Articulated arms in the 3D space and the local nilpotentizability of the underlyig rank-3 distribution

We note - after, among other contributions, the work [8] - that the kinematical system of a finite number, say , of articulated arms in the 3D space is a locally universal model for special 2-flags of that length (Because it is the outcome of a series of so-called generalized Cartan prolongations (‘gCp' for short - compare [4,5].) It is to be remembered that special -flags are effectively nilpotentizable in the sense that local polynomial pseudo-normal forms for such resulting naturally from sequences of gCp's give local nilpotent bases for. Moreover, the nilpotency orders of the generated real Lie algebras can be explicitly computed by means of standard linear algebra ( [4]; for = 1 the same was (re-)proved in [6]). As a consequence, upon specifying = 2, the articulated arms' systems in the 3D space are effectively locally nilpotentizable in the by-now-classical sense of [2]. This could prove useful in the motion planning problems for such space systems.