Abstract
Path-planning is a key technique in visual servoing, as it allows one to take into account various constraints and optimize a desired performance. This paper addresses the problem of planning image trajectories to be followed by using an image-based visual servoing controller. The proposed technique consists of parametrizing the camera trajectory in the 3D space via polynomials, and by imposing constraints satisfaction and performance optimization via the square matrix representation (SMR) and linear matrix inequalities (LMIs). Examples in the absence and in the presence of uncertainties illustrate and validate the proposed methodology.
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References
Chesi, G., Hashimoto, K. (eds.): Visual Servoing via Advanced Numerical Methods. Springer, Heidelberg (2010)
Thuilot, B., Martinet, P., Cordesses, L., Gallice, J.: Position based visual servoing: keeping the object in the field of vision. In: IEEE Int. Conf. on Robotics and Automation, Washington, D.C, pp. 1624–1629 (2002)
Hashimoto, K., Kimoto, T., Ebine, T., Kimura, H.: Manipulator control with image-based visual servo. In: IEEE Int. Conf. on Robotics and Automation, pp. 2267–2272 (1991)
Malis, E., Chesi, G., Cipolla, R.: \(2~1/2~\mbox{D}\) visual servoing with respect to planar contours having complex and unknown shapes. Int. Journal of Robotics Research 22(10), 841–853 (2003)
Corke, P.I., Hutchinson, S.: A new partitioned approach to image-based visual servo control. IEEE Trans. on Robotics and Automation 17(4), 507–515 (2001)
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 Trans. on Robotics 20(5), 908–913 (2004)
Lopez-Nicolas, G., Bhattacharya, S., Guerrero, J.J., Sagues, C., Hutchinson, S.: Switched homography-based visual control of differential drive vehicles with field-of-view constraints. In: IEEE Int. Conf. on Robotics and Automation, Rome, Italy, pp. 4238–4244 (2007)
Chesi, G., Vicino, A.: Visual servoing for large camera displacements. IEEE Trans. on Robotics 20(4), 724–735 (2004)
Tahri, O., Chaumette, F.: Point-based and region-based image moments for visual servoing of planar objects. IEEE Trans. on Robotics 21(6), 1116–1127 (2005)
Cowan, N.J., Chang, D.E.: Geometric visual servoing. IEEE Trans. on Robotics 21(6), 1128–1138 (2005)
Tarbouriech, S., Soueres, P., Gao, B.: A multicriteria image-based controller based on a mixed polytopic and norm-bounded representation of uncertainties. In: 44th IEEE Conf. on Decision and Control and European Control Conf., Seville, Spain, pp. 5385–5390 (2005)
Miura, K., Hashimoto, K., Inooka, H., Gangloff, J.A., de Mathelin, M.F.: Model-less visual servoing using modified simplex optimization. Journal Artificial Life and Robotics 2, 131–135 (2006)
Mezouar, Y., Chaumette, F.: Path planning for robust image-based control. IEEE Trans. on Robotics and Automation 18(4), 534–549 (2002)
Deng, L., Janabi-Sharifi, F., Wilson, W.J.: Hybrid motion control and planning strategy for visual servoing. IEEE Trans. on Industrial Electronics 52(4), 1024–1040 (2005)
Yao, Z., Gupta, K.: Path planning with general end-effector constraints. Robotics and Autonomous Systems 55(4), 316–327 (2007)
Chesi, G., Prattichizzo, D., Vicino, A.: Straight line path-planning in visual servoing. Journal of Dynamic Systems, Measurement and Control 129(4), 541–543 (2007)
Chesi, G., Hung, Y.S.: Global path-planning for constrained and optimal visual servoing. IEEE Trans. on Robotics 23(5), 1050–1060 (2007)
Chesi, G.: Visual servoing path-planning via homogeneous forms and LMI optimizations. IEEE Trans. on Robotics 25(2), 281–291 (2009)
Kazemi, M., Gupta, K., Mehran, M.: Global path planning for robust visual servoing in complex environments. In: IEEE Int. Conf. on Robotics and Automation, Kobe, Japan (2009)
Chesi, G., Tesi, A., Vicino, A., Genesio, R.: On convexification of some minimum distance problems. In: European Control Conf., Karlsruhe, Germany (1999)
Chesi, G., Garulli, A., Tesi, A., Vicino, A.: Solving quadratic distance problems: an LMI-based approach. IEEE Trans. on Automatic Control 48(2), 200–212 (2003)
Chesi, G.: On the gap between positive polynomials and SOS of polynomials. IEEE Trans. on Automatic Control 52(6), 1066–1072 (2007)
Chesi, G., Garulli, A., Tesi, A., Vicino, A.: Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems. Springer, Heidelberg (2009)
Malis, E., Chaumette, F.: 2 1/2 D visual servoing with respect to unknown objects through a new estimation scheme of camera displacement. Int. Journal of Computer Vision 37(1), 79–97 (2000)
Chesi, G., Hashimoto, K.: A simple technique for improving camera displacement estimation in eye-in-hand visual servoing. IEEE Trans. on Pattern Analysis and Machine Intelligence 26(9), 1239–1242 (2004)
Chesi, G.: Camera displacement via constrained minimization of the algebraic error. IEEE Trans. on Pattern Analysis and Machine Intelligence 31(2), 370–375 (2009)
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Chesi, G. (2011). Planning Image Trajectories for Visual Servoing via LMI-Based Optimization. In: Cetto, J.A., Filipe, J., Ferrier, JL. (eds) Informatics in Control Automation and Robotics. Lecture Notes in Electrical Engineering, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19730-7_11
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DOI: https://doi.org/10.1007/978-3-642-19730-7_11
Publisher Name: Springer, Berlin, Heidelberg
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