The concept of self-replicating machines was introduced more than fifty years ago by John von Neumann. However, a fully autonomous self-replicating robot has yet to be implemented. This paper discusses our ongoing research on self-replicating robots. Here we describe a semiautonomous prototype that can demonstrate replication under human supervision. This work builds on our previous results in remote-controlled robotic replication with the added feature that many subtasks in the replication process are now autonomously performed by the robot. We believe this to be an important step in the realization of fully autonomous self-replicating robots.