Vector polynomial based analytical inverse kinematics and configuration design of 6R robotic arms

Robotic arms with high precision play a crucial role in industries like aerospace and intelligent manufacturing. Currently, industrial robotic arms typically adopt spherical wrists to obtain analytical solutions; however, manufacturing-related structural errors significantly reduce the end effector's absolute positioning accuracy, impeding the development towards high-precision autonomous control. This study presents a series of kinematic modelling, configuration design, and analytical inverse solutions for robotic arms with the goal of delivering precise and effective inverse kinematic solutions, while taking the engineering limitation into consideration. Taking the vector polynomial system as the key premise, an iterative kinematic model with the fewest number of equations, independent variables, and orders of magnitude is then established. Through decoupling analysis of the position and attitude in the kinematic model, configuration designs of robotic arms with orthogonal or parallel axes are proposed without adhering to the restrictions of three-axis intersection. Additionally, the inverse kinematic issue is addressed by conversion into polynomial space using the Dixon elimination approach. Eight sets of inverse kinematic solutions are obtained for any reachable position and attitude in simulation. The computation time does not exceed 2 milliseconds, and both position and attitude relative errors are below 10–15, enhancing computational accuracy for robot kinematics. The work of this paper provides a practical kinematic theory for the development of robotic arms with high absolute positioning accuracy and efficiency.