Forward solution algorithm of Fracture reduction robots based on Newton-Genetic algorithm

The Fracture Reduction Robot (FRR) is a crucial component of robot-assisted fracture correction technology. However, long-term clinical experiments have identified significant challenges with the forward kinematics of the parallel FRR, notably slow computation speeds and low precision. To address these issues, this paper proposes a hybrid algorithm that integrates the Newton method with a genetic algorithm. This approach harnesses the rapid computation and high precision of the Newton method alongside the strong global convergence capabilities of the genetic algorithm. To comprehensively evaluate the performance of the proposed algorithm, comparisons are made against the analytical method and the Additional Sensor Algorithm (ASA) using identical computational examples. Additionally, iterative comparisons of iteration counts and precision are conducted between traditional numerical methods and the Newton-Genetic algorithm. Experimental results show that the Newton-Genetic algorithm achieves a balance between computation speed and precision, with an accuracy reaching the 10${}^{-4}\mathrm{mm}$ order of magnitude, effectively meeting the clinical requirements for fracture reduction robots in medical correction.