Generating Chen-Fliess-Sussmann equation via Campbell-Baker-Hausdorff-Dynkin formula

Generating and solving the Chen-Fliess-Sussmann (CFS) equation for a given representation of motion is a crucial step in deriving controls to steer nilpotent nonholonomic systems using the Lafferriere-Sussmann method. The equation can be quite complicated, and its derivation differs substantially from one representation to another. Therefore instead to derive CFS for a given hard-to-compute representation we propose to derive it for any easy-to-compute representation and then to transform it to the given representation. For this purpose the Campbell-Baker-Hausdorff-Dynkin formula is applied. This approach is illustrated on generating and solving CFS for forward, backward and canonical representations.