Optimization and evaluation of a proportional derivative controller for planar arm movement. Jagodnik, K. M. & van den Bogert, A. J. Journal of Biomechanics, 43(6):1086–1091, April, 2010.
doi  abstract   bibtex   
In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.
@article{jagodnik_optimization_2010,
	title = {Optimization and evaluation of a proportional derivative controller for planar arm movement},
	volume = {43},
	copyright = {All rights reserved},
	issn = {1873-2380},
	doi = {10.1016/j.jbiomech.2009.12.017},
	abstract = {In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.},
	language = {eng},
	number = {6},
	journal = {Journal of Biomechanics},
	author = {Jagodnik, Kathleen M. and van den Bogert, Antonie J.},
	month = apr,
	year = {2010},
	pmid = {20097345},
	pmcid = {PMC3853125},
	keywords = {Arm, Biomechanical Phenomena, Biomedical Engineering, Electric Stimulation Therapy, Feedback, Physiological, Humans, Models, Biological, Movement, Muscle Contraction, Muscle, Skeletal, Spinal Cord Injuries},
	pages = {1086--1091},
}
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