An efficient method to find a shortest path for a car-like robot

This paper proposes new formulae for Dubins' CSC family to find the shortest smooth path between the initial and final configurations of the carlike robot. The formulae are used for finding connection points explicitly between the circle of the initial configuration and the straight line segment, and the connection point of the straight line segment and the circle of the final configuration. Fast finding the connection points(C-S and S-C) are very useful for a real application. The formulae have simple forms mainly because they are transformed to the origin of their original configuration, and then they are converted to standard forms which are the representative configurations of type LSL and LSR, respectively. And a simple criterion for classifying 4 types of CSC, which are necessary for deciding any type of CSC prior to the conversion to the standard form, is presented.