J. M. Rendón–Mancha*¹, G. Sanahuja², P. Castillo², R. Lozano²

¹ Facultad de Ciencias, UAEM,Cuernavaca, México. *E–mail: rendon@uaem.mx

² Heudiasyc Laboratory, UMR CNRS 6599, Université de Technologie de Compiègne, Compiègne, France.

ABSTRACT

This paper presents a new hybrid control algorithm based on saturation functions and its real–time application to a ground vehicle. The hybrid control is developed from a nonlinear continuous control law and the objective is to obtain the optimal sampling period T to apply the controller in real experiences. The stability analysis was made in discrete time. The experimental platform is composed of a remote control toy car and a vision system. The vision system is built using a simple webcam and a diode laser. This system is fast, accurate, inexpensive and easy to implement. Simulations and experiments show the stability and robustness of the closed–loop system. The proposed control law performance is compared with a linear control algorithm.

Keywords: Nonlinear control, saturation functions, computer vision, experimental platform, laser.

RESUMEN

Este artículo presenta un nuevo algoritmo de control híbrido basado en funciones de saturación y su implementación en tiempo real en un vehículo terrestre. El control híbrido fue desarrollado a partir de una ley de control continua no lineal y el objetivo es obtener el período de muestreo óptimo T para aplicar el controlador en experimentos. La plataforma experimental se compone de un carro de juguete a control remoto y de un sistema de visión. El sistema de visión se construye usando una webcam y un diodo láser. El sistema es rápido, preciso, barato y fácil de implementar. Las simulaciones y los experimentos muestran la estabilidad y la robustez del sistema de lazo cerrado. Se realiza una comparación del desempeño de la ley de control propuesta con la de un algoritmo de control lineal.

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References

[I] H.J. Sussmann, E.D. Sontag and Y. Yang, A general result on the stabilization of linear systems using bounded controls, IEEE Transactions on Automatic Control, 93(12) pp. 2411–2425, 1994.         [ Links ]

[2] A. T. Fuller, In the large stability of relay and saturation control systems with linear controllers, International Journal of Control, 10 pp. 457–480, 1969.         [ Links ]

[3] A.R. Teel, Global stabilization and restricted tracking for multiple integrators with bounded controls, Systems and Control Letters, 1992.         [ Links ]

[4] E. N. Johnson and S. Kannan, Nested saturation with guaranteed real pole, American Control Conference, Brighton, pp. 497–502, 2003.         [ Links ]

[5] Y. Yang, E.D. Sontag, H.J. Sussmann, Global stabilization of linear discrete time systems with bounded feedback, Systems & Control Letters, 30, pp. 273–281, 1997.         [ Links ]

[6] N. Marchand and A. Hably, Global stabilization of multiple integrators with bounded controls, Automatica, 41(12), pp. 2147–2152, 2005.         [ Links ]

[7] Z. Lin and A. Saberi, Semi–global exponential stabilization of linear systems subject to input saturation via linear feedbacks, Systems & Control Letters, 21, pp.225–239, 1993.         [ Links ]

[8] Z. Lin and A. Saberi, Semi–global exponential stabilization of discrete–time systems subject to input saturation via linear feedbacks, Systems & Control Letters,24, pp. 125–132, 1995.         [ Links ]

[9] R. Lozano, J. Collado and A. Herrera, Semiglobal stabilization of continuous–time systems with bounded inputs, IEEE Transactions on Automatic Control, 44(12), pp 2318–2320, 1999.         [ Links ]

[10] J. Collado, R. Lozano, A. Ailon, Semi–global stabilization of discrete–time systems with bounded inputs using a periodic controller, Systems & Control Letters,36, pp. 267–275, 1999.         [ Links ]

[11] P. Castillo, R. Lozano & A. Dzul, Modelling and control of mini flying machines, Springer–Verlag, 2005. ISBN: 1–85233–957–8.         [ Links ]

[12] Josep Forest and Joaquim Salvi. A review of laser scanning three–dimensional digitisers. Proceedings of the IEEE/RDJ Intl. Conference on Intelligent Robots and Systems.EPFL, Laussanne, Switzerland. October 2002.         [ Links ]

[13] François Blais. Review of 20 years of range sensor development. Journal of Electronic Imaging. Vol. 13, No. 1, pp. 231–240. January 2004.         [ Links ]

[14] Thomas P. Koninckx and Luc Van Gool. Real–Time Range Acquisition by Adaptive Structured Light .IEEE. Transactions on Pattern Analysis and Machine Intelligence. Vol. 28, No. 3, March 2006.         [ Links ]

[15] David Acosta, Olmer García, Jorge Aponte, Laser Triangulation for Shape Acquisition in a 3D Scanner Plus Scan, Proceeding of the IEEE CERMA Electronics, Robotics and Automotive Mechanics Conference, Cuernavaca, México. pp. 14–19,2006.         [ Links ]

[16] Marco A. García Romero, Antonio Cárdenas Galindo, Juan M. Rendón and Emilio J. González Galván. A Camera Calibration Method Applied to Vision Based Control of a Manipulator Robot. IEEE Latin American Robotic Symposium– IX Congreso Mexicano de Robotica (4th IEEE LARS 07 – IX COMRob 07).         [ Links ]

[17] Danica Kragic and Henrik I Christensen.Survey on Visual Servoing for Manipulation.Research Report. Centre for Autonomous Systems, Numerical Analysis and Computer Science, Fiskartorpsv. 15 A. 100 44 Stockholm, Sweden. Jan. 2002. http://www.nada.kth.se/danik/VSpapers/report.pdf        [ Links ]

[18] Danica Kragic. Visual Servoing for Manipulation: Robustness and Integration Issues PhD. Thesis. CVAP–NADA, Royal Institute of Technology, Stockholm, Sweden. 2001. http://www.nada.kth.se/danik/thesis.pdf.gz        [ Links ]

[19] Djamel Khadraoui, Guy Motyl, Philippe Martinet, Jean Gallice, François Chaumette. Visual Servoing in Robotics Scheme using a Camera/Laser–Stripe Sensor. INRIA Rennes. Internal publication No. 898.IRISA.ISSN 1166–8687. January 1995.         [ Links ]

[20] A. C. Sanderson and L. E Weiss. Adaptive visual servo control of robots, In Pugh A. (editor). Robot Vision, I.F.S. Publications Ltd, pp. 107–116 1983.         [ Links ]

[21] Anand Sanchez, Pedro Castillo, Juan Antonio Escareño Castro, Hugo Romero, Rogelio Lozano. Simple Real–Time Control Strategy to Stabilize the PVTOL Air– craft Using Bounded Inputs, European Control Conference, ECC'07, Kos, Greece, July 2007.         [ Links ]

[22] Zhengyou Zhang, Flexible Camera Calibration By Viewing a Plane From Unknown Orientations, Microsoft Research, Redmond, WA 98052–6399, USA.         [ Links ]

[23] Richard Hartley and Andrew Zisserman. Multiple View Geometry in Computer Vision. Second Edition. Cambridge Press 2003.         [ Links ]

[24] Richard I. Hartley and Peter Sturm, Triangulation. Computer Vision and Image Understanding. Vol. 68, No. 2. November, pp. 146–157, 1997.         [ Links ]