Program Systems: Theory and Applications, 2012, Volume 3, Issue 1, Pages 3–29
This article is cited in 2 scientific papers (total in 2 papers)
Optimization Methods and Control Theory
Algorithms and Software Solving a Motion Planning Problem for Nonholonomic Five-dimensional Control Systems
A. P. Mashtakov
Program Systems Institute of RAS, Pereslavl'-Zalesskii, Yaroslavskaya obl.
In this paper we consider a motion planning problem for nonlinear fifth dimensional systems with two-dimensional linear control. An iterative algorithm based on nilpotent approximation finds the approximate solution of the problem in the classes of piecewise constant and optimal controls. We present implementation of the algorithm in a parallel package for Wolfram Mathematica. The package was applied for the plate-ball problem and for the motion planning problem of car with two trailers on a plain.
Key words and phrases:
Plate-ball problem, car with two trailers, nilpotent approximation, iterative algorithm, optimal control.
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A. P. Mashtakov, “Algorithms and Software Solving a Motion Planning Problem for Nonholonomic Five-dimensional Control Systems”, Program Systems: Theory and Applications, 3:1 (2012), 3–29
Citation in format AMSBIB
\paper Algorithms and Software Solving a Motion Planning Problem for Nonholonomic Five-dimensional Control Systems
\jour Program Systems: Theory and Applications
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This publication is cited in the following articles:
Andrey A. Ardentov, “Controlling of a Mobile Robot with a Trailer and Its Nilpotent Approximation”, Regul. Chaotic Dyn., 21:7-8 (2016), 775–791
A. P. Mashtakov, “O mnozhestve razreza na dvukhstupennykh svobodnykh gruppakh Karno”, Programmnye sistemy: teoriya i prilozheniya, 9:4 (2018), 319–360
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