Summary
This paper investigates efficient curve processing that originates from the localization and grasping of 2D curved objects.
The first algorithm locates the boundary section of an object traced out by a rolling finger based on the length and total curvature information obtained with the finger’s tactile sensor. The algorithm slides an imaginary segment along the object boundary by alternatively marching its two endpoints forward, stretching or contracting the segment if necessary.
The second algorithm computes all pairs of antipodal points on an object. Two fingers placed at such a pair of points can achieve a force-closure grasp in the presence of friction. Dissecting the boundary into segments everywhere convex or everywhere concave, the algorithm marches simultaneously on every two segments with opposing normals and alternates marching with numerical bisection recursively. It builds on a procedure that constructs common tangents of two curves with quadratic local convergence.
Completeness (up to numerical resolution) of the above algorithms is established by applying curvature-based analyses. Dissection and the coupling of marching with bisection introduced in this paper are potentially applicable to optimization problems involving curves and curved surfaces.
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Jia, YB. (2004). Computation on Parametric Curves with Applications in Localization and Grasping. In: Boissonnat, JD., Burdick, J., Goldberg, K., Hutchinson, S. (eds) Algorithmic Foundations of Robotics V. Springer Tracts in Advanced Robotics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45058-0_20
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DOI: https://doi.org/10.1007/978-3-540-45058-0_20
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