Optimal control, statistics and path planning

In this paper, some of the relationships between optimal control and statis tics are examined. In a series of earlier papers, we examined the relations hip between optimal control and conventional splines and between optimal co ntrol and the statistical theory of smoothing splines. In this paper, we pr esent a unified treatment of these two problems and extend the same framewo rk 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. W e show that these three major problems unite to give a satisfactory solutio n to the problem of trajectory or path planning. (C) 2001 Elsevier Science Ltd. All rights reserved.