A Better Trajectory for Approximately Feedback Linearized Systems

In this paper, we develop an approach for finding an approximate trajectory with limited aggressiveness that are close to a specified trajectory. B-splines is used to parametrize the trajectory with a certain level of smoothness. A constrained optimization problem is formulated for solving this problem. The resulting approximate trajectory is close to the specified trajectory within a given allowance, and the aggressiveness of this approximate trajectory is minimized. As a result, the approximate trajectory can be more effectively tracked by an approximately feedback linearized system.