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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

1 2012

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Closed-loop control algorithm for some class of nonholonomic systems using polar representation

Pazderski D., Szulczyński P., Kozłowski K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2012

Vol. 60, nr 3

521-535

This paper is focused on the convergence problem defined for some class of a two input affine nonholonomic driftless system with three-dimensional state. The problem is solved based on a polar transformation which is singular at the origin. The convergence is ensured using static-state feedback. The necessary conditions for construction of the algorithm are formally discussed. The solution, in general, is local, and the feasible domain is strictly related to the properties of the control system. In order to improve algorithm robustness a simple hybrid algorithm is formulated. The general theory is illustrated by two particular systems and the results of numerical simulations are provided.