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In response to the compliant tracking of surgical intent and adherence to safety range constraints in semi-active knee arthroplasty robots, a model predictive impedance control (MPIC) algorithm is proposed. First, to enhance this algorithm’s operational efficiency, the Stirling interpolation method is employed to linearize the dynamics model of the robotic arm as the predictive model. This method offers computational simplicity and high-precision solving accuracy. Second, based on the impedance model, the force-compliant control mechanism is used to identify the surgeon’s force intention, thereby generating the desired motion trajectory for the robotic arm. To facilitate programming implementation, the impedance model is discretized. Third, leveraging the rolling optimization and feedback correction properties of model predictive control, a virtual state enhancement is designed to improve the explicit constraint handling capability of the MPIC algorithm. This enhancement addresses the infeasibility issues encountered by traditional model predictive control near state constraint boundaries in practical applications. Transforming the model predictive problem into a quadratic programming problem reduces the difficulty of solving the model predictive problem and increases problem-solving speed. Finally, MPIC is integrated as the lower-level position-tracking controller for the robotic arm, with the impedance model serving as the upper-level task planning controller, thus forming the MPIC controller. Comparative experiments with three-loop PID (Proportional integral derivative) control are conducted on the ROKAE seven-axis collaborative robot experimental platform, confirming that the MPIC algorithm achieves better trajectory tracking accuracy and response speed, effectively realizing the desired impedance dynamics and yielding superior compliance. Additionally, further validation is conducted by installing a six-axis force sensor between the end-effector and the wrist of the robotic arm to measure human–robot interaction forces, confirming that the MPIC algorithm exhibits better compliance than traditional position-tracking control methods. Drag experiments are designed to verify the active constraint effect of MPIC on mechanically coupled robotic arms with complex system parameter structures, demonstrating that the control algorithm can actively constrain the motion of the robotic arm when it is manually manipulated to exceed the set state constraint range. Overall, the MPIC algorithm achieves better compliance and meets the safety requirements for knee arthroplasty surgery compared to traditional three-loop PID control methods. This advancement holds promise for further development and adoption of semi-active surgical robots, reducing the complexity of using surgical robots as surgeons and accelerating the widespread adoption of domestically produced surgical robots in hospitals. This paper should promote the practical application of semi-active surgical robots.