Subdivision of point-normal pairs with application to smoothing feasible robot path
This work addresses a specific issue in geometric modeling for robotics, offering incremental improvements to subdivision schemes for path smoothing.
The authors tackled the problem that previous subdivision schemes for point-normal pairs produced limit normals not matching the normals of the limit curves, by proposing a new averaging method and family of algorithms. They demonstrated improved editing capabilities and applied the technique to smooth feasible robot paths, though no concrete numerical results were provided.
In a previous paper [11] we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D, and converge to limit curves and limit normals. Such a scheme has the disadvantage that the limit normals are not the normals of the limit curve. In this paper we solve this problem by proposing a new averaging method, and obtaining a new family of algorithms based on it. We demonstrate their new editing capabilities and apply this subdivision technique to smooth a precomputed feasible polygonal point robot path.