Construction of a Measurement System and Analytical Solution for Docking Pose of Large Aircraft Components Based on Draw-wire Displacement Sensors

Abstract Relative pose detection is a key technology in large component automatic docking systems. In this paper, a measurement system has been developed to detect the relative pose of large aircraft components with draw-wire displacement sensors, while an analytical calculation method has been proposed to determine the docking pose of large aircraft components. This method establishes a measurement model for the docking pose of large components and separates the position and orientation solutions based on the distances between seven sets of measurement points measured by the draw-wire displacement sensors. First, the principle of three-dimensional rendezvous positioning is refined to ascertain the relative position of the components. Then, by analyzing the properties of the rotation matrix and the coupling relationship between the position and orientation variables of the movable component, 15 compatible equations containing only two variables with a maximum degree of four are obtained. Based on this set of equations, a unique solution for the rotation matrix was obtained through the variable substitution method, gradually eliminating higher-order terms. Finally, the correctness of the method is verified through numerical examples. Unlike typical parallel mechanism models, this model can directly obtain 15 compatible equations without the need for methods such as Gröbner bases. Moreover, compared to the measurement method using six draw-wire displacement sensors, a unique solution can be directly determined, solving the problem of multiple solution selection. This measurement method only requires measuring the distance between measurement points to solve the relative pose, with low equipment costs and less susceptibility to external environmental factors.