**3.4 Virtual fixture and safety force feedback strategy for virtual-real fusion**

A virtual fixture is constructed by introducing a gravitational potential field, with the reference point of the real instrument's end point in the image as the zero point of the potential energy, and the distance between this reference point and the twin instrument's end point used to represent the potential energy size. Dead zone and extreme value processing are performed on this potential energy to ensure model stability. Based on this, the potential energy generated by the virtual-real fusion is fed back to the primary operator as impedance force within the extreme value range. When the twin model's potential energy reaches the safety threshold, the system automatically generates feedback force to resist the driving force of the primary hand and waits for delayed motion to follow. If the feedback exceeds the limit value, the masterslave operation pause command is executed, and the remote robot motion is stopped within one network transmission and robot execution cycle (less than 40 ms).

Remote surgical operation delay is currently a critical factor affecting the success of remote surgeries and patient safety. To address the core challenge of operation delay in robot-assisted remote surgeries, remote surgeons combine artificial intelligence and digital twin technology. The AI system analyzes and deeply learns the basic principles of expressing delay based on the remote surgeon's ideal operation behavior in virtual space and the observed real operation behavior. It achieves quantitative expression in both visual and tactile dimensions, making delay a visible and tangible physical quantity. Based on this, the surgeon's operation process is intervened to provide safe and reliable guarantees for remote operations.
