Abstract—Bone drilling represents a fundamental procedure in orthopedic trauma surgery. Currently, this operation is predominantly executed manually using handheld instruments. While research on assistive bone drilling devices exists, these studies have largely employed serial mechanisms, which exhibit significant limitations including disturbance uncertainties and dynamic control deficiencies. Recent investigations have explored parallel mechanisms for drilling applications, focusing on position/force control at the drilling interface, force measurement protocols, and bone breakthrough detection. Bone drilling forces demonstrate substantial variation across a spectrum of parameters. Parallel robotic structures offer advantages through enhanced mechanical stiffness and reduced error propagation, providing rationale for this study’s development of a hybrid position/force control algorithm implemented on a 3-Degree of Freedom (DOF) parallel robot for bone drilling applications. The developed 3-DOF parallel robot consists of three arm components and three parallelogram mechanisms utilizing rotational and spherical joint configurations. Our research methodology encompasses: development of a mechanical structure incorporating three single-axis force sensors; derivation of dynamic equations through first-order Lagrangian formulation; and design of a position/force hybrid controller with synchronization calibration matrix integration. The force control algorithm utilizes an approximate Jacobian matrix of the parallel robot structure. MATLAB simulations demonstrate that this approximation reduces computational requirements by 50%. Experimental testing confirms the controller’s functional efficacy and measurement accuracy, validating its potential implementation in surgical applications.

Keywords—parallel robot, trajectory tracking control, position/force control, trajectory tracking, Jacobian approximation matrix, Particle Swarm Optimization (POS)

Cite: Quan Dam Hai, Thanh Bui Trung, Gam Le Thi Hong, and Ngoc Pham Van Bach, "Force/ Position Control Based on PSO and Approximately Jacobian for 3-DOF Parallel Robot for Bone Drilling," International Journal of Mechanical Engineering and Robotics Research, Vol. 14, No. 4, pp. 395-406, 2025. doi: 10.18178/ijmerr.14.4.395-406

Copyright © 2025 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).