RCM Constraint-Consistent Dynamic Control in Surgical Robots

Robotic-assisted minimally invasive surgery (RAMIS) requires accurate enforcement of the remote center of motion (RCM) constraint to ensure safe tool motion through a trocar. Existing virtual RCM controllers are commonly formulated either at the kinematic level or as task-space objectives, which makes torque-level enforcement under trocar motion and physical interaction difficult to formulate consistently. This paper models the RCM as a rheonomic holonomic constraint and incorporates it into a projection-based inverse-dynamics controller with explicit constrained/free-motion torque decomposition. The resulting formulation unifies kinematic RCM enforcement and task-space tracking at the torque level, while preserving a constraint-consistent structure for residual regulation and null-space compliance. The proposed controller is validated in simulation and on a RAMIS training platform against representative projection-based and constrained-dynamics baselines. Across spiral tracking, varying insertion depth, moving trocar conditions, and human interaction, the method achieves lower RCM residuals and smoother torque profiles while maintaining accurate tool-tip tracking. These results support the use of constraint-consistent torque control for reliable virtual RCM enforcement in surgical robotics. The project page is available at https://rcmpc-cube.github.io