1 Simultaneous Robot-World and Hand-Eye Calibration Fadi Dornaika and Radu Horaud, Member, IEEE Abstract|Recently, Zhuang, Roth, & Sudhakar [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a homogeneous matrix equation of the form AX = ZB. They use quat...

In this work, we began to take forward kinematics of the Gough–Stewart (G-S) platform as an unconstrained optimization problem on Lie group-structured manifold SE(3) instead simply relaxing its intrinsic orthogonal constraint when algorithms are updated six-dimensional local flat Euclidean space or adding extra unit norm orientation parts parametrized by a quaternion. With thought in mind, cons...

Let Hmxn be the set of all m x n matrices over real quaternion algebra. We call that A ? Hnxn is ?-Hermitian if = A?* where -?A*?,? {i,j,k},i,j,k are units. In this paper, we derive some solvability conditions and general solution to a system matrix equations. As an application, present necessary sufficient for existence systems also give expressions solutions these when they solvable. Some num...

Abstract Let L be a separable quadratic extension of either $${\mathbb {Q}}$$ Q or {F}}_q(t)$$ F q ( t ) . We exhibit efficient algorithms for finding isomorphisms between quatern...

In his work on modularity theorems, Wiles proved a numerical criterion for map of rings $R\to T$ to be an isomorphism complete intersections. He used this show that certain deformation and Hecke algebras associated mod $p$ Galois representation at non-minimal level are isomorphic intersections, provided the same is true minimal level. paper we study acting cohomology Shimura curves arising from...

We show that arithmetic lattices in $\mathrm{SL}_{2}(\mathbb{R})$, stemming from the proper units of an Eichler order indefinite quaternion algebra over $\mathbb{Q}$, admit a `small' covering set. In particular, we give bounds on diameter if quotient space is co-compact. Consequently, these small generators. Our techniques also apply to definite algebras where Ramanujan-strength certain Ramanuj...

In this paper we find a field such that the algebras obtained by the Cayley-Dickson process are division algebras of dimension 2t,∀t ∈ N. Subject Classification: 17D05; 17D99. From Frobenius Theorem and from the remark given by Bott and Milnor in 1958, we know that for n ∈ {1, 2, 4} we find the real division algebras over the real field R. These are: R, C, H(the real quaternion algebra), O(the ...

Dual quaternion algebra and its application to robotics have attracted considerable interest in the last two decades. quaternions great geometric appeal easily capture physical phenomena inside an algebraic framework, which is useful for both robot modeling control. Mathematical objects, such as points, lines, planes, infinite cylinders, spheres, coordinate systems, twists, wrenches, are all we...