A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 2 Issue 4
Oct.  2015

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 7.847, Top 10% (SCI Q1)
    CiteScore: 13.0, Top 5% (Q1)
    Google Scholar h5-index: 64, TOP 7
Turn off MathJax
Article Contents
Xiaoli Liu, Shengchao Zhen, Kang Huang, Han Zhao, Ye-Hwa Chen and Ke Shao, "A Systematic Approach for Designing Analytical Dynamics and Servo Control of Constrained Mechanical Systems," IEEE/CAA J. of Autom. Sinica, vol. 2, no. 4, pp. 382-393, 2015.
Citation: Xiaoli Liu, Shengchao Zhen, Kang Huang, Han Zhao, Ye-Hwa Chen and Ke Shao, "A Systematic Approach for Designing Analytical Dynamics and Servo Control of Constrained Mechanical Systems," IEEE/CAA J. of Autom. Sinica, vol. 2, no. 4, pp. 382-393, 2015.

A Systematic Approach for Designing Analytical Dynamics and Servo Control of Constrained Mechanical Systems


This work was supported by Natural Science Foundation of Anhui Province (1508085SME221).

  • A systematic approach for designing analytical dynamics and servo control of constrained mechanical systems is proposed. Fundamental equation of constrained mechanical systems is first obtained according to Udwadia-Kalaba approach which is applicable to holonomic and nonholonomic constrained systems no matter whether they satisfy the D'Alember's principle. The performance specifications are modeled as servo constraints. Constraint-following servo control is used to realize the servo constraints. For this inverse dynamics control problem, the determination of control inputs is based on the Moore-Penrose generalized inverse to complete the specified motion. Secondorder constraints are used in the dynamics and servo control. Constraint violation suppression methods can be adopted to eliminate constraint drift in the numerical simulation. Furthermore, this proposed approach is applicable to not only fully actuated but also underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration.


  • loading
  • [1]
    Lagrange J L. Mechanique Analytique. Paris: Mme ve Courcier, 1787.
    Gauss C F. Uber ein neues allgemeines grundgsetz der mechanik. Journal fur die Reine und Angewandte Mathematik, 1829, 4: 232-235
    Gibbs J W. On the fundamental formulae of dynamics. American Journal of Mathematics, 1879, 2(1): 49-64
    Appell P. Sur une forme generale des equations de la dynamique. Comptes Rendus de l'Academie des Sciences, 1899, 129: 459-460
    Pars L A. A Treatise on Analytical Dynamics. Connecticut: Ox Bow Press, 1979.
    Dirac P A M. Lectures on Quantum Mechanics. New York: Yeshiva University Press, 1964.
    Udwadia F E, Kalaba R E. A new perspective on constrained motion. Proceedings of the Royal Society, 1992, 439(1906), doi: 10.1098/rspa.1992.0158
    Udwadia F E, Kalaba R E. Analytical Dynamics: A New Approach. Cambridge, UK: Cambridge University Press, 1996.
    Udwadia F E, Kalaba R E. Explicit equations of motion for mechanical systems with nonideal constraints. Journal of Applied Mechanics, 2001, 68(3): 462-467
    Udwadia F E. On constrained motion. Applied Mathematics and Computation, 2005, 164(2): 313-320
    Maggi G A. Di alcune nuove forme delle equazioni della dinamica, applicabili ai sistemi anolonomi. Atti della Reale Accademia dei Lincei, Rendiconti, Classe di Scienze Fisiche, Matematiche e Naturali, 1901, 10: 287-291 (in Italian)
    Neimark J I, Fufaev N A. Dynamics of Nonholonomic Systems. Phode Island, Providence: American Mathematical Society, 1972.
    Hamel G. Die lagrange-eulersche gleichungen der mechanik. Zeitschrift fr Mathematik und Physik, 1904, 50: 1-57 (in German)
    Hamel G. Theoretische Mechanik. Berlin: Springer-Verlag, 1949. (in German)
    Cabannes H. General Mechanics (Second edition). Massachusetts, Waltham: Blaisdell/Ginn, 1968. (in English, translated from the original French)
    Kirgetov V I. The motion of controlled mechanical systems with prescribed constraints (servoconstraints). Journal of Applied Mathematics and Mechanics, 1967, 31(3): 465-477 (in English, translated from original Russian)
    Chen Y H. Constraint-following servo control design for mechanical systems. Journal of Vibration and Control, 2009, 15(3): 369-389
    Moore E H. On the reciprocal of the general algebraic matrix. Bulletin of the American Mathematical Society, 1920, 26: 294-395
    Penrose R. A generalized inverse for matrices. Proceedings of the Cambridge Philosophical Society, 1955, 51: 404-413
    Chen Y H. Second-order constraints for equations of motion of constrained systems. IEEE/ASME Transaction on Mechatronics, 1998, 3(3): 240-248
    Chen Y H. Equations of motion of constrained mechanical systems: given force depends on constraint force. Mechatronics, 1999, 9(4): 411-428
    Rosenberg R M. Analytical Dynamics of Discrete Systems. New York: Plenum Press, 1977.
    Papastavridis J G. Analytical Mechanics. New York: Oxford University Press, 2002.
    Chen Y H, Leitmann G, Chen J S. Robust control for rigid serial manipulators: a general setting. In: Proceedings of the 1998 American Control Conference. Philadelphia, PA, USA: IEEE, 1998. 912-916
    Udwadia F E, Kalaba R E. On motion. Journal of the Franklin Institute, 1993, 330(3): 571-577
    Bjerhammar A. Rectangular reciprocal matrices with special reference to geodetic calculations. Bulletin Godsique, 1951, 20(1): 188-220
    Baumgarte J. Stabilization of constraints and integrals of motion in dynamical systems. Computer Methods in Applied Mechanics and Engineering, 1972, 1(1): 1-16
    Asada H, Slotine J -J E. Robot Analysis and Control. New York: John Wiley and Sons, 1985.
    Slotine J -J E, Li W P. Applied Nonlinear Control. New Jersey: Prentice Hall, 1991.


    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

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1018) PDF downloads(8) Cited by()


    DownLoad:  Full-Size Img  PowerPoint