Article

Article title ROBUST MODALITY OF MOBILE ROBOT WITH PARAMETERS INTERVAL UNCERTAINTY AND TIME DELAY IN CONTROL CHANNEL
Authors I.A. Rybin, V.G. Rubanov
Section SECTION VI. MANAGEMENT SYSTEM
Month, Year 01-02, 2017 @en
Index UDC 681.5.037.2
DOI
Abstract Robust modality system for automatic mobile robot control with a fixed control device and object with interval uncertainty parameters, arising due to the change of its total mass, leading to a significant change in dynamics in the operation, is considered. This takes into account such feature as having a time-delay in the control channel associated with time spent on the survey sensors, computational procedures to form the manipulated controller in accordance with a control law, delays in the communication channel by remote control. On the basis of evidence sufficient criterion formulated robust modality as generalized dynamic properties of the system, including its sustainability and also reflects the quality of the transition process defined by the boundary of the dominant position of the roots in the complex plane of the roots. Well-known principle of zero exceptions puts in basis of the proof. The presence of the delay in the system leads to difficulties in determining the number of quadrants Mikhailov hodograph due to an infinite ascending phase introduced by the delay element. This difficulty is overcome by the use of auxiliary locus to determine the quadrant of its final position at the value of frequency equal to infinity. Formulated sufficient criterion for robust modality used to study the dynamics of a particular mobile robot in the management of its lateral movement. Analytical dependences for auxiliary locus Z(δ, ω) with a proportional and PID control laws, which allowed to build appropriate hodographs and illustrate the nature of the dynamics of change depending on the applied control law proposed by a sufficient criterion for robust modality system.

Download PDF

Keywords Mobile robot; mathematical model; control system; robustness; time-delay; quality control analysis; criterion of modality; Mikhailov hodograph.
References 1. Schulze L., Behling S., Buhrs S. Automated Guided Vehicle Systems: a Driver for Increased Business Performance, Proceedings of the International MultiConference of Engineers and Computer Scientists IMECS 2008, 19-21 March, 2008, Hong Kong, 2008, Vol. II, pp. 1275-1280.
2. Shneier M., Bostelman R. Literature Review of Mobile Robots for Manufacturing, National Institute of Standards and Technology (U.S.). Engineering Laboratory. Intelligent Systems Di-vision, May, 2015, 21 p.
3. Golovan Ju.V., Emel'janov V.K., Kozyr' T.V. Spasatel'naya tehnika i bazovye mashiny: Uchebnoe posobie [Rescue equipment and basic machine: Tutorial]. – Moscow: Izd-vo «Prospekt», 2015, 178 p.
4. Gates B. A Robot in Every Home, Scientific American, January 2007, pp. 58-65.
5. Martynenko Yu.G. Motion control of mobile wheeled robots, Journal of Mathematical Sciences, November 2007, Vol. 147, Issue 2, pp. 6569-6606.
6. Zolotuhin Ju.N., Kotov K.Ju., Mal'cev A.S., Nesterov A.A., Filippov M.N., Jan A.P. Korrektsiya transportnogo zapazdyvaniya v sisteme upravleniya mobil'nym robotom [Correction of a transport delay in mobile robot control system], Avtometriya [Autometry], 2011, Vol. 47, No 2, pp. 46-57.
7. Buzurovic I., Debeljkovic D. Lj., Misic V., Simeunovic G. Stability of the Robotic System with Time Delay in Open Kinematic Chain Configuration, Acta Polytechnica Hungarica, 2014, Vol. 11, No. 8, pp. 45-64.
8. Petersen I.R., Tempo R. Robust control of uncertain systems: Classical results and recent de-velopments, Automatica. Elsevier Ltd, 2014, Vol. 50, Issue 5, pp. 1315-1335.
9. Dzhuri E.I. Robastnost' diskretnykh sistem. Obzor [Robustness of discrete systems. Overview], Avtomatika i telemekhanika [Automation and Remote Control], 1990, No 5, pp. 3-28.
10. Kharitonov V.L. Robust stability analysis of time delay systems: A survey, Annual Reviews in Control. Elsevier Science Ltd, 1999, Vol. 23, pp. 185-196.
11. Cypkin Ja. Z., Poljak B. T. Robastnaya ustoychivost' lineynyh system [Robust stability of linear systems], Itogi nauki i tehniki. Tehnicheskaya kibernetika [The results of science and tech-nology. Technical cybernetics]. Moscow: VINITI, 1991, Vol. 32, pp. 3-13.
12. Kharitonov V.L. Asimptoticheskaya ustoychivost' semeystva sistem lineynykh differencial'nykh uravneniy [Asymptotic stability of a systems family of linear differential equations], Differentsial’nye uravneniya [Differential equations], 1978, Vol. 14, No 11, pp. 2086-2088.
13. Barmish В.R., Shi Z. Robust stability of perturbed systems with time delays, Automatica, 1989, Vol. 25, No. 3, pp. 371-381.
14. Polyak B.T., Tsypkin Ja.Z. Chastotnye kriterii robastnoy ustoychivosti i aperiodichnosti lineynyh system [Frequency criteria for robust stability and aperiodicity of linear systems]m Avtomatika i telemekhanika [Automation and Remote Control], 1990, No 9, pp. 45-54.
15. Podlesnyj V.N., Rubanov V.G. Prostoy chastotnyy kriteriy robastnoy ustoychivosti odnogo klassa lineynykh interval'nykh dinamicheskikh sistem s zapazdyvaniem [Simple frequency cri-terion for robust stability of a class of linear interval dynamic systems with time-delay], Avtomatika i telemekhanika [Automation and Remote Control], 1996, No 9, pp. 131-139.
16. Zotov M.G. O chastotnyh kriteriyah ustoychivosti [About frequency stability criterions], Avtomatizatsiya. Sovremennye tekhnologii [Automation. Modern technologies], 2016, No. 2, pp. 25-28.
17. Mamatov A.V., Podlesnyy V.N., Rubanov V.G. Obobshchennyy kriteriy robastnoy modal'nosti lineynykh sistem s ellepticheskoy neopredelennost'yu parametrov [The generalized criteria of robust modality of linear systems with ellipticheskoi uncertainty of parameters], Avtomatika i telemekhanika [Automation and Remote Control], 1999, No. 2, pp. 83-94.
18. Ullrich G. Automated Guided Vehicle Systems. A Primer with Practical Applications. Berlin: Springer, 2015, 227 p.
19. Rubanov V.G., Kizhuk A.S. Mobil'nye mikroprocessornye sistemy avtomatizatsii transportno-skladskikh operatsiy. Mobil'nye robototehnicheskie sistemy: monografiya [Mobile micropro-cessor systems of automation of transport and warehousing operations. Mobile robotic systems: monograph]. Belgorod: BGTU n.a. V.G. Shukhov, 2011, 289 p.
20. Gryazina E.M., Poljak B.T., Tremba A.A. Sintez regulyatorov nizkogo poryadka po kriteriyu H∞: parametricheskiy podkhod [Synthesis of low order regulators by criterion H∞: parametric approach], Avtomatika i telemekhanika [Automation and Remote Control], 2007, No. 3, pp. 93-105.

Comments are closed.