Optimal control, statistics and path planning

In this paper, some of the relationships between optimal control and statistics are examined. In a series of earlier papers, we examined the relationship between optimal control and conventional splines and between optimal control and the statistical theory of smoothing splines. In this paper, we present a unified treatment of these two problems and extend the same framework to include the concept of “dynamic time warping”, which is being seen as an important statistical tool as well as being of importance in physics. We show that these three major problems unite to give a satisfactory solution to the problem of trajectory or path planning.