zbMATH — the first resource for mathematics

Analytical synthesis of regulators for nonlinear systems with a terminal state method on examples of motion control of a wheeled robot and a vessel. (English) Zbl 1437.93033
Summary: The paper is devoted to several examples of control algorithm development for two-wheeled double-track robot and low-tonnage vessel-catamaran with two Azipods that show practical aspects of the application of one nonlinear system control method – terminal state method. This method, developed by the authors of the present paper, belongs to the class of methods for inverse dynamics problem solving. Mathematical models of control objects in the form of normal systems of third-order nonlinear differential equations for the wheeled robot and seventh-order ones for the vessel are presented. Design formulas of the method in general form for terminal and stabilizing controls are shown. A routine of obtaining calculation expressions for control actions is shown. Results of computer simulation of bringing the robot to a given point in a given time, as well as bringing the vessel to a given course during a “strong” maneuver, are described.
93B50 Synthesis problems
Full Text: DOI
[1] Isidori, A., Nonlinear Control Systems, (1995), New York, NY, USA: Springer, New York, NY, USA · Zbl 0569.93034
[2] Wu, W., Lyapunov-based design procedures for a state-delay chemical process, Proceedings of the 14th World Congress of IFAC
[3] Batenko, A. P., Sistemy terminalnogo upravleniya, System terminal control, M.: Radio i svyaz, pp. 160, 1984 · Zbl 0547.93029
[4] Shushlyapin, E. A., Upravlenie nelinejnymi sistemami na osnove prognoza konechnogo sostoyaniya neupravlyaemogo dvizheniya, Control of nonlinear systems based on the forecast end-state unmanaged traffic, Sevastopol, SevNTU, pp. 282, 2012
[5] Pupkova, K. A.; Egupova, N. D., Metody klassicheskoj i sovremennoj teorii avtomaticheskogo upravleniya: Uchebnik v 5-ti tt.; T.5: Metody sovremennoj teorii avtomaticheskogo upravleniya [Methods of classical and modern automatic control theory, Methods of modern theory of automatic control]. Edited. Methods of modern theory of automatic control]. Edited, Methods of modern theory of automatic control, 5, 784, (2004), Izdatelstvo MGTU im. N.EH. Baumana
[6] Xu, T.; Liu, X.; Yang, X., A novel approach for ship trajectory online prediction using bp neural network algorithm, Advances in Information Sciences and Service Sciences, 4, 11, (2012)
[7] Sedova, N. A., The formation of linguistic variables for task navigation, Operation of Mar-itime transport, 72, 19-23, (2013), Novorossijsk: Gosudarstvennyj morskoj universitet im, Admirala F.F. Ushakova, Novorossijsk
[8] She, M.; Tian, L., A novel path control algorithm for networked underwater robot, Journal of Robotics, 2018, (2018)
[9] Shushlyapin, E. A.; Bezuglaya, A. E., Control of two-wheeled platform-the carrier of measur-ing instruments, Environmental control systems, 23, (2016), Sebastopol, California, Calif, USA: Institute of natural and technical systems, Sebastopol, California, Calif, USA
[10] Afonina, A. A.; Bezuglaya, A. E.; Shushlyapin, E. A.; Podolskaya, O. G., Control two-wheeled robot discrete finite state metod, Nauka i mir: Mezhdu-nar.nauchn.zhurnal, 4, 32, 28-36, (2016)
[11] Shushlyapin, E. A.; Karapet’yan, V. A.; Afonina, A. A.; Filler, I. Y., The problem of unmanned naviga-tion and the mathe-matical model of the research vessel Pioneer-M, Proceedings of the Robotics and artificial intelligence: materials of the VIII all-Russian scientific-technical conference with international participation, BIK SFU
[12] Sposob avtomaticheskogo upravleniya dvizheniem sudna [Method of automatic control of ship motion]: pat. 2465169 Russia: MPK V63N 25/04. M.H. Dorri, G.E. Ostretsov, A.A. Roshchin; Uchrezhdenie Ros-sijskoj akademii nauk Institut problem upravleniya im. V.A. Trapeznikova RAN. [Institution of Russian Academy of Sciences Institute of problems of management. V. A. Trapeznikov Academy of Sciences (Rus-sia)]. No. 2011115525/11; zayavl., Byul. No. 30. – 9p, 2012
[13] Ostretsov, G. E.; Klyach-ko, L. M.; Pamuhin, S. G., A method of controlling movement of a vessel along a predetermined path , (2011), Institution of Russian Academy of Sciences Institute of problems of management. V. A. Trapeznikov Academy of Sciences
[14] Aguiar, A. P.; Pascoal, A. M., Dynamic positioning and way-point tracking of underactuated AUVs in the presence of ocean currents, Proceedings of the 41st IEEE Conference on Decision and Control
[15] Zhao, Y.; Huang, H.; Zhuang, Y.; Huang, B.; Yao, Y., The heading control of POD-driven ship using adaptive integra-tor backstepping, Proceedings of the Proceed-ings of the 5th Interna-tional Conference on Electrical Engineering and Automatic Control, Springer Berlin Heidelberg
[16] Ayedi, D.; Boujelben, M.; Rekik, C., Hybrid type-2 fuzzy-sliding mode controller for navigation of mobile robot in an environment containing a dynamic target, Journal of Robotics, 2018, (2018)
[17] Witkowska, A.; Smierzchalski, R., Designing a ship course controller by applying the adaptive backstepping method, International Journal of Applied Mathematics and Computer Science, 22, 4, 985-997, (2012) · Zbl 1283.93156
[18] Sutulo, S.; Moreira, L.; Guedes Soares, C., Mathematical models for ship path prediction in manoeuvring simulation systems, Ocean Engineering, 29, 1, 1-19, (2001)
[19] Yoshimura, Y., Mathematical Model for Manoeuvring Ship Motion (MMG Model), Proceedings of the Workshop on Mathemati-cal Models for Operations involving Ship-Ship Interaction
[20] Alekseev, V. M., On one estimate pertur-bations of ordinary differential equations, Vestn. Moskov. un-ta. Ser.1. Matematika, mekhanika, 2, 28-36, (1961)
[21] Vojtkunskogo, Y. I., Handbook of ship theory: In three vol-umes, L.: Sudostroenie
[22] Vagushchenko, L. L.; Tsymbal, N. N., System of automatic control of ship motion, M.: TransLit, pp. 376, 2007
[23] Bhattacharyya, R., Dynamics of Marine Vehicles, (1978), John Wiley and Sons, Inc
[24] McCallum, I. R., A ship steering mathematical model for all manoeuvring regimes, AVIMAR, 21, (1985)
[25] Shushlyapin, E. A.; Karapetyan, V. A.; Bezuglaya, A. E.; Afonina, A. A., Nonlinear regulators for deduction of the vessel on the set trajectory at “strong” maneuvers, SPIIRAS Proceedings, 4, 53, 178-200, (2017)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.