This paper focuses on a new type of control laws for oriented mechanical systems. The starting point is dual quaternion and its properties. Logarithm of dual quaternion is defined, based on which control laws are developed, tackling both regulation and tracking problems using logarithmic feedback. The control laws are shown to have several merits, including global asymptotically convergence, co...

An algorithm is presented that constructs a C 2-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of B-spline curves can be extended to generate B-spline quaternion curves Sch92]; however, the B-spline quaternion curves do not have C 2-continuity in SO(3). The authors KKS94a] recent...

3 Quaternion Representation 5 3.1 Axis-Angle to Quaternion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Quaternion to Axis-Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.3 Quaternion to Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Matrix to Quaternion . . . . . . . . . . ....

In this paper, through an in-depth study and analysis of dance motion capture algorithms in wearable sensor networks, the extended Kalman filter algorithm quaternion method are selected after analysing a variety commonly used data fusion pose solving algorithms. sensor-body coordinate system calibration based on hand-eye is proposed, which only requires three poses to complete whole-body system...

in the several past years, extended kalman filter (ekf) and unscented kalman filter (ukf) havebecame basic algorithm for state-variables and parameters estimation of discrete nonlinear systems.the ukf has consistently outperformed for estimation. sometimes least estimation error doesn't yieldwith ukf for the most nonlinear systems. in this paper, we use a new approach for a two variablesta...

A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under functional composition. Furthermore, the composition operation is symbolically identical to quaternion multiplication, making manipulation and reduction of sy...

A new method for 3D rigid motion estimation is derived under the most general assumption that the measurements are corrupted by inhomogeneous and anisotropic, i.e., heteroscedastic noise. This is the case, for example, when the motion of a calibrated stereo-head is to be determined from image pairs. Linearization in the quaternion space transforms the problem into a multivariate, heteroscedasti...

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

In this paper, a quaternion firefly algorithm is utilized to solve a multi-row facility layout design problem with the objective of minimizing the total cost of transportation. A quaternion firefly algorithm takes the motion of the firefly as a quaternion one. Consequently, the solution space is explored more accurately and the answers are of higher quality. That is, the answers are considerabl...

The orientation estimation filter proposed by Madgwick [1] for inertial and inertial/magnetic sensors have been successfully used as a core solution in a variety of commercial low-power motion tracking devices. The approach offers a high accuracy and reduces the computational cost compared to the state-of-the-art Kalman-based methods [10]. In this paper, we propose a modification to the Gradien...