Robotic manipulators have become indispensable tools in space operations. Over the past few decades, manipulators like Canadarm2 have played significant roles, ranging from repair tasks to the complex process of capturing servicing satellites. On this basis, the main objective of this research is to automate the satellite-catching process on the International Space Station (ISS). The study employs an image moment-based visual servoing to fulfill the task. Various image features have been introduced to control the manipulator’s movements using image moments. Yet, these features often face the challenging issue of coupling between six degrees of freedom movements, a problem that many researchers have aimed to solve. Nevertheless, previous literature has not completely addressed decoupling, which reveals the need for alternative approaches. In this research, two novel approaches, function-based visual servoing and deep neural network (DNN)-based visual servoing, were developed to address this challenge. In the first approach, we introduce a novel general image feature function whose numerator and denominator are the polynomials with terms consisting of various image moments and adjustable parameters. Through the optimization process, two distinct rotational features about the x and y axes are formulated with the optimally tuned parameters. The second approach integrates DNN to estimate the 6D pose of the camera, yielding six decoupled image features. Experimental results from the Denso manipulator confirm that decoupling image features can improve the controlling performance of the manipulator for capturing servicing satellites. The DNN-based visual servoing method could potentially enhance the performance of Canadarm2 in catching satellites, achieving a 32.04% average reduction in pose error and enhancing the velocity’s precision by 21.67% over traditional methods.