Localization and mapping using recursive smoothing splines

In this paper a recursive smoothing spline approach is proposed for mapping and localization in continuous-featured environments such as terrains. Periodic smoothing splines are used to approximate the contour of encountered obstacles and for trajectory planning around them. The splines are generated through minimizing a cost function subject to constraints imposed by a linear control system. The filtering effect of the smoothing splines allows for usage of noisy sensor data. An important assumption is that several data sets for the same closed contour can be obtained. Thus a recursive approach is used to obtain a series of splines with improved accuracy.