On an automatic generation of nilpotent systems

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 and benchmark problems in control and motion planning tasks.