With the development of space targets towards larger viewing distances and sizes, precise pose measurement has become a critical factor for the success of various space missions. To meet the demands of pose measurement, cooperative targets specifically designed for spacecraft are usually installed on the target spacecraft, allowing pose information to be obtained through target recognition. This makes the recognition of cooperative targets essential for the stable operation of spacecraft systems. Traditional multi-point geometric configuration recognition methods, such as template matching and geometry-based recognition, struggle to perform effectively at long distances and with large attitude variations due to the unique space environment and variable poses of the targets. To address the challenges of recognizing multi-point geometric configurations with unknown attitude angles in specific space environments, this paper proposes a method that combines prior configuration information and projective invariant features. By designing cooperative targets and constructing two pairs of cross-ratios as invariant features under different poses, this method enables recognition of multi-point geometric configurations at long distances and with unknown attitude angles. It aims to solve the problem of stable and accurate recognition of cooperative targets at different poses at a distance of 50 m in complex background environments. The proposed method achieves a recognition accuracy of over 95% within the pose range of 0^∘–85^∘, outperforming the other methods compared.