Abstract
In this paper, bases in the space of controls are evaluated for driftless nonholonomic systems. As a tool of the evaluation, the pre-control form of the generalized Campbell-Baker-Hausdorff-Dynkin formula is used. It appears that harmonic, Fourier basis is the best among the two other tested bases: polynomial (Legendre) basis and the simplest wavelet basis - the Haar basis. An impact of bases on motion planning for nonholonomic robots is explained.
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