MINIMAL CURVATURE-CONSTRAINED PATHS IN THE PLANE WITH A CONSTRAINT ON ARCS WITH OPPOSITE ORIENTATIONS
Peter Alexander Grossman, Marcus Brazil, Joachim Hyam Rubinstein, Doreen Anne Thomas · International Journal of Computational Geometry & Applications · 2013
The declines that provide vehicle access in an underground mine are typically designed as paths formed by concatenating line segments and circular arcs. In order to reduce wear on the ore trucks and the road surfaces and to enhance driver safety, such paths may be subject to a further constraint: each pair of consecutive arcs with opposite orientations must be separated by a straight line segment of at least a certain specified length. In order to reduce the construction and operational costs of the mine, it is desirable to minimize the lengths of such paths between any given pair of directed points. Some necessary and sufficient conditions are obtained for paths of this form to be locally or globally minimal with respect to length. In particular, it is shown that there is always a globally minimal path that contains at most four circular arcs.