On the codimension one motion planning problem (Q1774537)

The paper under review deals with the problem of motion planning for co-rank one sub-Riemannian metrics. The results are obtained in a constructive way, i.e., by computing metric complexity and finding asymptotic syntheses. The main results of the paper are as follows: For the 3-dimensional case an explicit exact expression of the metric complexity together with a corresponding asymptotic optimal synthesis is obtained. For other dimensions the results presented in the paper are deeper then in literature. For instance, the motion planning problem in the \(C^{\infty}\) category outside of a set of infinite co-dimension is solved here.