Abstract
A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end-effector paths. This paper compares two methods for choosing repeatable control strategies which minimize their distance from a nonrepeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse while the second method minimizes the distance of the null vectors associated with the desired and the repeatable inverses. It is then shown how the two techniques can be combined in order to obtain the advantages of both methods. As an illustrative example the pseudoinverse is approximated in a region of the joint space for a seven-degree-of-freedom manipulator.
References
Anderson, K. and Angeles, J.: Kinematic inversion of robotic manipulators in the presence of redundancies,Int. J. Robotics Res. 8(6) (1989), 80–97.
Baillieul, J.: Kinematic programming alternatives for redundant manipulators, inProc. IEEE Int. Conf. Robotics Automat., St. Louis, MO, March 25–28, 1985, pp. 722–728.
Baker, D. R. and Wampler, C. W., II: On the inverse kinematics of redundant manipulators,Int. J. Robotics Res. 7(2) (1988), 3–21.
Chiacchio, P., Chiaverini, S., Sciavicco, L. and Siciliano, B.: Closed-loop inverse kinematics schemes for constrained redundant manipulators with task space augmentation and task priority strategy,Int. J. Robotics Res. 10(4) (1991), 410–425.
Colbaugh, R. and Glass, K.: On controlling robots with redundancy,Robotics and Computer Integrated Manufacturing 9(2) (1992), 121–135.
Egeland, O.: Task-space tracking with redundant manipulators,IEEE J. Robotics Automat. RA-3(5) (1987), 471–475.
Klein, C. A. and Huang, C. H.: Review of pseudoinverse control for use with kinematically redundant manipulators,IEEE Trans. Syst., Man Cyber. SMC-13(3) (1983), 245–250.
Podhorodeski, R. P., Goldenberg, A. A. and Fenton, R. G.: Resolving redundant manipulator joint rates and identifying special arm configurations using Jacobian null-space bases,IEEE Trans. Robotics Automat. 7(5) (1991), 607–618.
Roberts, R. G. and Maciejewski, A. A.: Nearest optimal repeatable control strategies for kinematically redundant manipulators,IEEE Trans. Robotics Automat. 8(3) (1992), 327–337.
Roberts, R. G. and Maciejewski, A. A.: Repeatable generalized inverse control strategies for kinematically redundant manipulators,IEEE Trans. Automat. Contr. 38(5) (1993), 689–699.
Seraji, H.: Configuration control of redundant manipulators: Theory and implementation,IEEE Trans. Robotics Automat. 5(4) (1989), 472–490.
Shamir, T.: Remarks on some dynamical problems of controlling redundant manipulators,IEEE Trans. Automat. Contr. 35(3) (1990), 341–344.
Shamir, T. and Yomdin, Y.: Repeatability of redundant manipulators: Mathematical solution of the problem,IEEE Trans. Automat. Contr. 33(11) (1988), 1004–1009.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roberts, R.G., Maciejewski, A.A. Calculation of repeatable control strategies for kinematically redundant manipulators. J Intell Robot Syst 14, 105–130 (1995). https://doi.org/10.1007/BF01254010
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01254010