Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T16:39:02.795Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of null-space and minimal null-space control algorithms

Published online by Cambridge University Press:  01 September 2007

Bojan Nemec ,
Leon Žlajpah  and
Damir Omrčen
Bojan Nemec*
Affiliation:
Robotics Laboratory, Jožef Stefan Institute, Jamova 39, 1001 Ljubljana, Slovenia
Leon Žlajpah
Affiliation:
Robotics Laboratory, Jožef Stefan Institute, Jamova 39, 1001 Ljubljana, Slovenia
Damir Omrčen
Affiliation:
Robotics Laboratory, Jožef Stefan Institute, Jamova 39, 1001 Ljubljana, Slovenia
*
*Corresponding author. E-mail: bojan.nemec@ijs.si
Get access Rights & Permissions [Opens in a new window]

Summary

This paper deals with the stability of null-space velocity control algorithms in extended operational space for redundant robots. We compare the performance of the control algorithm based on the minimal null-space projection and generalized-inverse-based projection into the Jacobian null-space. We show how the null-space projection affects the performance of the null-space tracking algorithm. The results are verified with the simulation and real implementation on a redundant mobile robot composed of 3 degrees of freedom (DOFs) mobile platform and 7-DOF robot arm.

Keywords

Redundant manipulatorStability of the control algorithmsAutonomous motionObstacle avoidanceMobile manipulator
Type
Article
Information
Robotica , Volume 25 , Issue 5 , September 2007 , pp. 511 - 520
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Asada, H. and Slotine, J.-J. E., Robot Analysis and Control (Wiley, New York, 1986).Google Scholar
2.Chang, P. H., “A closed-form solution for inverse kinematics of robot manipulators with redundancy,” IEEE J. Robot. Autom. RA-3, 393–403 (1987).Google Scholar
3.Hsu, P., Hauser, J. and Sastry, S., “Dynamics control of redundant manipulators,” Proceedings of the IEEE Conference on Robotics and Automation, Philadelphia, PA (1988) pp. 183–187.Google Scholar
4.Featherstone, R. and Khatib, O., “Load independance of the dynamically consistent inverse of the Jacobian matrix,” Int. J. Robot. Res. 16 (2), 168–170 (1997).Google Scholar
5.Khatib, O., “Real-time obstacle avoidance for manipulators and mobile robots,” Int. J. Robot. Res. 5, 90–98 (1986).CrossRefGoogle Scholar
6.Khatib, O., “A unified approach for motion and force control of robot manipulators: The operational space formulation,” IEEE Trans. Robot. Autom. 3 (1), 43–53 (1987).Google Scholar
7.Khatib, O., “The argumented object and reduced effective inertia in robot systems,” Proceedings of the IEEE Conference on Robotics and Automation, Atlanta, GA (1988) pp. 2140–2147.Google Scholar
8.Kennedy, C. W. and Desai, J. P., “Model-based controller for the Mitsubishi PA-10 robot arm: Application to robot-assisted surgery,” Proceedings of the IEEE Conference on Robotics and Automation, New Orleans, LA (2004).Google Scholar
9.Luh, J. Y. S., “Convetional controller design for industrial robots–A tutorial,” IEEE Trans. Syst., Man, Cybern. SMC-13 (3), 298–316 (1983).Google Scholar
10.Luh, J. Y. S., Walker, M. W. and Paul, R. P. C., “Resolved acceleration control of mechanical manipulators,” IEEE Trans. Autom. Control AC-25 (3), 486–474 (1980).Google Scholar
11.Maciejewski, A. A. and Klein, C. A., “The singular value decomposition: Computation and application to robotics,” Int. J. Robot. Res. 8 (6), 63–79 (1989).Google Scholar
12.Maciejewski, A. A., “Kinetic limitation on the use of redundancy in robotic manipulators,”IEEE Trans. Robot. Autom. 7 (2), 205–210 (1991).CrossRefGoogle Scholar
13.Nash, J.-C., “A one-sided tranformation method for the singular value decomposition and algepraic eigenproblem,” Comput. J. 18 (1), 74–76 (1974).CrossRefGoogle Scholar
14.Natale, C., Siciliano, B. and Vilani, L., “Spatial impedance control of redundant manipulators,” Proceedings of the IEEE Internatinal Symposium on Robotics and Automation (ICRA'99), Detroit, MI (1999).Google Scholar
15.Nemec, B., “Force control of redundant robots,” Preprits of the 5th IFAC Symposium on Robot Control (SYROCO'97) (Guglielmi, M., ed.), Nantes, France (1997) pp. 215–219.Google Scholar
16.Nemec, B. and Zlajpah, L., “Null velocity control with dinamically consistent pseudo-inverse,” Robotica 18, 513–518 (2000).CrossRefGoogle Scholar
17.Nemec, B. and Zlajpah, L., “Experiments with force control of redundant robots in unstructured environment using minimal null-space formulation,” J. Adv. Comput. Intell. 5 (5), 263–268 (2001).Google Scholar
18.Nemec, B., Zlajpah, L. and Omrcen, D., “Stability of null-space control algorithms,” Proceedings of the 12th RAAD Workshop, Cassino, Italy (2003).Google Scholar
19.Nenchev, D. N., “Redundancy resolution through local optimization: A review,” J. Robot. Syst. 6 (6), 769–798 (1989).Google Scholar
20.Oh, Y., Chung, W. K., Youm, Y. and Suh, I., “Experiments on extended impedance control of redundant manipulator,” Proceedings of the IEEE/RJS International Conference on Intelligent Robots and Systems, Victoria, Canada (1998) pp. 1320–1325.Google Scholar
21.Omrcen, D., Zlajpah, L. and Nemec, B., “Autonomous motion of a mobile manipular using a combined torque and velocity control,” Robotica 22, 623–632 (2004).Google Scholar
22.O'Neil, K. and Chen, Y. C., “Instability of pseudoinverse acceleration control of redundant mechanisms,” Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA (2000) pp. 2575–2582.Google Scholar
23.O'Neil, K., “Divergence of linear acceleration-based redundancy resolution schemes,” IEEE Trans. Robot. Autom. 18 (4), 625–631 (2002).CrossRefGoogle Scholar
24.Park, J., Chung, W. and Youm, Y., “Weighted decomposition of kinematics and dynamics of kinematically redundant manipulators,” Proceedings of the IEEE Conference on Robotics and Automation, Minneapolis, MN (1996) pp. 480–486.Google Scholar
25.Park, J., Chung, W. and Youm, Y., “Characterization of instability of dynamic control for kinematically redundant manipulators,” Proceedings of the IEEE Conference on Robotics and Automation, Washington, DC (2002) pp. 2400–2405.Google Scholar
26.Simon, D., Kapellos, K. and Espiau, B., “Control laws, task and procedures with ORCCAD: Application to the control of an underwater arm,” Proceedings of the International Advanced Robotics Programme Workshop on Underwater Robotics, Toulon, France (1996) pp. 1027–1176.Google Scholar
27.Yoshikawa, T., Foundations of Robotics: Analysis and Control (MIT Press, Cambridge, MA, 1990).Google Scholar