Application of Udwadia-Kalaba Approach to Tracking Control of Surgical Robot

There is a significant anticipated shift from operating theater (OT) surgery to digital OT, with Robotic Assisted Surgery (RAS) emerging as the most representative aspect of this transformation. RAS which uses robot to assist the surgeon while operating a patient offers several technical advantages such as greater precision, and more accurate compared with conventional surgery. The paper introduces an explicit dynamic control equation for a surgical slave robot, leveraging the UK theory, which provides a succinct and precise equation of motion for constrained mechanical systems with holonomic or nonholonomic constraints. The performance specifications, including the required trajectory, are regarded as servo constraints in a second-order matrix format. These secondorder constraints are integrated into the dynamics and constraint-following control. The UK theory is utilized to derive a closed-form expression for the control force necessary to accurately guide the surgical robot along the predefined trajectory. Notably, no approximations, linearizations, or auxiliary variables like Lagrangian multipliers or pseudogeneralized speeds are employed in the dynamic modeling or analysis. Simulation results show the simplicity, efficacy and accuracy of the proposed approach when applied to the surgical robot.