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In this paper a detailed description of constructive algorithms aimed at generating controllable nilpotent systems is presented. Exemplary nilpotent systems with varied degree of nilpotency, number of generators and state space dimensionality are provided. Some combinatorial questions concerning a structure of the systems are stated and answered. Nilpotent systems can serve as useful models for practical...
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...
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