Path planning for non linear systems using trigonometric splines

This paper deals with the use of trigonometric splines (also call Schoenberg's polynomials) in order to increasing the performances of a nonlinear closed-loop system. In the first part, it is recalled that for linear systems, the couple "setting time/overshoot" can be largely improved if a path planning is used instead of a classical step input. The concept of trigonometric splines is then introduced. The remainder of this paper treats of nonlinear systems and in particular differentially flat system. After having pointed out the necessity for this kind of system to have a smooth trajectory generator, it is shown, in particular through the example of the crane, the contribution that this technique can bring. A comparison with a classical polynomials approach is performed.