ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

Chaos in Robot Control Equations

Lankalapalli, Shrinivas and Ghosal, Ashitava (1997) Chaos in Robot Control Equations. In: International Journal of Bifurcation and Chaos, 7 (3). pp. 707-720.

Full text not available from this repository. (Request a copy)


The motion of a feedback controlled robot can be described by a set of nonlinear ordinary differential equations. In this paper, we examine the system of two second-order, nonlinear ordinary differential equations which model a simple two-degree-of-freedom planar robot, undergoing repetitive motion in a plane in the absence of gravity, and under two well-known robot controllers, namely a proportional and derivative controller and a model-based controller. We show that these differential equations exhibit chaotic behavior for certain ranges of the proportional and derivative gains of the controller and for certain values of a parameter which quantifies the mismatch between the model and the actual robot. The system of nonlinear equations are non-autonomous and the phase space is four-dimensional. hence, it is difficult to obtain significant analytical results. In this paper, we use the Lyapunov exponent to test for chaos and present numerically obtained chaos maps giving ranges of gains and mismatch parameters which result in chaotic motions. We also present plots of the chaotic attractor and bifurcation diagrams for certain values of the gains and mismatch parameters. From the bifurcation diagrams, it appears that the route to chaos is through period doubling

Item Type: Journal Article
Publication: International Journal of Bifurcation and Chaos
Publisher: World Scientific
Additional Information: Copyright of this article belongs to World Scientific.
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 09 Mar 2007
Last Modified: 27 Aug 2008 12:35
URI: http://eprints.iisc.ac.in/id/eprint/9655

Actions (login required)

View Item View Item