Optimal path generation for wheeled mobile robots with eta3-splines

This paper deals with the generation of optimal paths planned by means of eta3-splines, a recently devised planning primitive used for the automated steering of wheeled mobile robots. The shape of eta3-splines can be easily modified by acting on a set of free parameters. This capability can be used, for example, to satisfy an assigned optimality criterion. In this paper it will be used to minimize the curvature variability in order to reduce the lateral solicitations affecting an autonomous robot. Evidently, curvature derivative could be minimized by means of an optimization algorithm. However, this approach cannot be suitably used in an online application which continuously requires the curve updating. For this reason, closed form expressions have been devised and proposed in this paper in order to efficiently evaluate optimal curves on the sole basis of the interpolating conditions. As a further characteristic, the proposed heuristic method permits obtaining, when appropriate interpolating conditions are given, eta3-splines which at the best emulate circular arcs and clothoids.