In this paper, we propose a nonlinear adaptive position and attitude tracking controller for a rigid body that requires no information about the mass and inertia matrix of the body. Moreover, we provide sufficient conditions on the reference trajectory that guarantee mass and inertia matrix identification. The controller is shown to be almost globally asymptotically stable and can handle large ...

As we know, quaternions are very efficient for representing rotations with clear geometric meaning (rotation axis and angle) and only one redundancy. Unfortunately, they do not handle translations, which meanwhile can be made multiplicative along with rotations via the use of homogeneous coordinates. Despite also being 4-tuples, homogeneous coordinates are algebraically incompatible with quater...

We express Maxwell’s equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equati...

Conformal Geometric Algebraic (CGA) provides ideal mathematical tools for construction, analysis and integration of classical Euclidean, Inversive & Projective Geometries, with practical applications to computer science, engineering and physics. This paper is a comprehensive introduction to a CGA tool kit. Synthetic statements in classical geometry translate directly to coordinate-free algebrai...

In this paper, we introduce the definition of generalized reduced biquaternions and propose a real representation biquaternion matrix. By using matrix representation, discuss least-squares problems classic equation AXC = B. The solution to above is formulated by its corresponding equation. Furthermore, two numerical examples are given illustrate our results.

Quaternions are well suited to describe and combine rotations in the usual 3D euclidian space. Therefore, an increasing interest has been shown especially by engineers for symbolically computing with quaternions. To give the ability to perform manipulations on symbolic expressions involving quaternions, we designed Quaterman, a Maple package and Quaternica, a Mathematica package. We present the...