A Nonlinear Trigonometric Series Parameterization Approach for Smooth Trajectory Generation

This paper introduces a parameterization method for generating trajectories with smooth control commands based on a trigonometric series, where the formulation is nonlinear with respect to the series coefficients. The proposed method aims to achieve a steadier behavior when a path constraint is temporarily active, which is often encountered with e.g., a minimum-time performance index. To this end, first, the control derivatives are parameterized instead of the control variables. Furthermore, the newly developed formulation includes a filtering function depending on the original trigonometric series. This function reduces the series value when it is within a specifiable neighborhood of zero. The performance of the proposed method is tested in two numerical benchmark problems in which a minimum-time and a minimum-effort cost function are considered, respectively.     «

This paper introduces a parameterization method for generating trajectories with smooth control commands based on a trigonometric series, where the formulation is nonlinear with respect to the series coefficients. The proposed method aims to achieve a steadier behavior when a path constraint is temporarily active, which is often encountered with e.g., a minimum-time performance index. To this end, first, the control derivatives are parameterized instead of the control variables. Furthermore, the...     »