Abstract
In this paper, a control architecture is developed for the closed chain motion of two six-joint manipulators holding a rigid object in a three-dimensional workspace. Dynamic and kinematic constraints are combined with the equations of motion of the manipulators to obtain a dynamical model of the entire system in the joint space. Reduced-order dynamic equations are then developed with regard to the position and force control variables. Robust control laws are then determined such that the force and position control design is decoupled. The control laws that will be discussed are: a robust position tracking controller that yields an exponentially stable position tracking error result, and a robust force tracking controller that yields adjustable bounds on the force tracking error.
Similar content being viewed by others
References
KoivoA.J., and BekeyG.A., Report of workshop on coordinated multiple robot manipulators: Planning, Control, and Applications, IEEE J. Robotics Automat. 4, 91–93 (1988).
Orin, D.E., and Oh, S.Y., Control of force distribution in robotic mechanisms containing closed kinematic chains, ASME, J. Dynam. Systems Meas. Control 102, (1981).
Ryuh, B.S., and Pennock, G.R., Dynamic formulation for multiple cooperating robots forming closed kinematic chains, Proc. IASTED Internat. Symp. Robotics and Automation, Santa Barbara, CA, (1988), pp. 64–68.
Walker, I.D., Freeman, R.A., and Marcus, S.E., Dynamic task distribution for multiple cooperating robot manipulators, Proc. 1988 IEEE Internat. Conf. Robotics and Automation, vol. 2, Philadelphia, PA, (1988), pp. 1288–1290.
LuhJ.Y.S., and ZhengY.F., Constrained relations between two coordinated industrial robots for motion control, Internat. J. Robotics Res. 6(3), 60–70 (1987).
McClamroch, N.H., Singular systems of differential equations as dynamic models for constrained robot systems, IEEE Internat. Conf. Robotics and Automation, vol. 1, San Francisco, CA (1986), pp. 21–28.
Hayati, S., Hybrid position/force control of multi-arm cooperating robots, IEEE Internat. Conf. Robotics and Automation, San Francisco, CA, (1986), pp. 82–89.
Kreutz, K., and Lokshin, A., Load balancing and closed chain multiple arm control, Proc. 1988 ACC, vol. 3, Atlanta, GA, (1988), pp. 2148–2155.
Pittelkau, M.E., Adaptive load-sharing force control for two-arm manipulators, Proc. 1988 IEEE Internat. Conf. Robotics and Automation, vol. 1, Philadelphia, PA (1988), pp. 498–503.
TaoJ.M., LuhJ.Y.S., and ZhengY.F., Coordination control of two moving industrial robots, IEEE Trans. Robotics Automat. 6, No. 3, June 1990, pp. 322–330.
PittelkauM.E., Adaptive load-sharing force control for two-arm manipulators, Proc. 1988 IEEE Internat. Conf. Robotics and Automation, vol. 1, Philadelphia, PA (1988), pp. 498–503.
KankaanrantaR.K., and KoivoH.N., Dynamics and simulation of compliant motion of a manipulator, IEEE J. Robotics Automat. 4, 163–173 (1988).
UnserenM.A., and KoivoA.J., Rduced order model and decoupled control achitecture for two manipulators holding an object, IEE Internat. Conf. Robotics and Automat., Scottsdale AZ, vol. 2, (1989), pp. 1240–1245.
SpongM., and VidyasagarM., Robot Dynamics and Control, Wiley, New York, (1989).
EppingerS., and SeeringP., Introduction to dynamic models for robot force control, IEEE Control Systems Magazine 7(2), 48–52 (1987).
VidyasagarM., Nonlinear Systems Analysis, Prentice Hall, New Jersey (1978).
Dawson, D., Qu, Z., Lewis, F., and Dorsey, J., Robust control for the tracking of robot motion, Proc. IEEE Amer. Control Conf., San Diego, CA. (1990), pp. 722–726.
CraigJ.J., Introduction to Robotics, Addison Wesley, Boston (1986).
CorlessM., and LeitmannG., Continuous state feedback guaranteeing uniform ultimate boundness for uncertain dynamic systems, J. Automat. Controls AC 26, 1139–1143 (1981).
Dawson, D., and Qu, Zhihua, Rethinking the robust control of robot manipulators, submitted to Internat. J. Robust and Nonlinear Control, (1991).
HustonR.L., Multibody Dynamics, Butterworth-Heinemann, Boston, (1990).
PaulR.P., and ZhangHong, Computationally efficient kinematics for manipulators with spherical wrists based on the homogeneous transformation representation, in J.M.McCarthy (eds), Kinamatics of Robot Manipulators, MIT Press, Boston (1987).
Sasiadek, J., and Srinivasan, R., Adaptive control of dual arm, IEEE Internat. Conf. Systems Man Cybernet. (1987), pp. 690–694.
Walker, M., Kim, D., and Dionise, J., Adaptive coordinated motion control of two manipulator arms, IEEE Internat. Conf. Robotics Automat. (1989), pp. 1084–1090.
Hu, Y., and Goldenberg, A., An adaptive approach to motion and force control of multiple coordinated robot arms, IEEE Internat. Conf. Robotics Automat. (1989), 1091–1096.
Qu, Z., and Dorsey, J., Robust control of dynamic systems with high order nonlinear uncertainties by a linear feedback law, Automatica, submitted for publication (1989).
UchiyamaM., and YamashitaT., Asymmetric hybrid control of positions and forces of a dual arm robot to share loads, in V.Hayward and O.Khatib (eds), Experimentatl Robotics I: The First International Symposium, Montreal, June 1989, Lecture Notes in Control and Information Sciences, 139, Springer-Verlag, New York (1989), pp. 100–115.
Uchiyama, M., and yamashita, T., Adaptive load sharing for hybrid controlled two coordinative manipulators, Proc. IEEE Internat. Conf. Robotics and Automat., Sacramento, CA (1989), pp. 986–991.
Zheng, Y.F., and Luh, J.Y.S., Optimal load distribution for two industrial robots handling a single object, Proc. 1988 IEEE Internat. Conf. Robotics and Automat., vol. 1, Philadelphia, PA (1988), pp. 344–349.
GantmacherF.R., The Theory of Matrices, vol. 1, Chelsea Publishing, New York (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gao, X., Dawson, D. & Qu, Z. On the robust control of two manipulators holding a rigid object. J Intell Robot Syst 6, 107–119 (1992). https://doi.org/10.1007/BF00314701
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00314701