Line-of-sight path-following along regularly parametrized curves solved as a generic maneuvering problem

In the traditional maneuvering problem, the objective has been to solve a geometric task and a dynamic task, where the former is to converge to and follow a 1-dimensional manifold, a path, in the output space of the system, and the latter is to satisfy a desired dynamic behavior along the path. In this paper the objective is to generalize this problem statement, by rather stabilizing more general manifolds of higher dimension. With the system output constrained to the desired manifold, the dynamic task becomes to satisfy a dynamic assignment that ensures that the underlying control objective is solved with sufficient performance. In order to exemplify the theory, a case study is performed where a line-of-sight (LOS) algorithm is used to steer a simplified vessel to and along a desired parametrized path. In this case the desired manifold, which is of dimension 3, is defined as the set in which the LOS method is effectuated. The LOS algorithm then ensures, as the dynamic task, that the vessel steers correctly towards and along the path. A simulation study is provided to illustrate the effectiveness and properties of the resulting dynamic control law.