A Research Based On Dual Quaternion For Relative Position And Attitude Determination Of RVD Spacecrafts

Space rendezvous and docking (RVD) for spacecrafts is a very complex process, and one of its keyissues is how to measure the relative position and attitude information of the target spacecraft and thetracking spacecraft real-timely and precisely. Mathematically, this problem can be attributed to thecommon problem of screw transformation.The general spatial rigid body motion is completely equivalent to coordinate system’stransformation. In describing the general rigid body motion, compared to the spliting way ofrepresenting rotation and translation separately, the dual quaternion can represent them in a unifiedpattern, and thus more concise and easier to operate. Inspired by this fact, this paper presents a novalmethod by utlizing the new mathematical tool--dual quaternion and proposes a unified model todescribe the relative position and attitude information between the tracker and target, which is the abreakthrough to the traditional ways. This model has a very simple and unified form, which makescomputation simpler and more efficient.Any measurement can not be implemented without the corresponding sensors. In this paper, aimingat the the most critical final approach phase in RVD process, we select the CCD cameras as the opticalimaging sensor for measurement. A single CCD camera measurement has the inherent defect oflacking the depth of imaging projects. Compared with the monocular vision way, binocular visionalgorithm can reconstruct the space points, and does not need iteration for solving nonlinear equations.So it has good real-time performance and higher measurement accuracy.This paper first briefly introduces the spacecraft rendezvous and docking and computer visionmeasurement technology, and then describes the concept of the dual quaternion and analyzes itsgeometric meaning. Then this paper derives the dual vector representation for projected lines, andthen makes noise analysis. Finally, to get relative position and attitude information of the two RVDspacecrafts, this paper establishes a model based on the dual quaternion and proposes a two-stepanalysis algorithm. This algorithm is successful in solving the relative position and orientationinfomation real-timely. Simulation results show that this algorithm can satisfy the measuringrequirement of the spacecrafts, and also has strong stability. So it is of great value to real-timeon-orbit measurement of relative position and attitude for RVD spacecrafts.