This paper considers the problem of linear calibration and presents two estimators arising from a synthesis of classical and inverse calibration approaches Their performance properties are analyzed employing the small error asymptotic theory Using the criteria of bias and mean squared error the proposed estimators along with the traditional classical and inverse calibration are compared Finally...

Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models these robots are typically parametrized by joint angles, generating complicated mapping between robot configuration end-effector pose. Alternatively, kinematic model task constraints can be represented using invariant distances points attached t...

The Paulsen problem is a basic open problem in operator theory: Given vectors u1, . . . , un ∈ R d that are ǫ-nearly satisfying the Parseval’s condition and the equal norm condition, is it close to a set of vectors v1, . . . , vn ∈ R that exactly satisfy the Parseval’s condition and the equal norm condition? Given u1, . . . , un, the squared distance (to the set of exact solutions) is defined a...

This paper provides closed form expressions for the squared distance between the joint density functions of k successive inter-arrival times of two MAPs. The squared distance between the autocorrelation functions of two MAPs is expressed in a closed form as well. Based on these results a simple procedure is developed to approximate a RAP by a MAP, in order to reduce the number of phases or to o...

Inverse kinematics (IK) is the problem of finding robot joint configurations that satisfy constraints on position or pose one more end-effectors. For robots with redundant degrees freedom, there often an infinite, nonconvex set solutions. The IK further complicated when collision avoidance are imposed by obstacles in workspace. In general, closed-form expressions yielding feasible do not exist,...

k-means is the basic method applied in many data clustering problems. As is known, its natural modification can be applied to projection clustering by changing the cost function from the squared-distance from the point to the squared distance from the affine subspace. However, to apply thus approach we need the beforehand knowledge of the dimension. In this paper we show how to modify this appr...