A passive convex optimal control algorithm for teleoperating a redundant robotic arm in minimally invasive surgery

In recent years, the remote center of motion (RCM) constraint has moved from purely mechanical to software implementation, enabling the use of serial manip- ulators in robotic-assisted minimal invasive surgery. However, ensuring safety with software-based RCM presents challenges. This article addresses this issue by introducing a novel control algorithm for a 7-DOF redundant robotic arm, taking into account a software RCM while considering system passivity and kinematic constraints. The algorithm is both a control optimizer and a robot kinematics inversion, enabling precise and dexterous control for various surgi- cal tasks and other control applications. By formulating a quadratic optimization problem under linear constraints, the algorithm guarantees the robotic arm’s performance, safety, and stability under communication delay. Experimental validation demonstrates the effectiveness and accuracy of the control algorithm in executing a surgical training task (peg-and-ring) during bilateral teleopera- tion. The results highlight the successful implementation of the RCM constraint, ensuring patient safety and optimizing the manipulation capabilities of the robotic arm.