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Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

Ravishankar, AS and Ghosal, Ashitava (1999) Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots. In: The International Journal of Robotics Research, 18 (1). pp. 93-108.

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Official URL: http://ijr.sagepub.com/content/18/1/93.abstract


The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Item Type: Journal Article
Publication: The International Journal of Robotics Research
Publisher: Sage Publications
Additional Information: Copyright of this article belongs to Sage Publications.
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 29 Jun 2011 06:16
Last Modified: 29 Jun 2011 06:16
URI: http://eprints.iisc.ac.in/id/eprint/38693

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