for acrobot. J. Intell. Robot. Syst. , 209 - 248
-
10)
- Shiriaev, A., Sandberg, A., Canudas-de-Wit, C.: `Motion planning and feedback stabilization of periodic orbits for an Acrobot', Proc. 43rd IEEE Conf. Decision and Control, December 2004, Paradise Island, Bahamas, p. 290–295.
-
11)
- M. Krstic , I. Kanellakopoulos , P.V. Kokotovic . (1995) Nonlinear and adaptive control design.
-
12)
- Leavitt, J., Bobrow, J.E., Sideris, A.: `Robust balance control of a one-legged, pneumatically-actuated, acrobot-like hopping robot', Proc. IEEE Int. Conf. Robotics and Automation, May 2004, Leuven, Belgium, p. 4240–4245.
-
13)
- X.-Z. Lai , M. Wu , J.-H. She . Control of acrobot based on Lyapunov function. J. Central South Univ. Technol. , 210 - 215
-
14)
- D.E. Davison , S.A. Bortoff . Stabilization using pseudolinearization and high-gain feedback. Automatica , 245 - 251
-
15)
- M.W. Spong . The swing up control problem for the acrobot. IEEE Control Syst. Mag. , 49 - 55
-
16)
- M.S. Branicky . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control , 4 , 475 - 482
-
17)
- Henmi, T., Deng, M., Inoue, A.: `Swing-up control of the acrobot using a new partial linearization controller based on the Lyapunov theorem', Proc. IEEE Int. Conf. Networking, Sensing and Control, April 2006, Florida, USA, p. 60–65.
-
18)
- X.-Z. Lai , J.-H. She , Y. Ohyama . A fuzzy control strategy for acrobot combining model-free and model-based control. IEE Proc., Control Theory Appl. , 505 - 511
-
19)
- A. Leonessa , W.M. Haddad , V. Chellabonia . Nonlinear system stability via hierarchical switching control. IEEE Trans. Autom. Control , 17 - 28
-
20)
- Mahindrakar, A.D., Astolfi, A., Ortega, R.: `Further constructive results on interconnection and damping assignment control of mechanical systems: the acrobot example', Proc. American Control Conf., June 2006, Minnesota, USA, p. 5584–5589.
-
21)
- Smith, M.H., Lee, M.A., Ulieru, M.: `Design limitation of PD versus fuzzy controllers for the acrobot', Proc. IEEE Int. Conf. Robotics and Automation, April 1997, New Mexico, USA, p. 1130–1135.
-
22)
- Yazici, A., Karamancioglu, A.: `Robust stabilization of acrobot by using its real structured uncertainty model', Proc. 2nd Int. Conf. Recent Advances in Space Technologies, June 2005, Istanbul, Turkey, p. 265–270.
-
23)
- Zheng, Y., Jing, Y.W.: `Fuzzy variable structure control for acrobot based on T-S model', Proc. IEEE Int. Conf. Mechatronics and Automation, July 2005, Niagara Falls, Canada, p. 842–846.
-
24)
- Luca, A.D., Oriolo, G.: `Stabilization of the acrobot via iterative state steering', Proc. IEEE Int. Conf. Robotics and Automation, 1998, p. 3581–3587.
-
25)
- Xin, X., Kaneda, M.: `New analytical results of the energy based swinging up control of the acrobot', Proc. 43rd IEEE Conf. Decision Control, December 2004, Paradise Island, Bahamas, p. 704–709.
-
26)
- Malmborg, J., Bernhardsson, B., Åström, K.J.: `A stabilizing switching scheme for multi controller systems', IFAC 13th World Cong., July 1996, San Francisco, USA, p. 229–234.
-
27)
- Kobayashi, T., Komine, T., Suzuki, S.: `Swing-up and balancing control of acrobot', Proc. 41st SICE Annual Conf., August 2002, Osaka, Japan, p. 3072–3075.
-
28)
- X. Xin , T. Mita , M. Kaneda . The posture control of a two-link free flying acrobot with initial angular momentum. IEEE Trans. Autom. Control , 1201 - 1206
-
29)
- Xin, X., Kaneda, M.: `The swing up control for the acrobot based on energy control approach', Proc. 41st IEEE Conf. Decision and Control, December 2002, Nevada, USA, p. 3261–3266.
-
1)