Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-16T19:32:05.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Manipulating robots along helical trajectories

Published online by Cambridge University Press:  09 March 2009

J. M. Selig  and
A. I. Ovseevitch
J. M. Selig
Affiliation:
School of Elec. Electronic & Info. Eng. South Bank. University, 103 Borough Road. London SE1 OAA (U.K.).
A. I. Ovseevitch
Affiliation:
Institute for Problems in Mechanic, Prospect Vernadsgogo 101, Moscow (Russia).
Get access Rights & Permissions [Opens in a new window]

Summary

Current industrial robots are highly non-linear systems. However, the control strategies in most commercially available robots largely ignore the non-linearity. The resulting linear approximations are only valid at low speeds. Any improvement would allow robots to move faster and hence be more productive. There has been much academic research into robot control, but this has almost always separated the control and the trajectory planning. In this work we seek to combine these tasks and hence simplify the computations required. We investigate how to control a general robot in such a way that it's gripper follows straight line, circular or helical paths. These simple paths are both one parameter subgroups for the group of proper rigid motions and geodesies for certain metrics on the group. This suggests a non-linear feedback control law which turns the closed loop dynamics of the robot into the equations for geodesies. Although these equations are not completely stable we are able to modify the control law so that the resulting closed loop dynamics are stable. Hence, the end-effector of the robot will follow straight line, helical or circular trajectories.

Keywords

Helical trajectoriesRobot controlDifferent pathsNon-linear feedback
Type
Article
Information
Robotica , Volume 14 , Issue 3 , May 1996 , pp. 261 - 267
Copyright
Copyright © Cambridge University Press 1996

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.Samuel, A. E., McAree, P. R. & Hunt, K. H., “Unifying screw geometry and matrix transformations”, Int. J., Robotics Research 10(5), 454–472 (1991).CrossRefGoogle Scholar
2.Hunt, K. H., “Manipulating a body through a finite screw displacement.” Proceedings of the 7th World Congress,Seville(1987) volume 1, pp. 187–191.Google Scholar
3.Spong, M. W. and Vidyasagar, M., Robot Dynamics and Control (John Wiley and Sons, New York, 1989), section 7.6.1.Google Scholar
4.Hunt, K. H., Kinematic Geometry of Mechanisms Clarendon Press, Oxford (1978) Section 2.8.Google Scholar
5.Brockett, R. W., Robotic Manipulators and Products of Exponential Formula, volume 58 of Lecture Notes in Computer Science (Springer Verlag, New York, 1984)Google Scholar
Proceedings of conference held in Beer Sheva 1983; pp. 120–129.Google Scholar
6.Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces, volume 80 of Pure and Applied Mathematics (Academic Press, New York, 1978) Page 224.Google Scholar
7.Milnor, J., Morese Theory, volume 51 of Annals of Mathematics Studies, (Princeton University Press, New Jersey, 1969) Page 113.Google Scholar
8.Sternberg, S., Lectures on Differential Geometry (Prentice-Hall, New Jersey. 1964) Page 232.Google Scholar
9.Selig, J. M., “Robot dynamics using screw theory”. In: (Warwick, K., editor) Robotics: Mathematical and Computational Aspects (Institute of Mathematics and its Applications. 1993) pp. 293–307.Google Scholar
10.Paul, R. P., Robot Manipulators: Mathematics. Programming and Control (M.I.T. Press, Cambridge, Mass., 1981).Google Scholar
11.Schutz, B. F., Geometrical Methods of Mathematical Physics (Cambridge University Press, Cambridge, 1980).CrossRefGoogle Scholar
12.Cotsaftis, M. & Vibet, C., “A direct application of the decoupling method to euler-lagrange formalism.” Int. J. Robotics Research, 11(1), 64–74 (1992).CrossRefGoogle Scholar
13.Youcef-Toumi, K. & Kuo, A. T. Y., “High-speed trajectory control of a direct-drive manipulator.” IEEE Trans. Robotics and Automation, 9(1), 102–108 (1993).CrossRefGoogle Scholar