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Trajectory tracking for a mobile robot with skid-slip compensation in the Vector-Field-Orientation control system

100%
Michałek M., Dutkiewicz P., Kiełczewski M., Pazderski D.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 4
547-559
EN
The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking in the presence of skid-slip effects. The kinematic control concept presented in the paper is the Vector Field Orientation (VFO) feedback approach with a nonlinear feed-forward skid-slip influence compensation scheme. The VFO control law guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena. The paper includes a control law design description, stability and convergence analysis of a closed-loop system, and practical verification of the proposed control concept. The experimental results illustrate control quality obtained on a laboratory setup equipped with vision feedback, where the Kalman filter algorithm was used in order to practically estimate skid-slip components.
2
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Motion planning and feedback control for a unicycle in a way point following task: The VFO approach

88%
Michałek M., Kozłowski K.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 4
533-545
EN
This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of waypoints which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation of way-points leading to simplified task description and its subsequent realization. The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task. The unique features of the resultant VFO control system, namely, predictable vehicle transients, fast error convergence, vehicle directing effect together with very simple controller parametric synthesis, may prove to be useful in practically motivated motion tasks.
3
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High order representation formulas and embedding theorems on stratified groups and generalizations

75%
Lu G., Wheeden R. L.
Studia Mathematica
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2000
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tom 142
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nr 2
101-133
EN
We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable $L^1$ to $L^1$ Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and $L^1$ to $L^1$ Poincaré inequalities involving high order derivatives are known to hold. We apply the formulas to derive embedding theorems and potential type inequalities involving high order derivatives.
4
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Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem

75%
Jakubczyk B.
Annales Polonici Mathematici
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2000
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tom 74
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nr 1
117-132
EN
We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.
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