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To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom (6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative (PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion. [ABSTRACT FROM AUTHOR]

In this paper, a unified representation of relative position and attitude based on dual-quaternion is proposed for RVD spacecrafts, which is a breakthrough to the traditional patterns for treating position and orientation separately. First, the model of relative position and attitude of RVD spacecrafts is established by using binocular vision and dual quaternion. Different from the traditional methods such as Euler angles and quaternion, this model has a very simple and unified form. And then, the two-step algorithm is proposed to solve the model. Simulation results show that this algorithm can satisfy the measurement requirement for the spacecrafts, and it has strong stability. So it is of great value to real-time on-orbit measurement of relative position and attitude for RVD spacecrafts. [ABSTRACT FROM AUTHOR]

To unify the description of relative position and attitude of the formation flying satellites, a boating algorithm based on dual quaternion was proposed. Using the dual-quaternion method, the kinematics model of formation flying satellites was established and its physical meanings were analyzed. This algorithm combined the solutions for relative position and attitude calculating. Simulation results indicate that the algorithm can effectively describe the relative position and attitude of formation flying satellites in a scientific and rational way. [ABSTRACT FROM AUTHOR]