Real-time inverse kinematics for robotic manipulation under remote center-of-motion constraint using memetic evolution

Abstract

Robotic manipulation in surgical applications often demands the surgical instrument to pivot around a fixed point, known as remote center of motion (RCM). The RCM constraint ensures that the pivot point of the surgical tool remains stationary at the incision port, preventing tissue damage and bleeding. Precisely and efficiently controlling tool positioning and orientation under this constraint poses a complex Inverse Kinematics (IK) problem that must be solved in real-time to ensure patient safety and minimize complications. To address this problem, we propose PivotIK, an efficient IK solver that combines efficient evolutionary exploration with multi-objective Jacobian-based optimization. PivotIK can track desired tool poses accurately while satisfying the RCM constraint in real-time. We evaluated PivotIK through simulations and real-world experiments using redundant robotic manipulators with multi-degree-of-freedom surgical instruments. We compare PivotIK with other IK solvers in terms of solve rates, computation times, tracking errors, and RCM errors under various scenarios, including unconstrained and RCM-constrained trajectories. Our results show that PivotIK achieves superior performance, solving the IK problem in less than 1 ms with errors below 0.01 and 0.1 mm for tracking and RCM, respectively. Our real-world experiments confirm the effectiveness of PivotIK in ensuring smooth trajectory tracking and RCM compliance. PivotIK offers a promising solution for real-time IK for robotic manipulation under RCM constraints in surgical applications.