Ants and bracket generating distributions in dimensions 5 and 6

We consider a mechanical system of three ants on the floor, which move according to two independt rules: Rule A - forces velocity any given ant always point at neighboring ant, and B every be parallel line defined by other ants. observe that equips 6-dimensional configuration space with structure homogeneous (3,6) distribution, foliates this onto 5-dimensional leaves, each is equiped (2,3,5) distribution. The symmetry properties Bryant-Cartan local invariants these distributions are determined. In case we study determine singular trajectories (abnormal extremals) corresponding distributions. show satisfy an interesting ODEs Fuchsian type.