Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations. (January 2014)

• Record Type: Journal Article
• Authors: Bretl, Timothy; McCarthy, Zoe
• Is Part Of: International journal of robotics research. Volume 33:Number 1(2014:Jan.)
• Page Start: 48
• Page End: 68
• Publication Date: 2014-01
• Subjects: Manipulation planning -- manipulation -- path planning for manipulators -- manipulation -- mechanics -- design and control; Robots -- Periodicals; Robots, Industrial -- Periodicals; 629.89205
• DOI: 10.1177/0278364912473169
• Languages: English
• ISSNs: 0278-3649

Abstract

Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. Any curve traced by this wire when in static equilibrium is a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. We prove that the set of all local solutions to this problem over all possible boundary conditions is a smooth manifold of finite dimension that can be parameterized by a single chart. We show that this chart makes it easy to implement a sampling-based algorithm for quasi-static manipulation planning. We characterize the performance of such an algorithm with experiments in simulation.