A Human-Robot Collaborative System for Maxillofacial Osteotomy Assisted by Virtual Fixtures Based on Admittance Control

Precise and safe execution of maxillofacial osteotomy remains challenging due to complex anatomy and dynamic human-robot interaction. This study proposes a collaborative control system combining parametrized-surface virtual fixtures and admittance-based hybrid force-position control. The osteotomy surface is extracted from preoperative CT data, projected and spline-fitted to generate virtual constraint. An anisotropic admittance model ensures compliant motion in the cutting direction while enforcing geometric constraints in normal and depth directions. The control scheme was implemented on a UR5e manipulator and validated through three experimental trials on identical anatomical mandible models. Postoperative CT scans were registered to preoperative plans, and cutting accuracy was evaluated using 13 anatomical landmarks per model. The overall mean error was 0.81 mm, with a maximum deviation of 1.48 mm and a standard deviation of 0.53 mm. 3D error map revealed localized deviations. The robot demonstrated stable and responsive behavior across trials, with smooth tool interaction and no safety violations. These results confirm that the proposed system achieves millimeter-level precision while supporting intuitive human-robot cooperation, offering a promising basis for future clinical translation.