Optimal control theoretic splines and its application to mobile robot

Splines have been investigated as a basic tool of applied mathematics. First, the dynamics splines based on control theory were used in trajectory planning. Many researchers have studied some of the basic properties of splines from the viewpoint of optical control. We consider the method for generating smoothing splines using a control theoretic approach. Namely, we make generalized splines by solving an optimal control problem for linear systems. Then, we treat dependence on initial conditions. The important contribution in this paper is as follows: We introduce the new smoothing splines by optimizing not only over the control but also over the initial condition data.