Fourier series based method of generating continuous controls for driftless nonholonomic systems

A computationally effective method is presented able to generate controls steering a driftless nonholonomic system in a desired direction. By using the Campbell-Baker-Hausdorff-Dynkin formula piecewise constant controls are obtained that realize the desired motion. Then, the controls are expanded into the Fourier series with filtered out higher frequencies. Resulting continuous controls are applied to a driftless nonholonomic system in order to identify a linear combination of Ph. Hall basis elements corresponding to the controls. This approach allows us to generate a desired vector field of the lowest degree keeping at the same time under control the influence of higher degree vector fields.