Practical and flexible path planning for car-like mobile robot using maximal-curvature cubic spiral

This paper presents a nonholonomic path planning method, aiming at taking into considerations of curvature constraint, length minimization, and computational demand, for car-like mobile robot based on cubic spirals. The generated path is made up of at most five segments: at most two maximal-curvature cubic spiral segments with zero curvature at both ends in connection with up to three straight line segments. A numerically efficient process is presented to generate a Cartesian shortest path among the family of paths considered for a given pair of start and destination configurations. Our approach is resorted to minimization via linear programming over the sum of length of each path segment of paths synthesized based on minimal locomotion cubic spirals linking start and destination orientations through a selected intermediate orientation. The potential intermediate configurations are not necessarily selected from the symmetric mean circle for non-parallel start and destination orientations. The novelty of the presented path generation method based on cubic spirals is: (i) Practical: the implementation is straightforward so that the generation of feasible paths in an environment free of obstacles is efficient in a few milliseconds; (ii) Flexible: it lends itself to various generalizations: readily applicable to mobile robots capable of forward and backward motion and Dubins' car (i.e. car with only forward driving capability) ; well adapted to the incorporation of other constraints like wall-collision avoidance encountered in robot soccer games; straightforward extension to planning a path connecting an ordered sequence of target configurations in simple obstructed environment.