The non-orthogonal Serret-Frenet parametrization applied to the path following problem of a manipulator with partially known dynamics

In this paper an application of the Serret-Frenet parametrization of a curve to the path following task is presented. This curvilinear parametrization method is used to obtain a control object description relative to the desired curve defined in the three-dimensional space. In order to derive proper equations, the innovative approach of the non-orthogonal projection of a con-trol object on the given path is investigated. The non-orthogonal projection allows to design a global control algorithm. The proposed solution results in a cascade structure of the control system. Thus, the backstepping integrator algorithm was applied to create a control law. Due to the partial knowledge of control object dynamic parameters, an adaptive algorithm is taken into account. Theoretical considerations are confirmed with simulation study. Conducted simula-tions illustrated following paths at different levels of complexity by a holonomic non-redundant manipulator with a fixed base.