Vision Autonomous Relative Navigation Algorithm for Distributed Micro/Nano Satellite Earth Observation System Based on Motor Algebra

Along with the development of space science and technology, it is not a heart-stirring thing to launch a satellite successfully any more. But we pay greatly attention to space autonomous rendezvous and docking (AR&D) in space operations, such as maintaining, assembling, attacking etc. And that autonomous relative position and pose is one of key technologies of these space actions. Currently, celestial Navigation System (CNS), Inertial Navigation System (INS), Global Navigation Satellite System (GNSS), such as GPS, GLONASS, GALILEO and Compass etc, and the integrations of them are some methods of autonomous navigation for space. But these methods must be depended on the high speed links of the communications network. Moreover, the precision of CNS is always worse, and can not meet the rigorous requirement of the space activities. INS can not be used for long-term space navigation applications for its errors being accumulated. High accuracy can be met by Carrier Differential Global Positioning System (CDGPS), but it is difficult to calculate the ambiguities of CDGPS. Fortunately, autonomous relative position and pose based on machine vision is a direction all over the world currently, and is very suitable for autonomous spacecraft navigation because it has some advantages, such as low-cost, high precision, autonomous ability, easy practicality etc. However, there are some disadvantages of some relative navigation algorithms based-on machine vision, such as complicated description, huge calculation burden, and lack of real-time ability etc. Whereas, the rigid motion of 3D objects can be represented by motor algebra, and the rotation and translation transformations can be calculated simultaneously. So it is more effective for dealing with relative navigation of distributed micro/nano satellite earth observation system. In this paper, on the basis of the attitude dynamics of spacecrafts and the theory of machine vision, an autonomous relative navigation algorithm for distributed micro/nano satellites based on motor algebra and EKF (Extended Kalman Filtering) is proposed. Firstly, how to represent a line transform unit using motor algebra is introduced. Then, the feature line point of the line transform unit is defined. And then, on the basis of the attitude dynamics of spacecrafts and the theory of EKF, we build the state and observation equations. Finally, the simulations show that this algorithm is an accurate valid method in relative navigation of distributed micro/nano satellite earth observation system.