The digital control system of mobile robots (MR) control is considered. It is shown that sequential interpretation of control algorithm operators, unfolding in physical time, suggests the occurrence of time delays between inputting data from sensors and outputting data to actuators. Another destabilizing control factor is presence of backlash in the joints of an actuator with an executive unit. Complex model of control system, which takes into account the dynamics of the MR, the dynamics of the digital controller and backlash in actuators, is worked out. The digital controller model is divided into two parts: the first part describes the control law embedded in the controller in the form of a control program that realizes a polling procedure when organizing transactions to sensors and actuators. The second part of the model describes the time delays that occur in the Von Neumann-type controller when processing data. To estimate time intervals, the algorithm is represented in the form of an ergodic semi-Markov process. For an ergodic semi-Markov process of common form, a method is proposed for estimation a wandering time from one arbitrary state to another arbitrary state. Example shows how the backlash and time delays affect the quality characteristics of the MR control system functioning.
[1] Tzafestas S.G. Introduction to Mobile Robot Control. Elsevier, 2014. 692 Pp.
[2] Kahar S., Sulaiman, R., Prabuwono, A.S., Akma N. Ahmad S.A., Abu Hassan M.A. A Review of Wireless Technology Usage for Mobile Robot Controller // 2012 International Conference on System Engineering and Modeling (ICSEM 2012). International Proceedings of Computer Science and Information Technology IPCSIT. Vol. 34. Pp. 7 - 12.
[3] Cook G. Mobile robots: Navigation, Control and Remote Sensing. Wiley-IEEE Press, 2011. 319 Pp.
[4] Siciliano B. Springer Handbook of Robotics. Springer-Verlag Berlin Heidelberg. 2008. 1611 Pp.
[5] Landau I.D., Zito G. Digital Control Systems, Design, Identification and Implementation. Springer, 2006. 484 p.
[6] Aström J., Wittenmark B. Computer Controlled Systems: Theory and Design. Tsinghua University Press. Prentice Hall, 2002. 557 p.
[7] Larkin E.V., Ivutin A.N., Kotov V.V., Privalov A.N. Semi-Markov Modeling of Command Execution by Mobile robots // Interactive Collaborative Robotics (ICR 2016) Budapest, Hungary, Lecture Notes in Artificial Intelligence. Subseries of Lecture notes in Computer Science. Springer, 2016. Pp. 189 - 198.
[8] Wu R., Fan D., Iu H.H.-C., Fernando T. Adaptive fuzzy dynamic surface control for uncertain discrete-time non-linear pure-feedback mimo systems with network-induced time-delay based on state observer // International Journal of Control. 2019. Vol. 92. N. 7. Pp. 1707 - 1719.
[9] Li D., Chen G. Impulses-induced p-exponential input-to-state stability for a class of stochastic delayed partial differential equations // International Journal of Control. 2019. Vol.: 92, N.: 8, Pp. 1805 - 1814.
[10] Wu M., He Y., She J.H., Liu G.P., Delay-dependent criteria for robust stability of time-varying delay systems // Automatica, 2004. Vol. 40, N. 8. Pp. 1435 – 1439,
[11] Limnios N., Swishchuk A. Discrete-Time Semi-Markov Random Evolutions and their Applications // Adv. in Appl. Probab. 2013. V. 45, N. 1. Pp. 214 – 240.
[12] Bielecki T.R., Jakubowski J., Niewęgłowski M. Conditional Markov chains: Properties, construction and structured dependence // Stochastic Processes and their Applications. 2017. V. 127, N. 4. Pp. 1125–1170.
[13] Janssen J., Manca R. Applied Semi-Markov processes. Springer US, 2005. 310 Pp.
[14] Arnold K. A. Timing analysis in embedded systems // In Embedded hardware by J. Ganssler, K. Arnold et all. MA. 01803 USA. Elsevier Inc. 2008. Pp. 239 - 272.
[15] Fadali M.S., Visioli A. Digital control engineering: Analysis and design. - Elsevier Inc. 2013. Pp. 239 - 272.
[16] Pavlov A.V. About the equality of the transform of Laplace to the transform of Fourier // Issues of Analysis. 2016. Vol.5(23). N.4(76). Pp. 21 - 30.
[17] Li J., Farquharson C.G., Hu X. Three effective inverse Laplace transform algorithms for computing time -domain electromagnetic responses // Geophysics. 2015. Vol. 81. N. 2. Pp. E75 - E90.
[18] Yeh Y.-C., Chu Y., Chiou C.W. Improving the sampling resolution of periodic signals by using controlled sampling interval method // Computers & Electrical Engineering, 2014. Vol. 40. N. 4. Pp. 1064 - 1071.
[19] Pospiŝil M. Representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via Z-transform // Applied mathematics and computation. 2017. V. 294. Pp. 180 - 194.
[20] Larkin E.V. Bogomolov A.V.; Privalov, A.N. A Method for Estimating the Time Intervals between Transactions in Speech-Compression Algorithms // Automatic Documentation and Mathematical Linguistics. 2017. Vol: 51. Iss. 5. Pp.: 214 - 219.
[21] Kobayashi H., Marl B.L., Turin W. Probability, Random processes and statistical analysis: Cambridge University Press. 2012. 812 p.
[22] Pukelsheim F. The Three sigma Rule // American statistician. 1994. Vol. 48. Iss. 2. Pp. 88 - 91.
[1] Tzafestas S.G. Introduction to Mobile Robot Control. Elsevier, 2014. 692 Pp.
[2] Kahar S., Sulaiman, R., Prabuwono, A.S., Akma N. Ahmad S.A., Abu Hassan M.A. A Review of Wireless Technology Usage for Mobile Robot Controller // 2012 International Conference on System Engineering and Modeling (ICSEM 2012). International Proceedings of Computer Science and Information Technology IPCSIT. Vol. 34. Pp. 7 - 12.
[3] Cook G. Mobile robots: Navigation, Control and Remote Sensing. Wiley-IEEE Press, 2011. 319 Pp.
[4] Siciliano B. Springer Handbook of Robotics. Springer-Verlag Berlin Heidelberg. 2008. 1611 Pp.
[5] Landau I.D., Zito G. Digital Control Systems, Design, Identification and Implementation. Springer, 2006. 484 p.
[6] Aström J., Wittenmark B. Computer Controlled Systems: Theory and Design. Tsinghua University Press. Prentice Hall, 2002. 557 p.
[7] Larkin E.V., Ivutin A.N., Kotov V.V., Privalov A.N. Semi-Markov Modeling of Command Execution by Mobile robots // Interactive Collaborative Robotics (ICR 2016) Budapest, Hungary, Lecture Notes in Artificial Intelligence. Subseries of Lecture notes in Computer Science. Springer, 2016. Pp. 189 - 198.
[8] Wu R., Fan D., Iu H.H.-C., Fernando T. Adaptive fuzzy dynamic surface control for uncertain discrete-time non-linear pure-feedback mimo systems with network-induced time-delay based on state observer // International Journal of Control. 2019. Vol. 92. N. 7. Pp. 1707 - 1719.
[9] Li D., Chen G. Impulses-induced p-exponential input-to-state stability for a class of stochastic delayed partial differential equations // International Journal of Control. 2019. Vol.: 92, N.: 8, Pp. 1805 - 1814.
[10] Wu M., He Y., She J.H., Liu G.P., Delay-dependent criteria for robust stability of time-varying delay systems // Automatica, 2004. Vol. 40, N. 8. Pp. 1435 – 1439,
[11] Limnios N., Swishchuk A. Discrete-Time Semi-Markov Random Evolutions and their Applications // Adv. in Appl. Probab. 2013. V. 45, N. 1. Pp. 214 – 240.
[12] Bielecki T.R., Jakubowski J., Niewęgłowski M. Conditional Markov chains: Properties, construction and structured dependence // Stochastic Processes and their Applications. 2017. V. 127, N. 4. Pp. 1125–1170.
[13] Janssen J., Manca R. Applied Semi-Markov processes. Springer US, 2005. 310 Pp.
[14] Arnold K. A. Timing analysis in embedded systems // In Embedded hardware by J. Ganssler, K. Arnold et all. MA. 01803 USA. Elsevier Inc. 2008. Pp. 239 - 272.
[15] Fadali M.S., Visioli A. Digital control engineering: Analysis and design. - Elsevier Inc. 2013. Pp. 239 - 272.
[16] Pavlov A.V. About the equality of the transform of Laplace to the transform of Fourier // Issues of Analysis. 2016. Vol.5(23). N.4(76). Pp. 21 - 30.
[17] Li J., Farquharson C.G., Hu X. Three effective inverse Laplace transform algorithms for computing time -domain electromagnetic responses // Geophysics. 2015. Vol. 81. N. 2. Pp. E75 - E90.
[18] Yeh Y.-C., Chu Y., Chiou C.W. Improving the sampling resolution of periodic signals by using controlled sampling interval method // Computers & Electrical Engineering, 2014. Vol. 40. N. 4. Pp. 1064 - 1071.
[19] Pospiŝil M. Representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via Z-transform // Applied mathematics and computation. 2017. V. 294. Pp. 180 - 194.
[20] Larkin E.V. Bogomolov A.V.; Privalov, A.N. A Method for Estimating the Time Intervals between Transactions in Speech-Compression Algorithms // Automatic Documentation and Mathematical Linguistics. 2017. Vol: 51. Iss. 5. Pp.: 214 - 219.
[21] Kobayashi H., Marl B.L., Turin W. Probability, Random processes and statistical analysis: Cambridge University Press. 2012. 812 p.
[22] Pukelsheim F. The Three sigma Rule // American statistician. 1994. Vol. 48. Iss. 2. Pp. 88 - 91.
@article{"International Journal of Electrical, Electronic and Communication Sciences:80796", author = "E. V. Larkin and T. A. Akimenko and A. V. Bogomolov and A. N. Privalov", title = "Mobile Robot Control by Von Neumann Computer", abstract = "The digital control system of mobile robots (MR) control is considered. It is shown that sequential interpretation of control algorithm operators, unfolding in physical time, suggests the occurrence of time delays between inputting data from sensors and outputting data to actuators. Another destabilizing control factor is presence of backlash in the joints of an actuator with an executive unit. Complex model of control system, which takes into account the dynamics of the MR, the dynamics of the digital controller and backlash in actuators, is worked out. The digital controller model is divided into two parts: the first part describes the control law embedded in the controller in the form of a control program that realizes a polling procedure when organizing transactions to sensors and actuators. The second part of the model describes the time delays that occur in the Von Neumann-type controller when processing data. To estimate time intervals, the algorithm is represented in the form of an ergodic semi-Markov process. For an ergodic semi-Markov process of common form, a method is proposed for estimation a wandering time from one arbitrary state to another arbitrary state. Example shows how the backlash and time delays affect the quality characteristics of the MR control system functioning. ", keywords = "Mobile robot, backlash, control algorithm, Von Neumann controller, semi-Markov process, time delay.", volume = "16", number = "5", pages = "64-5", }
