An integrated approach for inverse kinematics of unconventional manipulators using Monte Carlo random sampling method and Newton iterative method

Accurate determination of the inverse kinematics for the drilling arm of a drilling and anchoring robot is crucial in achieving automatic support in coal mine roadways. Addressing issues such as poor accuracy, limited real-time performance, and susceptibility to local optima, this study presents a novel approach for solving the inverse kinematics problem of an unconventional mechanical arm by combining Monte Carlo random sampling method and Newton iteration method. Initially, a kinematics model is established based on the structure of the drilling arm, and individual coordinate systems are defined for each joint to enable forward kinematics solutions. The Monte Carlo method is employed to determine the motion space of the drill boom. By subdividing the motion space into smaller cubes with a defined step size, a mapping relationship is established between the spatial coordinates of these cubes and the corresponding joint variable values. Using the transformation matrix associated with a given target space point, an index function is employed to identify the relevant small cubes. The points within these cubes, which are closest to the target space point, are calculated, and their corresponding joint variable values are used as initial values. The Newton iteration method is then introduced, utilizing the iterative formula for multivariate functions to determine the variation of each joint variable. The inverse kinematics solution for the unconventional manipulator is obtained through iterative cycles. The simulation results show that, compared with Newton-Raphson iterative method based on random initial values and the particle swarm optimization algorithm, the corresponding average angle error of the calculation results of this method is reduced by 64.98% and 57.34%, and the average time consumption is reduced by 35.90% and 22.33%, respectively, thereby enhancing solution accuracy and real-time performance. The feasibility and effectiveness of the proposed Monte Carlo and Newton iteration method for solving the inverse kinematics problem in unconventional manipulators are verified. Overall, this research provides evidence supporting the practicality and efficiency of the proposed Monte Carlo random sampling method and Newton iteration method for accurate inverse kinematics solutions in unconventional manipulators.