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The International Journal of Robotics Research, Vol. 24, No. 11, 951-969 (2005)
DOI: 10.1177/0278364905059065

Semidifferential Invariants for Tactile Recognition of Algebraic Curves

Rinat Ibrayev

Department of Computer Science, Iowa State University, Ames, IA 50011-1040, USA, rinat{at}cs.iastate.edu

Yan-Bin Jia

Department of Computer Science, Iowa State University, Ames, IA 50011-1040, USA, jia{at}cs.iastate.edu

In this paper we study the recognition of low-degree polynomial curves based on minimal tactile data. Euclidean differential and semidifferential invariants have been derived for quadratic curves and special cubic curves that are found in applications. These invariants, independent of translation and rotation, are evaluated over the differential geometry at up to three points on a curve. Their values are independent of the evaluation points. Recognition of the curve reduces to invariant verification with its canonical parametric form determined along the way. In addition, the contact locations are found on the curve, thereby localizing it relative to the touch sensor. Simulation results support the method despite numerical errors. Preliminary experiments have also been carried out with the introduction of a method for reliable curvature estimation. The presented work distinguishes itself from traditional model-based recognition in its ability to simultaneously recognize and localize a shape from one of several classes, each consisting of a continuum of shapes, by the use of local data.

Key Words: touch sensing • differential invariant • semidifferential invariant • curvature • signature curve • shape parameter • resultant


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