面向在轨服务的相对位姿单目视觉确定的凸松弛优化方法

A Convex Relaxation Optimization Method of On-Orbit Servicing Pose Estimation Using Monocular Vision

针对非合作目标之间基于特征点的相对位姿单目视觉确定问题,考虑利用自然特征导致误差增大等因素,提出一种基于凸松弛理论和LMI算法的相对位姿求解迭代方法。该方法在基于逆投影线构建的优化模型基础上,首先利用松弛理论将姿态矩阵的单位正交非凸等式约束松弛为不等式凸约束,并证明了松弛后的优化问题与原问题等价,即松弛后的凸问题取得最值时,姿态矩阵满足原等式约束。进一步将松弛后的姿态矩阵不等式凸约束表示成线性矩阵不等式形式,进而利用内点法进行求解,并利用全局收敛性定理证明了该算法的全局收敛性。以在轨服务为背景,仿真试验表明,利用该算法相对位姿可在7次迭代达到收敛,与传统SVD算法相比,在噪声较大的情况下,该算法计算精度提高近一倍,能够快速收敛并具有较强的鲁棒性。

Aiming at pose（ relative attitude and position） estimation of non-cooperative spacecraft,an algorithm is developed based on monocular vision and some natural feature points. Considering the increasing estimated error caused by using the natural features,this paper introduces an iterative solution based on convex relaxation optimization and LMI algorithm to solve this problem. The optimization model in this paper is built on adverse projection. First,using relaxation algorithm,turn the non-convex and equality constrained attitude matrix to a convex and inequality constrained matrix. Then,this paper can prove that the convex problem is equal to the original problem. That is,when the convex problem gets extremum, the attitude matrix still satisfies the original equality and non-convex constrain. To further simplify this problem, we can express the convex and unequal constrain as linear matrix inequalities. At last,we can solve it with the developed interior point method and prove convergence of this algorithm.Finally,in the background of on-orbit servicing,the simulation experiment shows that this algorithm can converge within 7 iterations. Compared with SVD,this algorithm nearly doubles accuracy when noise increases gradually. And the results show that this algorithm is robust and efficient.