An Optimal Control Approach with Decoupled Space Constraints for the Magnetic-Assisted Surgical Robot

Magnetic-assisted surgical robots represent an innovative direction within the field of medical robotics, due to their significant potential in addressing the instrument interference challenge during the single-port laparoscopic surgery. This paper proposes an optimal control approach for controlling the magnetic-assisted surgical manipulator translating and rotating in the single-dimensional space to execute specific surgical procedure. Firstly, we delineate the manipulator tasks and describe how to utilize a medical foot pedal to control it. Secondly, we model the tasks as an optimization problem, taking manipulator kinematics, task constraints, and safety requirements into consideration. Thirdly, in order to map foot pedal control commands to end-effector movements and achieve precise motion control in single-dimensional space, we propose Decoupled Space Constraints (DSCs) and use the Differential Dynamic Programming (DDP) to solve the optimization problem. Finally, simulation experiments are conducted on a 7-DOF manipulator and the result shows that our approach effectively improves trajectory planning accuracy in single-dimensional space and demonstrates reliable performance in addressing multiple constraints for the magnetic-assisted surgical robot.