For automatic derivation of control algorithms, the decoupling method is applied to Euler-Lagrange's formal ism. Explicit expressions to derive directly from the Lagrangian the nonlinear control laws of mechanisms and of a dynamically driven robot are given. Finally, a simple two-degree-of-freedom system driven by DC electric motors is used to illustrate the flexibility of the proposed approach over the other design methods.
Get full access to this article
View all access options for this article.
References
1.
Bejczy, A., and Tarn, T.1988. Dynamic control of robot arms in task space using nonlinear feedback. Anwendungsaufsatz Automatisierungstechnik36(10):374-388.
2.
Cotsaftis, M.1987. Impulse effects in polyarticulated systems dynamics. Report B-204. UGRA-CENFAR, 92260Fontenay aux Roses, France.
3.
Cotsaftis, M., and Vibet, C.1987(San Diego). A derivation of robot control algorithms from the Lagrange formalism. In Radharamanan, R. (ed.): Proc. 2nd Int. Conf. on Robotics and Factories of the Future. San Diego. New York: Springer Verlag, pp. 461-465.
4.
Cotsaftis, M., and Vibet, C.1988a. Consistent impulse conditions in Lagrangian system dynamics . Robotica6(4):339-341.
5.
Cotsaftis, M., and Vibet, C.1988b. Control law decoupling for 2D biped walking system . IEEE Eng. Med. Biol. 7(3):41-45.
6.
Cotsaftis, M., and Vibet, C.1988c. Modeling of robot system dynamics for CAD based robot programming. In Ravani, B. (ed.): CAD Based Programming for Sensory Robots, NATO Series F, vol. 50. New York: Springer-Verlag, pp. 493-509.
7.
Cotsaftis, M., and Vibet, C.1989(Snowbird, UT, August 7-11). Simultaneous derivation of control laws and of dynamical model equations for controlled mechanisms . In Haug, E. and R. Deyo (eds.). Real-Time Integration Methods for Mechanical System Simulation. NATO ARW series F: Computer and systems sciences, vol. 69, pp. 301-327. New York: Verlag.
8.
Cotsaftis, M., and Vibet, C.1990. Control law synthesis and sensitivity analysis from Lagrangian formulation with impulse conditions. Advanced Robot . 4(1):59-70.
9.
Craig, J., Hsu, P., and Sastry, S.1986. Adaptive control of mechanical manipulators. IEEE Conf. on Robotics, pp. 190-195.
10.
Craig, J., Hsu, P., and Sastry, S.1987. Adaptive control of mechanical manipulators. Int. J. Robot. Res. 6(2):16-28.
11.
D'Andrea, B., and Levine, J.1988. Synthesis of nonlinear state feedback for the stabilization of a class of manipulators. Information Decision Technol . 14:145-168.
12.
Egeland, O.1987. Cartesian control of industrial robots with redundant degree of freedom. Ph.D. thesis, 87-18W ; University of Trondheim, Norway.
13.
Freund, E.1973. Decoupling and pole assignment in nonlinear systems . Electr. Lett. 9(16):373-374.
14.
Freund, E.1980. The principle of nonlinear decoupling of systems with application to industrial robots. (In German). Anwendungsaufsatz Regelungstechnik28(3):80-86.
15.
Freund, E.1982. Fast nonlinear control with arbitrary pole-placement for industrial robots and manipulators. Int. J. Robot. Res. 1(1):65-78.
16.
Freund, E., and Syrbe, M.1977. Control of industrial robots by means of microprocessors. In Lecture Notes in Control and Information Sciences. New York: Springer-Verlag, pp. 167-185.
17.
Gavel, D., and Hsia, T.1988. Decentralized adaptive control experments with the PUMA robot arm. IEEE Conf. on Robotics and Automation , pp. 1022-1027.
18.
Gu, Y.-L., and Loh, N.K.1967(Raleigh, NC). Control system modeling for robot manipulators by use of canonical transformations. Proc. IEEE Int. Conf. on Robotics and Automation, pp. 484-489.
19.
Hollerbach, J., and Sahar, G.1984. Wrist-partitioned inverse kinematics acceleration and manipulators dynamics. IEEE Conf. on Robotics , pp. 152-161.
20.
Isidorei, A., Krener, A.J., Gori-Giorgi, C., and Monaco, S.1981. Nonlinear decoupling via feedback: A differential geometric approach. IEEE Trans. Automat. Controls AC -26(2):331-345.
21.
Khatib, O.1983(New Delhi). Dynamic control of manipulators in operational space. Sixth IFTOMM Congress on Theory of Machines and Mechanisms (preprint, pp. 1-10).
22.
Khatib, O.1985(Tokyo). The operational space formulation in robot manipulator control. 15th ISIR, pp. 165-172.
23.
Khatib, O., and Burdick, J.1986. Motion and force control of robot manipulators . Proc. IEEE Int. Conf. on Robotics, pp. 1381-1386.
24.
Lentini, D., Nicolò, F., Nicosia, S., and Vecchio, L.1980. Decoupling and nonlinearities compensation in robot control systems. Report R 80-08. Instituto di Automatica, Univ. di Roma.
25.
Luh, J., Walker, W., and Paul, R.1980. Resolved-acceleration control of mechanical manipulators . IEEE Trans. Automat. Controls AC-25(3):468-474.
26.
Porter, W.1969. Decoupling of and inverses for time-varying linear systems . IEEE Trans. on AC-14, pp. 378-380.
27.
Seraji, H.1986. An adaptive Cartesian control scheme for manipulators . IEEE Conf. on Robotics, pp. 157-162.
28.
Seraji, H.1989. Decentralized adaptive control of manipulators : Theory, Simulation and Experimentation. IEEE Trans. on Robotics and Automation5(2): 183-201.
29.
Slotine, J.-J.E.1988. Putting physics in control; the example of robotics . IEEE Control Sys. Mag. 8(6):12-18.
30.
Slotine, J.-J.E., and Weiping, L.1988a. Adaptive manipulator control, a case of study . IEEE Trans. Automat. Controls AC-33(11):995-1003.
31.
Slotine, J.-J.E., and Weiping, L.1988b. Composite adaptive control of robot manipulators . Automatica25(4):509-519.
32.
Niemeyer, G., and Slotine, J.-J.E.1989. Performance in adaptive manipulator control. To be published in Int. J. Robot. Res.
33.
Tarn, T.J., Bejczy, A.K., Isidori, A., and Chen, Y.L.1984(Las Vegas). Nonlinear feedback in robot arm control . Proc. of the 23rd IEEE Conf. on Decision and Control .
34.
Tarn, T., Bejczy, A., and Yun, X.1987. Design of dynamical control of two cooperating robot arms: Closed chain formulation. IEEE Conf. on Robotics and Automation, pp. 1-7.
35.
Tarn, T., Bejczy, A., and Yun, X.1988. New nonlinear control algorithms for multiple robot arms . IEEE Trans. Aerospace Electronic Sys . 24(5):571-583.
36.
Tarn, T., and Bejczy, A.1988. Software elements. In International Encyclopedia of Robotics, Applications and Automation. New York : John Wiley, pp. 1608-1626.
37.
Verdier, M., Rouff, M., and Fontaine, J.G.1989. Nonlinear control robot: A phenomenological approach to linearization by static feedback. Robotica7:315-321.
38.
Vibet, C.1987. Initial conditions and different equations. Simulation48(5):210-212.
39.
Vibet, C.1988. General method of finding initial conditions. IEEE Trans. Educ. E-31(1):46-48.
40.
Yoshikawa, T.1984. Analysis and control of robot manipulators with redundancy . In Brady, M., and Paul, R. (eds.): Robotics Research, The First International Symposium. Cambridge, MA: MIT Press.