Approximate feedback linearization around a trajectory: application to trajectory planning

In this paper, we consider the approximate feedback linearization of a nonlinear system with one input in a neighborhood of a trajectory. We obtain a normal form for the dynamics in a neighborhood of a given trajectory. The normal form can be used to find a more aggressive trajectory in a vicinity of the original trajectory. The process can be repeated several times, yielding an iterative procedure for designing aggressive trajectories. An example is given to illustrate the approach