Julien Alexandre dit Sandretto and Milan Hladík. Solving over-constrained systems of non-linear interval equations - And its robotic application. Appl. Math. Comput., 313:180–195, 2017.
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This paper presents and describes in details an original method developed to solve over-constrained systems of non-linear interval equations that arise namely in parameter identification problems deriving from physical models and uncertain measurements. Our approach consists of computing an interval enclosure of the least square solution set and an inner box of tolerable solution set. This method is applied in a detailed example and some interesting results obtained for the calibration of a cable-driven robot are shown.
@article{SanHla2017a,
author = "dit Sandretto, Julien Alexandre and Milan Hlad\'{\i}k",
title = "Solving over-constrained systems of non-linear interval equations - {And} its robotic application",
journal = "Appl. Math. Comput.",
fjournal = "Applied Mathematics and Computation",
volume = "313",
pages = "180-195",
year = "2017",
doi = "10.1016/j.amc.2017.05.077",
issn = "0096-3003",
url = "http://www.sciencedirect.com/science/article/pii/S0096300317303892",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.amc.2017.05.077",
abstract = "This paper presents and describes in details an original method developed to solve over-constrained systems of non-linear interval equations that arise namely in parameter identification problems deriving from physical models and uncertain measurements. Our approach consists of computing an interval enclosure of the least square solution set and an inner box of tolerable solution set. This method is applied in a detailed example and some interesting results obtained for the calibration of a cable-driven robot are shown.",
keywords = "Interval analysis; Resolution; Over-constrained system; Least squares",
}
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