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Optimization in Control of Robots

  • F. L. Chernousko
Chapter
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 115)

Abstract

Optimization of control algorithms and parameters of industrial robots is regarded as an effective means for improving their operational characteristics. Various possible versions of optimization problems for robots were considered in the scientific literature over the last 20 years. The paper presents a brief survey of research carried out in this field.

Keywords

Optimal Control Problem Robotic Manipulator Gear Train Redundant Manipulator Optimal Control Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Ailon, A. and Langholz, G., On the existence of time-optimal control of mechanical manipulators, J. of Optimization Theory and Applications, 46, 1, 1985.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Akulenko, L. D. and Bolotnik, N. N., Synthesis of optimal control of transport motions of manipulation robots, Mechanics of Solids, 21 (4), 18, 1986.Google Scholar
  3. [3]
    Akulenko, L. D., Bolotnik, N. N., Chernousko, F. L., and Kaplunov, A. A., Optimal control of manipulation robots, in Proc. of the Ninth Triennial World Congress of IFAC, Volume 1, Gertler, J., and Keviczky, L., Eds., Pergamon Press, Oxford, 1985, 331.Google Scholar
  4. [4]
    Akulenko, L. D., Bolotnik, N. N., and Kaplunov, A. A., Some control modes for industrial manipulators, Izvestiya AN SSSR. Tekhnicheskaya Kibernetika, No. 6, 44, 1985.Google Scholar
  5. [5]
    Avetisyan, V. V., Akulenko, L. D., and Bolotnik, N. N., Optimization of control modes of manipulation robots with regard of the energy consumption, Izvestiya AN SSSR. an electromechanical manipulator with a high degree of positioning accuracy, Mechanics of Solids, 25 (5), 32, 1990.Google Scholar
  6. [6]
    Avetisyan, V. V., Bolotnik, N. N., Suboptimal control of an electromechanical manipulator with a high degree of positioning accuracy, Mechanics of Solids, 25 (5), 1990.Google Scholar
  7. [7]
    Avetisyan, V. V., Bolotnik, N. N., and Chernousko, F. L., Optimal programmed motion of a two-link manipulator, Soviet J. Computer and Systems Sciences, 23 (5), 65, 1985.Google Scholar
  8. [8]
    Berbyuk, V. E. and Yanchak, Ya. I., Minimum-time optimization of transport motions of a gantry robot, Izvestiya AN SSSR. Tekhnicheskaya Kibernetika, No. 1, 126, 1991 (in Russian).Google Scholar
  9. [9]
    Bobrow, J. E., Optimal robot path planning using the minimum-time criterion, IEEE J. Robotics and Automation, 4, 443, 1988.CrossRefGoogle Scholar
  10. [10]
    Bobrow, J. E., Dubowsky, S., and Gibson, J. S., Time-optimal control of robotic manipulators along specified paths, Int. J. Robotics Research, 4, 3, 1985.CrossRefGoogle Scholar
  11. [11]
    Bolotnik, N. N. and Chernousko, F. L., Optimization of manipulation robot control, Soviet J. Computer and Systems Sciences, 28 (5), 127, 1990.MathSciNetzbMATHGoogle Scholar
  12. [12]
    Bolotnik, N. N., Gorbachev, N. V., and Shukhov, A. G., Optimization of control of an electromechanical system with respect to the minimax performance index, Izvestiya AN SSSR. Mekhanika Tverdogo Tela, No. 6, 30, 1992 (in Russian).Google Scholar
  13. [13]
    Bolotnik, N. N. and Kaplunov, A. A., Optimal rectilinear transfer of a load by means of a two-link manipulator, Izvestiya AN SSSR. Tekhnicheskaya Kibernetika, No. 1, 160, 1982 (in Russian).MathSciNetGoogle Scholar
  14. [14]
    Bolotnik, N. N. and Kaplunov, A. A., Optimization of control and configurations of a two-link manipulator, Izvestiya AN SSSR. Tekhnicheskaya Kibernetika, No. 4, 144, 1983 (in Russian).Google Scholar
  15. [15]
    Borisov, V. F. and Zelikin, M. I., Modes with switchings of increasing frequency in the problem of controlling a robot, J. Appl. Maths. Mechs., 52, 731, 1988.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    Chen, Y., Existence and structure of minimum-time control for multiple robot arm handling a common object, Int. J. Control, 53, 855, 1991.zbMATHCrossRefGoogle Scholar
  17. [17]
    Chernousko, F. L., Models and optimal control of robotic systems, System Modelling and Optimization, Proc. 14th IFIP-Conference, Lecture Notes in Control and Information Sciences, Sebastian, H.-J., and Tammer, K., Eds., 143, 1, 1990.Google Scholar
  18. [18]
    Chernousko, F. L., Decomposition and suboptimal control in dynamical systems, J. Appl. Maths. Mechs., 54, 727, 1990.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Chernousko, F. L., Decomposition and synthesis of control in dynamical systems, Soviet J. Computer and Systems Sciences, 29 (5), 126, 1991.MathSciNetGoogle Scholar
  20. [20]
    Chernousko, F. L., Decomposition and suboptimal control in dynamic systems, Optimal Control Applications and Methods, 14, 1993 (to appear).Google Scholar
  21. [21]
    Chernousko, F. L., Akulenko, L. D., and Bolotnik, N. N., Time-optimal control for robotic manipulators, Optimal Control Applications and Methods, 10, 293, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    Dubowsky, S., Norris, M. A., and Shiller, Z., Time optimal trajectory planning for robotic manipulators with obstacle avoidance: A CAD approach, in Proc. of IEEE Int. Conf. on Robotics and Automation, San Francisko CA, 1986.Google Scholar
  23. [23]
    Geering, H. P., Guzzella, L., Hepner, S. A. R., and Onder, C. H., Time-optimal motions of robots in assembly tasks, IEEE Trans. on Automatic Control, AC-31, 512, 1986.CrossRefGoogle Scholar
  24. [24]
    Hanafusa, H., Yoshikawa, T., and Nakamura, Y., Analysis and control of articulated robot arm with redundancy, in Prepr. of the 8th IFAC World Congress, 1981, August, XIV-78.Google Scholar
  25. [25]
    Heimann, B., Loose, H., Schmidt, K. D., Rothe, H., and Lyubushin, A. A. Dynamics and optimal control of manipulation robots, Advances in Mechanics, 7, 1984 (in Russian).Google Scholar
  26. [26]
    Hollerbach, J. M. and Suh, K. C., Redundancy resolution of manipulators through torque optimization, IEEE J. Robotics and Automation, RA-3, 308, 1987.CrossRefGoogle Scholar
  27. [27]
    Huang, H. P. and McClamroch, N. H., Time-optimal control for a robotic contour following problem, IEEE J. Robotics and Automation, 4, 140, 1988.CrossRefGoogle Scholar
  28. [28]
    Kahn, M. E. and Roth, B., The near-minimum-time control of open-loop articulated kinematic chains, Trans ASME. J. Dynamic Syst. Measurem. and Control, 93, 165, 1971.Google Scholar
  29. [29]
    Kazerounian, K. and Wang, Z., Global versus local optimization in redundancy resolution of robotic manipulator, Int. J. Robotics Research, 7, 3, 1988.CrossRefGoogle Scholar
  30. [30]
    Khadem, S. E. and Dubey, R. V., A global Cartesian space obstacle avoidance scheme for redundant manipulators, Optimal Control Applications and Methods, 12, 279, 1991.zbMATHCrossRefGoogle Scholar
  31. [31]
    Kiriazov, P. and Marinov, P., Robot control synthesis in conjunction with moving workpieces, in Prepr. 6th CISM-IFToMM Symp. on Theory and Practice of Robots and Manipulators, Ro. Man. Sy. ’86, Crakow, 1986, 284.Google Scholar
  32. [32]
    Kobrinskii, A. A. and Kobrinskii, A. E., Manipulation Systems of Robots, Nauka, Moscow, 1984 (in Russian).Google Scholar
  33. [33]
    Konzelmann, J., Bock, H. G., and Longman, R. W., Time-optimal trajectories of elbow robots by direct methods, in Proc. of the AIAA Guidance, Navigation, and Control Conference, Boston, August 1989, 895.Google Scholar
  34. [34]
    Konzelmann, J., Bock, H. G., and Longman, R. W., Time-optimal trajectories of polar robot manipulators by direct methods, Modeling and Simulation, 20, 1933, 1989.Google Scholar
  35. [35]
    Liegeois, A., Automatic supervisory control of the configuration and behavior of multi-body mechanisms, IEEE Trans. Sysyt. Man. Cybern., SMC-7, 868, 1977.Google Scholar
  36. [36]
    Loose, H., Rothe, H., and Schmidt, C.-D., Verfahren und Programme zur Optimalen Steuerung von Industrierobotern, Z. Angew. Math. und Mech, 64, M 476, 1984.Google Scholar
  37. [37]
    Luh, J. Y. S. and Lin, C. S., Optimum path planning for mechanical manipulators, Trans. ASME. J. Dynamic Syst. Measurem. and Control, 102, 142, 1981.CrossRefGoogle Scholar
  38. [38]
    Marinov, P. and Kiriazov, P., A direct method for optimal control synthesis of manipulator point-to-point motion, in Prepr. 9th IFAC World Congress, Budapest, Hungary, 1984, Volume IX, Mac Farlane, A. G. J., and Rauch, H. E., Volume Eds, Budapest, 1984, 219.Google Scholar
  39. [39]
    Meier, E. B. and Bryson, A. E., Efficient algorithm for time-optimal control of a two-link manipulator, J. Guidance, 13, 859, 1990.MathSciNetzbMATHCrossRefGoogle Scholar
  40. [40]
    Nakamura, Y. and Hanafusa, H., Optimal redundancy control of robot manipulators, Int. J. Robotics Research, 6, 32, 1986.CrossRefGoogle Scholar
  41. [41]
    Oberle, H. J., Numerical computation of singular control functions for a two-link robot arm, in Proc. of the Conference on Optimal Control and Variational Calculus, Bulirsch, R., Miele, A., Stoer, J., and Well, K. H., Springer Verlag, Berlin, 1987, 244.Google Scholar
  42. [42]
    Osipov, S. N. and Formalskii, A. M., The problem of the time-optimal turning of a manipulator, J. Appl. Maths. Mechs., 52, 725, 1988.MathSciNetzbMATHCrossRefGoogle Scholar
  43. [43]
    Pfeiffer, F., Geometrical solution of a manipulator optimization problem, in Control Applications of Nonlinear Programming and Optimization 1989, Proc. of the 8th IFAC Workshop, Siguerdidjane, H. B., and Bernhard, P., Eds, Pergamon Press, Oxford, 1989, 83.Google Scholar
  44. [44]
    Pfeiffer, F. and Johanni, R., A concept for manipulator trajectory planning, IEEE J. Robotics and Automation, RA-3, 115, 1987.CrossRefGoogle Scholar
  45. [45]
    Sahar, G. and Hollerbach, J. M., Planning of minimum-time trajectories for robot arms, Int. J. Robotics Research, 5, 90, 1986.CrossRefGoogle Scholar
  46. [46]
    Sato, O., Shimojima, H., and Kitamura, Y., Minimum-time control of a manipulator with two degrees of freedom, Bull. JSME, 26, 1404, 1983.Google Scholar
  47. [47]
    Sato, O., Shimojima, H., Kitamura, Y., and Yoinara, H., Minimum-time control of a manipulator with two degrees of freedom (2nd Report, Dynamic characteristics of gear train and axes), Bull. JSME, 28, 959, 1985.Google Scholar
  48. [48]
    Sato, O., Shimojima, H., and Kitamura, Y., Minimum-energy control of a manipulator with two degrees of freedom, Bull. JSME, 29, 573, 1986.Google Scholar
  49. [49]
    Schmitt, D., Soni, A. H., Srinvasan, V.,and Nagamathan, G., Optimal motion programming of robot manipulators, J. of Mechanisms, Transmissions and Automation in Design, 107, 239, 1985.CrossRefGoogle Scholar
  50. [50]
    Steinbach, M., Bock, H. G., and Longman, R., Time optimal control of SCARA robots, in Proc. of the AIAA Guidance, Navigation, and Control Conference, Portland, Oregon, 1990.Google Scholar
  51. [51]
    Stepanenko, Yu. A., Problem of optimal control of a manipulator, in Theory of Machines of Automatic Action, Nauka, Moscow, 1970 (in Russian).Google Scholar
  52. [52]
    Takano, M., and Susaki, K., Time optimal control of PTP motion of a robot with collision avoidance, in Proc. of the 3-rd Conf. on Robotics, ICAR 87, Versailles, 1987.Google Scholar
  53. [53]
    Troch, I., Time-suboptimal quasi-continuous path generation for industrial robots, Robotica, 7, 297, 1989.CrossRefGoogle Scholar
  54. [54]
    Vukobratovic, M. and Kircanski, M., A method for optimal synthesis of manipulation robotic trajectories, Trans ASME J. Dynamic Syst. Measurem. and Control, 102, 69, 1980.CrossRefGoogle Scholar
  55. [55]
    Vukobratovic, M. and Kircanski, M., A dynamic approach to nominal trajectory synthesis for redundant manipulators, IEEE Trans. Syst. Man. Cybernet, SMC-14, 1984.Google Scholar
  56. [56]
    Weinreb, A. and Bryson, A. E., Optimal control systems with hard control bounds, IEEE J. Automatic Control, AC-30, 1135, 1985.CrossRefGoogle Scholar
  57. [57]
    Whitney, D. E., The mathematics of coordinated control of prosthetic arms and manipulators, Trans. ASME. J. Dynamic Syst. Measurem. and Control, 94, 303, 1972.CrossRefGoogle Scholar
  58. [58]
    Wie, B., Chuang, C. H., and Sunkel, J., Minimum-time pointing control of a two-link manipulator, J. Guidance, 13, 867, 1990.zbMATHCrossRefGoogle Scholar
  59. [59]
    Yashi, O. S. and Ozgoren, K., Minimal joint motion optimization of manipulators with extra degrees of freedom, Mechanism and Machine Theory, 19, 325, 1984.CrossRefGoogle Scholar
  60. [60]
    Zhang, W. and Wang, R. K. C., Collision-free time optimal control of a two-link manipulator, Int. J. Robotics and Automation, 1, 96, 1986.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1994

Authors and Affiliations

  • F. L. Chernousko
    • 1
  1. 1.Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

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