Abstract
A special type of polynomial curves in implicit representation is proposed. They can be applied to form a desired path (DP) that is close to a physically realizable one. The algorithm designed with the use of transverse feedback linearization provides for precision stabilization of a mobile object or a vehicle on such a path.
Similar content being viewed by others
References
Flixeder, S., Gluuck, T., Boock, M., and Kugi, A., Combined Path Following and Compliance Control with Application to a Biaxial Gantry Robot http://dx.doi.org/. doi 10.1109/CCA.2014.6981438
Dovgobrod, G.M., Real-time generation of smooth execution paths, Gyroscopy and Navigation, 2015, vol. 6, no. 3, pp. 246–251.
Lekkas, A.M., Guidance and path-planning systems for autonomous vehicles. Thesis for the degree of philosophiae doctor. Trondheim, April 2014.
Krstic, M., Kanellakopoulos, I., and Kokotovic, P., Nonlinear and Adaptive Control Design, New York: John Wiley & Sons, Inc., 1995.
Cayero, J., Cuguero, J., and Morcego, B. Backstepping with virtual filtered command: Application to a 2D autonomous vehicle. julen.cayero at upc.edu. http://upcommons.upc.edu/handle/2117/25003
Dovgobrod, G.M., Design of an adaptive algorithm for ship motion control on a curvilinear path using backstepping, Giroskopiya i Navigatsiya, 2011, no. 4, pp. 22–31.
Lapierre, L., Soeteanto, D., and Pascoal, A., Nonlinear path following with applications to the control of autonomous underwater vehicles, Proc. CDC2003, 42nd IEEE Conference on Decision and Control, Hawai, USA, 2003.
Pelevin, A.E., Ship motion stabilization on a curvilinear path, Giroskopiya i Navigatsiya, 2002, no. 2, pp. 3–11.
Miroshkin, I.V., Teoriya avtomaticheskogo upravleniya. Nelineinye i optimal’nye sistemy (Automatic Control Theory. Nonlinear and Optimal Systems), St. Petersburg: Piter, 2006.
Isidori, A., Nonlinear Control Systems, 5th edition, Berlin: Springer-Verlag, 1995.
Kapitanyuk, Yu.A. and Chepinskii, S.A., Mobile robot control on a preset piecewise smooth path, Giroskopiya i Navigatsiya, 2013, no. 2, pp. 42–52.
Nielsen, C. and Maggiore, M., Maneuver regulation via transverse feedback linearization: Theory and examples. In Proc. IFAC Symposium on Nonlinear Control Systems (NOLCOS), Stuttgart, Germany, September 2004.
Cox, D., Little, J., and O’Shea, D., Idealy, mnogoobraziya i algoritmy (Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra), Translated into Russian, Moscow: Mir, 2000.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © G.M. Dovgobrod, 2016, published in Giroskopiya i Navigatsiya, 2016, No. 3, pp. 143–151.
Rights and permissions
About this article
Cite this article
Dovgobrod, G.M. Generation of a highly-smooth desired path for transverse feedback linearization. Gyroscopy Navig. 8, 63–67 (2017). https://doi.org/10.1134/S2075108717010023
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2075108717010023