@ARTICLE{Duleba_Ignacy_Sub-optimal_2023,
 author={Duleba, Ignacy and Karcz-Duleba, Iwona},
 volume={71},
 number={3},
 journal={Bulletin of the Polish Academy of Sciences Technical Sciences},
 pages={e145684},
 howpublished={online},
 year={2023},
 abstract={In this paper three algorithms of motion planning for two-input, one-chained nonholonomic systems are presented. The classical Murray-Sastry algorithm is compared with two original algorithms aimed at optimizing energy of controls. Based on the generalized Campbell- Baker-Hausdorff-Dynkin formula applied to the systems, some observations are made concerning the optimal relationship between amplitudes and phases of harmonic controls. The observations help to optimize a selection of controls and to design new algorithms for planning a sub- optimal trajectory between given boundary configurations. It was also shown that for those particular systems the generalized C-B-H-D formula is valid not only locally (as in a typical case) but also globally. Simulations performed on the five-dimensional chain system facilitate distinguishing the proposed algorithms from the Murray-Sastry algorithm and to illustrate their features. Systems in a chained form are important from a practical point of view as they are canonical for a class of systems transformable into this form. The most prominent among them are mobile robots with or without trailers.},
 type={Article},
 title={Sub-optimal motion planning of one-chained, two-input nonholonomic systems},
 URL={http://www.czasopisma.pan.pl/Content/127001/PDF/BPASTS-03491-EA.pdf},
 doi={10.24425/bpasts.2023.145684},
 keywords={nonholonomic systems, chained form, optimization, algorithm, Lie algebraic method},
}