Jacobian matrix and p-basis

A Random Matrix Approach to Manipulator Jacobian

Traditional kinematic analysis of manipulators, built upon a deterministic articulated kinematic modeling often proves inadequate to capture uncertainties affecting the performance of the real robotic systems. While a probabilistic framework is necessary to characterize the system response variability, the random variable/vector based approaches are unable to effectively and efficiently charact...

Indecomposability of Polynomials via Jacobian Matrix

Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives sharp bounds for the indecomposability problem.

Matrix Identities Connected with the Jacobian Conjecture

Let f ∈ C[x, y] be a polynomial in two variables with complex coefficients. f is said to be a component of an automorphism if there exists a polynomial g ∈ C[x, y] such that F := (f, g) : C −→ C is a polynomial automorphism of C (i.e. there exists F and it is also polynomial). In turn, f is said to be a Keller’s component if there exists g ∈ C[x, y] such that the jacobian Jac(f, g) of the mappi...

Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian Conjecture

Image Based Visual Servoing: Estimated Image Jacobian by Using Fundamental Matrix VS Analytic Jacobian

This paper describes a comparative study of performance between the estimated image Jacobian that come from taking into account the geometry epipolar of a system of two cameras, and the well known analytic image Jacobian that is utilized for most applications in visual servoing. Image Based Visual Servoing architecture is used for controlling a 3 d.o.f. articular system using two cameras in eye...