Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T14:51:50.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Contribution to the modelling of impact with robotic systems

Published online by Cambridge University Press:  09 March 2009

Vojin Drenovac  and
Veljko Potkonjak
Get access Rights & Permissions [Opens in a new window]

Summary

This paper discusses the problem of impact with robotic systems. The original method for the solution of impact is presented. The main idea is the replacement of impact with a singularity and hence the approach is called the IVSA (Impact-Via-Singularity-Analysis) Method. This goal is achieved by considering the obstacle as a unilateral constraint and introducing the new set of generalized coordinates so as to incorporate the constraint in the dynamic model. Using the IVSA Method the impact is not described by algebraic equations but by a reduced set of differential equations resulting directly from the initial dynamic model. The integration of dynamic equations over the impact points is thus possible. A numerical example is presented.

Type
Research Article
Information
Robotica , Volume 11 , Issue 5 , September 1993 , pp. 445 - 452
Copyright
Copyright © Cambridge University Press 1993

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.Kirćanski, M., “Contribution to the Path-Planning of Redundant Robots Ph.D. Thesis (Faculty of Electrical Engineering, Belgrade, 1985).Google Scholar
2.Khatib, O., “Real-time obstacle avoidance for maniuulators and mobile robots” Int. J. Rob. Res. 5, No. 1, 245–253 (1986).CrossRefGoogle Scholar
3.Potkonjak, V. and Vukobratovic, M., “Dynamics of Manipulation Mechanisms with Constrained Gripper Motion” (Part I and Part II) J. Robotic Systems 3(3), 321–347 (1986).CrossRefGoogle Scholar
4.Potkonjak, V., “Application of Redundant Robots to Constrained-Motion Tasks” Robotica 10, part 1, 397–407 (1992).CrossRefGoogle Scholar
5.Vukobratović, M. and Potkonjak, V., Applied Dynamics and CAD of Manipulation Robots (Springer-Verlag, Berlin, 1985).CrossRefGoogle Scholar
6.Vukobratovic, M. and Potkonjak, V., Dynamics of Manipulation Robots (Springer-Verlag, Berlin, 1982).CrossRefGoogle Scholar
7.Paul, R., Robot Manipulators (MIT Press, Boston, Mass., 1981).Google Scholar
8.Schiehlen, W. and Kreuzer, E., “Generation of Equations of Motion of Multibody Systems Supported by a Computer” (in German) Ingenieur-Archiv 46, 185–194 (1977).Google Scholar
9.Tichonow, N.A., “System of Differential Equations Containing Small Parameters at Derivatives” Mat. sb. 31 (73), No. 3, 575–586 (1952).Google Scholar
10.Tichonow, N.A., “On the Dependence of the Solution of Differential Equations on Small Parameters” Mat. sb. 22 (64), No. 2, 193–204 (1948).Google Scholar
11.Tichonow, N.A., “On System of Differential Equations Containing Parameters” Mat. sb. 27 (69), No. 1, 147–156 (1950).Google Scholar
12.Schiehlen, O.W., “Nonlinear Oscillations in Multibody Systems” Proc. of the IXth ICNO, Kiev (1981) pp. 301–303.Google Scholar
13.Drenovac, V., “A Method for the Numerical Integration of Mechanical Systems with Unilateral Constraints” Math, and Computers in Simulation (North-Holland) 29, 413–420 (1987).CrossRefGoogle Scholar
14.Drenovac, V., “A Method for the Numerical Integration of Equations of Motion of Singular Multibody Systems (in German)“ Ph.D. Thesis, (University Stuttgart, 1985).Google Scholar
15.Arnold, I.V., Mathematical Methods in Classical Mechanics (Springer-Verlag, New York, 1978).CrossRefGoogle Scholar
16.Drenovac, V., “A Contribution to the Analysis of Impact in Multibody Systems” (in German) Z. Angew. Math. & Mech. 6, No. 5, 306–308 (1989).Google Scholar
17.Drenovac, V., “A Contribution to the Computation of Impact in Robotic Systems” (in German). Z. Angew. Math. & Mech. 73, No. 4 (to appear in 1993).Google Scholar