A penalized nonparametric method for nonlinear constrained optimization based on noisy data

Autonomous vehicle, B-splines, Consistent estimator, Confidence ellipses, Constrained optimization, Nonparametric method,

Monte carlo algorithm for trajectory optimization based on markovian readings

This paper describes an efficient algorithm to find a smooth trajectory joining two points A and B with minimum length constrained to avoid fixed subsets. The basic assumption is that the locations of the obstacles are measured several times through a mechanism that corrects the sensors at each reading using the previous observation. The proposed algorithm is based on the penalized nonparametric method previously introduced that uses confidence ellipses as a fattening of the avoidance set. In this paper we obtain consistent estimates of the best trajectory using Monte Carlo construction of the confidence ellipse. © Springer Science+Business Media, LLC 2010.This paper describes an efficient algorithm to find a smooth trajectory joining two points A and B with minimum length constrained to avoid fixed subsets. The basic assumption is that the locations of the obstacles are measured several times through a mec511305321CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO475504/2008-9; 301542/2007-4; 301530/2007-62006/02095-5Asseo, S.J., In-flight replanning of penetration routes to avoid threat zones of circular shapes (1998) Aerospace and Electronics Conference, 1998, pp. 383-391. , NAECON 1998. Proceedings of the IEEE 1998 NationalAström, K.J., Murray, R.M., (2008) Feedback Systems: An Introduction for Scientists and Engineers, , Princeton University Press, PrincetonAyache, N., Faugeras, O.D., Building, registrating, and fusing noisy visual maps (1988) Int. J. Robot. Res., 7 (6), pp. 45-65Azarbayejani, A., Pentland, A.P., Recursive estimation of motion, structure, and focal length (1995) IEEE Trans. Pattern Anal. Mach. Intell., 17, pp. 562-575Barraquand, J., Latombe, J.-C., Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles (1993) Algorithmica, 10 (2-4), pp. 121-155. , Computational robotics: the geometric theory of manipulation, planning, and controlBetts, J.T., Survey of numerical methods for trajectory optimization (1998) Journal of Guidance, Control, and Dynamics, 21 (2), pp. 193-207Brockwell, P.J., Davis, R.A., (1996) Introduction to Time Series and Forecasting, , Peter J. Brockwell and Richard A. Davis. Springer, New YorkBroida Ted, J., Chandrashekhar, S., Chellappa Rama, Recursive 3-D motion estimation from a monocular image sequence (1990) IEEE Transactions on Aerospace and Electronic Systems, 26 (4), pp. 639-656. , DOI 10.1109/7.55557Chapuis, R., Aufrere, R., Chausse, F., Accurate road following and reconstruction by computer vision (2002) IEEE Transactions on Intelligent Transportation Systems, 3 (4), pp. 261-270. , DOI 10.1109/TITS.2002.804751Choset, H., Lynch, K., Hutchinson, S., Kantor, G., Burgardand, W., Kavraki, L., Thrun, S., (2005) Principles of Robot Motion: Theory, Algorithms and Implementations, , MIT Press, CambridgeDias, R., Garcia, N.L., Zambom, A.Z., A penalized nonparametric method for nonlinear constrained optimization based on noisy data (2008) Comput. Optim. Appl., , doi:10.1007/s10589-008-9185-6Fliess, M., Levine, J., Martin, P., Rouchon, P., On differentially flat nonlinear-systems (1992) C. R. Acad. Sci., Ser. 1 Math., 315 (5), pp. 619-624Fliess, M., Lévine, J., Rouchon, P., Flatness and defect of nonlinear systems: Introductory theory and examples (1995) Int. J. Control, 61, pp. 1327-1361Grundel, D., Murphey, R., Pardalos, P., Prokopyev, O., Cooperative systems, control and optimization (2007) Lecture Notes in Economics and Mathematical Systems, 588. , Springer, BerlinHarvey, A.C., (1990) Forecasting, Structural Time Series Models and the Kalman Filter, , Cambridge University Press, CambridgeHirsch, M.J., Pardalos, P., Murphey, R., Grundel, D., Advances in cooperative control and optimization (2007) Lecture Notes in Control and Information Sciences, 369. , Springer, Berlin Papers from a meeting held in Gainesville, FL, January 31-February 2Laumond, J.-P., Robot motion planning and control (1998) Lecture Notes in Control and Information Science, 229. , http://www.laas.fr/jpl/book.html, Springer, Berlin onlineLavalle, S., (2006) Planning Algorithms, , Cambridge University Press, CambridgeMatthies, L., Kanade, T., Szeliski, R., (1989) Kalman Filter-based Algorithms for Estimating Depth from Image SequencesPerrollaz, M., Labayrade, R., Gallen, R., Aubert, D., A three resolution framework for reliable road obstacle detection using stereovision (2007) MVA, pp. 469-472Tiwari, A., Chandra, H., Yadegar, J., Wang, J., Constructing optimal cyclic tours for planar exploration and obstacle avoidance: A graph theory approach (2007) Advances in Variable Structure and Sliding Mode Control, , Springer, Berli