Volume 24 Issue 5 - Publication Date: 1 May 2005
Tool Center Trajectory Planning for Industrial Robot Manipulators Using Dynamical Systems
L.-P. Ellekilde and J.W. Perram Maersk Mc-Kinney Moller Institute for Production Technology, University of Southern Denmark, DK-5230 Odense M, Denmark
In this paper we generalize previous work in which the fixed points of dynamical systems were used to construct obstacle-avoiding, goalattracting trajectories for robots to more complex attractors such as limit cycles in the form of closed planar curves. Following the development of a formalism for dealing with a mechanical system, some of whose coordinates are constrained to follow the trajectories of a set of coupled differential equations, we discuss how to construct, analyze, and solve a planar dynamical system whose limit set is one or more user-specified closed curves or limit cycles. This work finds its relevance in a wide range of applications. Our focus has mainly been on planning tool trajectories for industrial robot manipulators with applications such as welding and painting. However, the generalization from fixed points to limit cycles is also applicable when controlling automatic guided vehicles.
Multimedia Key
= Video = Data = Code = Image
Example One: Double pendulum model of PA10 following a path made of a hippopede. (0.3 MB)
Example Two: The PA10 robot following the path from extension 1. (0.9 MB)

Example Three: Double pendulum model of PA10 following the path created in Section 3. (0.4 MB)

Example Four: Java applet with a number of predefined systems but with the possibility of freely selected initial positions. (0.9 MB)
Example Five: 12 car-like robots moving on simple continous curvature paths (before coordination). (29KB ZIP file)
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