Nonclassical Parametric Variational Technique to Manipulability Control of a Serial‐Link Robot That Is Used in Treatment of Femoral Shaft Fractures

Robot‐assisted intramedullary nailing is a minimally invasive surgical procedure commonly used to treat femur fractures. Despite its benefits, there are several disadvantages associated with this technique, such as frequent malalignment, physical fatigue, and excessive radiation exposure for medical personnel. Therefore, it is crucial to ensure that robotic surgery for fracture reduction is precise and safe. Precise calculation and regulation of the robot’s reduction force are of utmost importance. In this study, we propose a manipulator that utilises robot assistance and indirect contact with the femur to effectively reduce fractures in the shaft. The dynamics of the reduction robot are analysed using the implicit function theorem, which allows us to address the reduced problem. A parametric approach is presented to tackle the initial algebraic constraints, enabling the approximation of the state‐space solution while simultaneously controlling the class of constraints in a multiway manner. This approach simplifies the problem from an infinite‐dimensional one to a finite‐dimensional one, leading to an approximate solution obtained by solving a set of control linear algebraic equations. The proposed robotic‐assisted system enhances fracture repositioning while reducing radiation exposure for both the patient and the medical staff. Through numerical results and their practical application, we have developed an efficient method that yields positive outcomes.