On a computationally simple form of the generalized Campbell–Baker–Hausdorff–Dynkin formula

In this paper a computationally simple form of the generalized Campbell–Baker–Hausdorff–Dynkin formula (GCBHD) is given. Simplifications arise from both combinatorial (explicit) as well as algorithmic (implicit) arguments. On generating the Ph. Hall basis in a special form, and introducing a specific structure representation of the vector field, vector fields appearing in GCBHD are automatically transformed into the reduced Ph. Hall basis. The formula can be exploited in nonholonomic motion planning what is illustrated with examples.