Semidifferential Invariants for Tactile Recognition of Algebraic Curves

Abstract

This paper studies the recognition of low-degree polynomial curves based on minimal tactile data. Euclidean differential and semi-differential 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.

Robotic tactile perception of object properties: A review

“…Different from the point cloud based approaches, a non-linear model-based inversion is proposed in [137] to recover surface curvatures by using a cylindrical tactile sensor. In more recent works [138]- [140], the curvatures at curve intersection points are analyzed and thus a patch is described through polynomial fitting; in [141], estimation of nonparametric shapes is demonstrated using binary sensing (collision and no collision) and ergodic exploration.…”

iCLAP: shape recognition by combining proprioception and touch sensing

“…Different from the point cloud based approaches, a non-linear model-based inversion is proposed in [24] to recover surface curvatures by using a cylindrical tactile sensor. In more recent works [25]- [27], the curvatures at curve intersection points are analyzed and thus a patch is described through polynomial fitting. Tactile array sensors have also been utilized to obtain the spatial distribution of the object in space.…”

Surface patch reconstruction by touching

“…In (26), two rounds of local fitting over tactile data from a 2D shape were applied to robustly estimate the curvature and its derivative with respect to arc length.…”

“…Then we fit over those data points very close to p and estimate the tangent T α and the curvature κ α at the point. A quadratic polynomial is used in the fitting because locally the curve resembles the osculating circle of α at p. The curvature (along with its derivative) can be estimated very accurately this way, as shown in (26).…”