Analytical Kinematic Model and RCM Control of a Parallel-Serial Steady-Hand Eye Robot

Maintaining a precise remote center of motion is essential for safe and accurate tool manipulation in retinal microsurgery. However, existing numerical Jacobian identification methods for parallel manipulators often exhibit nonlinear, workspace-dependent inaccuracies and require frequent recalibration, limiting their reliability and clinical applicability. To address these challenges, this study presents an analytical kinematic framework for a hybrid parallel-serial robot designed for retinal surgery, known as the Steady-Hand Eye Robot (SHER 3.0). Closed-form solutions for forward and inverse kinematics, as well as analytical formulations of the direct and inverse Jacobians, are derived to ensure consistent motion estimation across the workspace. The kinematic performance of SHER 3.0 is analyzed to evaluate the manipulability and workspace efficiency. Building on these models, a model predictive control strategy is implemented on SHER 3.0, which maintains the remote center of motion constraint at the sclerotomy with sub-millimeter accuracy, with a root mean square error of 0.55 ± 0.12 mm, in a pilot study on a teleoperation experiment. Experimental results demonstrate the effectiveness of the proposed analytical models and control framework in enhancing robot motion stability and robustness of the controller in maintaining the remote center of motion constraints, enabling safe robot-assisted retinal microsurgery.