The planning of the trajectory of uav group with the performance of pythagorean hodograph and bernstein-bezier composite curves in the plane
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 70-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this article, the method of trajectory building of motion of unmanned aerial vehicles group by approximation of Pythagorean Hodograph and Bernstein-Bezier composite polynomials has been presented.
Keywords: unmanned aerial vehicles
Mots-clés : Bernstein-Bezier polynomial, Pythagorean Hodograph.
@article{VKAM_2020_31_2_a4,
     author = {D. L. Vinokursky and K. Yu. Ganshin and O. S. Mezentseva and Ph. V. Samoylov},
     title = {The planning of the trajectory of uav group with the performance of pythagorean hodograph and bernstein-bezier composite curves in the plane},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {70--78},
     year = {2020},
     volume = {31},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a4/}
}
TY  - JOUR
AU  - D. L. Vinokursky
AU  - K. Yu. Ganshin
AU  - O. S. Mezentseva
AU  - Ph. V. Samoylov
TI  - The planning of the trajectory of uav group with the performance of pythagorean hodograph and bernstein-bezier composite curves in the plane
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2020
SP  - 70
EP  - 78
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a4/
LA  - ru
ID  - VKAM_2020_31_2_a4
ER  - 
%0 Journal Article
%A D. L. Vinokursky
%A K. Yu. Ganshin
%A O. S. Mezentseva
%A Ph. V. Samoylov
%T The planning of the trajectory of uav group with the performance of pythagorean hodograph and bernstein-bezier composite curves in the plane
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2020
%P 70-78
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a4/
%G ru
%F VKAM_2020_31_2_a4
D. L. Vinokursky; K. Yu. Ganshin; O. S. Mezentseva; Ph. V. Samoylov. The planning of the trajectory of uav group with the performance of pythagorean hodograph and bernstein-bezier composite curves in the plane. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 70-78. http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a4/

[1] Kolushev A., Bodanov A., “Multiple-Agent Optimal Path Planning for Mobile Robot in Environment with Obstacles”, Proceedings of the third international Andrei Ershov memorial conference on Perspective System Informatics, 1999, 503-510

[2] Tarapata Z., “Military Route Planning in Battle Field Simulation, Effectiveness Problem and Potential Solution”, Proceeding of 4th WSEAS international conference on Computer Engineering and Application CEA 10., 2003, 47-56

[3] Hart P., Nilsson N., “A Formal Basis for the Heuristic Determination of Minimum Cost Paths”, Syst Sci Cybern, 2 (1968), 100-107 | DOI

[4] Yang D., Hong S., “Road Map Construction Algorithm for Mobile Robot Path Planning using Skeleton Map”, Advance Robotic, 21 (2007), 51-63 | DOI

[5] Tokuta A., “Extending the Visibility Graph Algorithm for Robot Path Planning”, Technical Report Department of Mathematics and Computer Science

[6] Santos R., Steffen V., “Robot Path Planning in Constrained Work Space using Optimal Control Techniques”, Multibody System Dynamics, 2006, 159-177

[7] Constantinescu D., Croft E., “Robot Smooth and Time Optimal Trajectory Planning for Industrial Manipulators along Specified Paths”, J. Robotics syst., 17 (2000), 223-249

[8] Vukdbralovic M., Kircanski M., “One Method for simplified Manipulator Model Construction and its Application in Quazioptimal Trajectory Synthesis”, Mechanism and Machine Theory, 17 (1982), 369-378 | DOI

[9] Pfeifer F., Johanni A., “Concept for Manipulator Trajectory Planning. IEEE Trans”, IEEE Trans Robotic Automat 3(3), 1987, 115-123 | DOI

[10] Singh S., Leu C., “Optimal Trajectory Generation for Robot Manipulators Using Dynamic Programming”, J. Dyn. Sys. Meas Control 109 (2), 1987, 88-96 | DOI

[11] Lee M., Takagi H., “Integrating Design Stages of Fuzzy Systems Using Genetic Algortithms”, Proc. 2nd IEEE Int. Conf. Fuzzy Systems, San Francisco, 1993, 612-617 | DOI

[12] Belarbi K., Titel F., “Genetic algorithm for the design of a class of fuzzy controllers: An alternative approach”, IEEE Transactions on Fuzzy Systems, 8 (2000), 398-405 | DOI | MR

[13] Goldberg D., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing Co., Inc.75 Arlington Street, Suite 300 Boston, MAUnited States, 1989, 372 pp.

[14] Whitley D., “A Genetic Algorithm Tutorial”, Technical Report CS-93-103, Colorado State University, 1994, 65-85

[15] Subchan S., White B. et al., “Pythagorean Hodograph (PH) path planning for tracking airborne contaminant using sensor swarm.”, Instrumentation and Measurement Technology Conference Proceeding 2008, IMTC 2008, 2008, 501-506 | DOI

[16] Armando A., Campos F., “A Path Planning Algorithm for UAVs with Limited Climb Angle”, The 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems October 11-15, 2009 St. Louis, US, 2009

[17] Farouki R., Sakkalis T., “Pythagorean hodographs”, IBM Journal of Research and Development, 1990, no. 5, 736-752 | DOI | MR

[18] Farouki R., Neff C., “Hermite interpolation by Pythagorean hodograph quintics”, Mathematics of Computation, 1995, 1589-1609 | DOI | MR

[19] Moon H., Farouki C. et al., “Construction and shape analysis of PH quintic Hermite interpolants”, Comput. Aided Geom. Design., 2001, no. 2, 93-115 | DOI | MR

[20] Farouki R., “The elastic bending energy of Pythagorean hodograph curves”, Comput. Aided Geom. Design., 1996, no. 2, 227-241 | DOI | MR

[21] Grigor'ev M., Malozemov V., “Polinomy Bernshteyna i sostavnye krivykh Bez'e.”, Zh. vychisl. matem. i matem. fiz., 2006, 1962–1971

[22] Kozak J., Knez M. et al., “On interpolation by planar cubic G2 Pythagorean-hodograph spline curves”, Mathematics of Computation, 2010, 305–326 | MR

[23] Singh I., Achille M. et al., “Modeling of Continuum Manipulators Using Pythagorean Hodograph Curves”, Soft Robotics, 2018

[24] Dhulkefl E., Durdu A. et al., “Path Planning Algorithms for Unmanned Aerial Vehicles”, International Journal of Trend in Scientific Research and Development, 3:4 (2019), 359–362 | DOI

[25] Wang X., Meng X. et al., “UAV Online Path Planning Based on Improved Genetic Algorithm”, 2019 Chinese Control Conference (CCC), Guangzhou, 2019, 4101-4106 | DOI

[26] Wu C., Chiu Z. et al., “Time-Optimal Trajectory Planning along Parametric Polynomial Lane-Change Curves with Bounded Velocity and Acceleration: Simulations for a Unicycle Based on Numerical Integration”, Modelling and Simulation in Engineering, 2018, 1-19

[27] Ma J., Liu Y. et al., “Robot Path Planning Based on Genetic Algorithm Fused with Continuous Bezier Optimization”, Comput Intell Neurosci, 2020, 1-10 | DOI