Currently, research on peg-in-hole (PiH) compliant assembly is predominantly limited to circular pegs and holes, with insufficient exploration of various complex-shaped PiH tasks. Furthermore, the degree of freedom for rotation about the axis of the circular peg cannot be constrained after assembly, and few studies have covered the complete process from autonomous hole-searching to insertion. Based on the above problems, a novel cross-shaped peg and hole design has been devised. The center coordinates of the cross-hole are obtained during the hole-searching process using the three-dimensional reconstruction theory of a binocular stereo vision camera. During the insertion process, 26 contact states of the cross-peg and the cross-hole were classified, and the mapping relationship between the force-moment sensor and relative errors was established based on a backpropagation (BP) neural network, thus completing the task of autonomous PiH assembly. This system avoids hand-guiding, completely realizes the autonomous assembly task from hole-searching to insertion, and can be replaced by other structures of pegs and holes for repeated assembly after obtaining the accurate relative pose between two assembly platforms, which provides a brand-new and unified solution for complex-shaped PiH assembly.