Abstract
This chapter presents an application of advanced control techniques to the design of a multicriteria image-based controller for robotics application. The problem of positioning a 3 degrees of freedom (DOF) camera with respect to a mobile visual target with unknown square integrable velocity is considered. The proposed controller allows to stabilize the camera and determine the associated region of stability in spite of unknown values of the target points depth, bounds on admissible visual features errors to guarantee visibility, and limits on the camera velocity and acceleration. The description of the closed-loop system is based on a mixed polytopic and norm-bounded representation of uncertainties combined with an original sector condition. With this representation, the unknown target velocity is considered as a disturbance limited in energy and linear matrix inequality (LMI)-based optimization schemes are used to compute the feedback gain that leads to the maximization of the size of the region of stability associated to the closed-loop system. Two applications of the method are studied and simulated by considering a model of car-like robot equipped with proximity sensors and supporting a camera mounted on a plan-platform. The interest of the control approach for linking dynamically a sequence of sensor-based navigation tasks for a mobile robot is illustrated.
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References
Bellot, D., Danès, P.: Handling visual servoing schemes through rational systems and LMIs. In: IEEE Conference on Decision and Control (2001)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
Castelan, E.B., Tarbouriech, S., Gomes da Silva Jr., J.M., Queinnec, I.: \(\mathcal{L}_2\)-stabilization of continuous-time systems with saturating actuators. International Journal of Robust and Nonlinear Control 16, 935–944 (2006)
Chaumette, F., Hutchinson, S.: Visual servo control part II: Advanced approaches. IEEE Robotics and Automation Magazine 14(1), 109–118 (2007)
Chesi, G.: Visual servoing path-planning via homogeneous forms and LMI optimizations. IEEE Transactions on Robotics 25(2), 281–291 (2009)
Chesi, G., Hashimoto, K., Prattichizzo, D., Vicino, A.: Keeping features in the field of view in eye-in-hand visual servoing: a switching approach. IEEE Transactions on Robotics 20(5), 908–913 (2004)
Chesi, G., Vicino, A.: Visual servoing for large camera displacements. IEEE Transactions on Robotics 20(4), 724–735 (2004)
Coutinho, D.F., Gomes da Silva Jr., J.M.: Estimating the region of attraction of nonlinear control systems with saturating actuators. In: American Control Conference (2007)
Cuvillon, L., Laroche, E., Gangloff, J., de Mathelin, M.: GPC versus H1 control for fast visual servoing of medical manipulator including exibilities. In: IEEE Conference on Decision and Control (2005)
Espiau, B., Chaumette, F., Rives, P.: A new approach to visual servoing in robotics. IEEE Transactions on Robotics and Automation 8(3), 313–326 (1992)
Gao, B.: Contribution to multicriteria 2d image-based controller design (in french). Ph.D. thesis, University Paul Sabatier (2006), http://tel.archives-ouvertes.fr/tel-00119789
Gomes da Silva Jr., J.M., Tarbouriech, S.: Anti-windup design with guaranteed regions of stability: an LMI-based approach. IEEE Transactions on Automatic Control 50(1), 106–111 (2005)
Hadj-Abdelkader, H., Mezouar, Y., Martinet, P., Chaumette, F.: Catadioptric visual servoing from 3d straight lines. IEEE Transactions on Robotics 24(3), 652–665 (2008)
Malis, E., Rives, P.: Robustness of image-based visual servoing with respect to depth distribution errors. In: IEEE International Conference on Robotics and Automation (2003)
Marchand, E., Chaumette, F.: Feature tracking for visual servoing purposes. In: Robotics and Autonomous Systems (2005)
Mezouar, Y., Chaumette, F.: Path planning for robust image-based control. IEEE Transactions on Robotics and Automation 18(4), 534–549 (2002)
Petersen, I.R.: A stabilisation algorithm for a class of uncertain linear systems. Systems and Control Letters 8(4), 351–356 (1987)
Pissard-Gibollet, R., Rives, P.: Applying visual servoing techniques to control a mobile hand-eye system. In: IEEE International Conference on Robotics and Automation (1995)
Souères, P., Cadenat, V., Djeddou, M.: Dynamical sequence of multi-sensor based task for mobile robots navigation. In: IFAC Symposium on Robot Control (2003)
Tarbouriech, S., Prieur, C., Gomes da Silva Jr., J.M.: Stability analysis and stabilization of systems presenting nested saturations. IEEE Transactions on Automatic Control 51(8), 1364–1371 (2006)
Tarbouriech, S., Souères, P.: Advanced control strategies for the visual servoing scheme. In: IFAC Symposium on Robot Control (2000)
Tarbouriech, S., Souères, P., Gao, B.: A multicriteria image-based controller based on a mixed polytopic and norm-bounded representation. In: Joint IEEE Conference on Decision and Control and European Control Conference, CDC-ECC (2005)
Valmorbida, G., Tarbouriech, S., Garcia, G.: State feedback design for input-saturating nonlinear quadratic systems. In: American Control Conference (2009)
Zachi, A.R.L., Hsu, L., Lizarralde, F.: Performing stable 2D adaptive visual positionning/tracking control without explicit depth measurement. In: IEEE International Conference on Robotics and Automation (2004)
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Tarbouriech, S., Souères, P. (2010). Image-based Visual Servo Control Design with Multi-Constraint Satisfaction. In: Chesi, G., Hashimoto, K. (eds) Visual Servoing via Advanced Numerical Methods. Lecture Notes in Control and Information Sciences, vol 401. Springer, London. https://doi.org/10.1007/978-1-84996-089-2_15
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DOI: https://doi.org/10.1007/978-1-84996-089-2_15
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