Three dimensional statics for continuum robotics. Jones, B. A., Gray, R. L., & Turlapati, K. In 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 2659–2664, October, 2009.
doi  abstract   bibtex   
This paper introduces a method for computing the shape of a continuously-flexible (continuum) robot in 3-D space which includes gravity loading by applying Cosserat rod theory to a continuum robot. With this theory, the shape of the rod can be determined using force-torque balance equations obtained from a simple free body diagram that represents the continuum robot. Real-time performance of 125 Hz makes this approach viable for the control of a continuum robot, enabled by avoiding boundary-value conditions in the solution.
@inproceedings{jones_three_2009,
	title = {Three dimensional statics for continuum robotics},
	doi = {10.1109/IROS.2009.5354199},
	abstract = {This paper introduces a method for computing the shape of a continuously-flexible (continuum) robot in 3-D space which includes gravity loading by applying Cosserat rod theory to a continuum robot. With this theory, the shape of the rod can be determined using force-torque balance equations obtained from a simple free body diagram that represents the continuum robot. Real-time performance of 125 Hz makes this approach viable for the control of a continuum robot, enabled by avoiding boundary-value conditions in the solution.},
	booktitle = {2009 {IEEE}/{RSJ} {International} {Conference} on {Intelligent} {Robots} and {Systems}},
	author = {Jones, B. A. and Gray, R. L. and Turlapati, K.},
	month = oct,
	year = {2009},
	keywords = {3D statics, Continuum robotics, Cosserat rod theory, Gravity, Intelligent robots, Orbital robotics, Predictive models, Real time systems, Robot sensing systems, Robots, Tongue, USA Councils, boundary-value conditions, boundary-value problems, continuously-flexible robot, force control, force-torque balance equations, shape control, statics},
	pages = {2659--2664}
}

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