Control n MRI-powered actuators

Plots the position of n MRI rotors being controlled simultaneously to
desired positions by an MRI gradient field. The MRI gradient field is
defined by three (3) linear gradients in the x,y, and z axes. This
system is underactuated since 3 is much less than n. A Control Lyapunov
Function (CLF) is used to control the position of each rotor
independently.

The rotors are modeled after the real, single -DOF actuators reported
in
P. Vartholomeos, C. Bergeles, L. Qin, P. E. and Dupont, "An MRI-powered
and Controlled Actuator Technology for Tetherless Robotic
Interventions", Int. J. Robotics Research, vol. 32, no. 13, pp.
1536-1552, 2013.
a pdf is available at:
http://robotics.tch.harvard.edu/publications/pdfs/vartholomeos2013MRI.pdf

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Author: Aaron Becker
Boston Children's Hospital
Date: 10/18/2013
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Companion code for IROS 2014 paper submission (http://www.iros2014.org/), "Simultaneously Powering and Controlling Many Actuators With a Clinical MRI Scanner", by Aaron Becker, Ouajdi Felfoul, and Pierre Dupont