Path planning for minimal energy curves of constant length
Moll, M.; Kavraki, L.E.
Robotics and Automation, 2004. Proceedings. ICRA apos;04. 2004 IEEE International Conference on
Volume 3, Issue , 26 April-1 May 2004 Page(s): 2826 - 2831 Vol.3
Digital Object Identifier   10.1109/ROBOT.2004.1307489
Summary: In this paper we present a new path planning technique for a flexible wire. We first introduce a new parametrization designed to represent low-energy configurations. Based on this parametrization we can find curves that satisfy endpoint constraints. Next, we present three different techniques for minimizing energy within the self-motion manifold of the curve. We introduce a local planner to find smooth minimal energy deformations for these curves that can be used by a general path planning algorithm. Using a simplified model for obstacles, we can find minimal energy curves of fixed length that pass through specified tangents at given control points. Finally, we show that the parametrization introduced in this paper is a good approximation of true minimal energy curves. Our work has applications in surgical suturing and snake-like robots.

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