Kinematical modeling of circular and elliptical polarization of the polarized light via screw transformation

In this paper, it is shown that the motion of a polarized light wave in an optical fiber has a special meaning that relates the scalar and vector part of the dual quaternion to the kinematics concept of a screw. We describe the circular and elliptical polarization of a light wave according to how the electric field vector varies in a projection onto a plane perpendicular to the propagation direction using the Clifford algebra of the dual quaternion. Also, we determine the circular-Rytov curve (CR ) and elliptical-Rytov curve (ER ), which described the paths traced out by the tip of the electric field vector as it propagates in space, related to the polarization state of the electric field ε. The elliptical and circular polarization states are expressed by using the four Stokes parameters and their matrix form. Furthermore, some motivating examples are given and visualized their images with the help of the MAPLE program.

Dual Quaternion Based Close Proximity Operation for In-Orbit Assembly via Model Predictive Control

This paper studies the problem of guidance and control for autonomous in-orbit assembly. A six-degree-of-freedom (6-DOF) motion control for in-orbit assembly close proximity operation between a service satellite and a target satellite is addressed in detail. The dynamics based on dual quaternion are introduced to dispose the coupling effect between translation and rotation in a succinct frame, in which relevant perturbation and disturbance are involved. With the consideration of economical principle for fuel consume, a generic control system based on model predictive control (MPC) is then designed to generate a suboptimal control sequence for rendezvous trajectory considering actuator output saturation. The stability and robustness issues of the MPC-based control system are analyzed and proved. Numerical simulations are presented to demonstrate the effectiveness and robustness of the proposed control scheme, while additional comparisons for diverse horizons of the MPC are further conducted.