Pre-control form of the generalized Campbell–Baker–Hausdorff–Dynkin formula for affine nonholonomic systems

In this paper a pre-control form of the generalized Campbell–Baker–Hausdorff–Dynkin (gCBHD) formula is presented. This form is dedicated to nonholonomic (affine) systems often encountered in robotics. The simplest possible expression for the pre-control gCBHD is obtained as control-dependent functions pre-multiply elements of the Ph. Hall basis. Algorithmic aspects of deriving the formula are highlighted. An application of the pre-control form of the gCBHD formula in motion planning of nonholonomic systems is also reported.