Abstract
Two cost functions of paths for smoothness are defined; Path curvature and the derivative of path curvature. Through these definitions, two classes of simple paths are obtained; the set of circular arcs and the set of cubic spirals. A cubic spiral is a curve whose tangent direction is described by a cubic function of path distance s. These sets of simple paths are used for solving path planning problems of symmetric posture (position and orientation) pairs. For a non-symmetric posture pair, we use two simple paths as a solution. In order to find those paths, we use the fact that the locus of split postures is a circle or a straight line. A posture q is said to be a split posture of a pair (p 1,p 2) of postures, if p 1 and q are symmetric and so are q and p 2. The resultant solutions are smoother than those obtained by one of the authors using clothoid curves. This algorithm has been successfully implemented on the autonomous mobile robot Yamabico-11 at UCSB.
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Kanayama, Y., Hartman, B.I. (1990). Smooth Local Path Planning for Autonomous Vehicles. In: Cox, I.J., Wilfong, G.T. (eds) Autonomous Robot Vehicles. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8997-2_6
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DOI: https://doi.org/10.1007/978-1-4613-8997-2_6
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