Geodesic
Path coordinates in 3D path following problem
Matematičeskoe modelirovanie, Tome 29 (2017) no. 10, pp. 5-19

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Two approaches to 3D path coordinates using in path following problem for aerial vehicles are proposed. The first one consists in reducing to two dimensional case by means of projection. The second one is based on introducing of an adapted frame in the target point. The choice of an adapted frame detects a complexity of the control synthesis algorithm. It is shown that the parallel transport frame, or Bishop frame, is most convenient.
Keywords: path following, path coordinates, adapted frame, stabilized control. 
@article{MM_2017_29_10_a1,
     author = {A.N. Kanatnikov and W. Liu and S. B. Tkachev},
     title = {Path coordinates in {3D} path following problem},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {5--19},
     publisher = {mathdoc},
     volume = {29},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_10_a1/}
}
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A.N. Kanatnikov; W. Liu; S. B. Tkachev. Path coordinates in 3D path following problem. Matematičeskoe modelirovanie, Tome 29 (2017) no. 10, pp. 5-19. http://geodesic.mathdoc.fr/item/MM_2017_29_10_a1/