Polynomial-Based Trajectory Planning for Affine Dynamical Systems under State and Input Constraints

In this note we deal with analytical time polynomial based motion planning considerations. A class of differentially flat affine dynamical systems that can be rendered as a set of second-order controlled subsystems is analyzed. It is shown that state and input box constraints can be readily accounted for by proper choice of time of motion or/and initial or final values of some of the state variables and their time derivatives.