Deflection estimation of industrial robots with flexible joints

The application of industrial robots in manufacturing industries has received considerable concerns due to the high flexibility, multifunctionality, and cost-efficiency. It is well known that the robot positioning accuracy is susceptible to the load and motion of robots owing to the insufficient stiffness of robots. Therefore, the machining accuracy improvement has been a research focus in the robotic manufacturing industries in the last decade. To overcome the measurement difficulty of the joint torque and position as well as the complex dynamic coupling between rotors and links, two forward dynamics algorithms for the robot deflection estimation are proposed in this paper. The robot kinematics and dynamics algorithms considering the dynamic coupling between rotors and links are developed based on Lie theory. The forward dynamics equations of robots are solved via the proposed algorithms: the implicit numerical integration algorithm and numerical iterative estimation algorithm. When only the motor position is available, the implicit numerical integration algorithm is employed to solve the forward dynamics equations to estimate the joint torque and position. At the same time, when both the motor position and torque are available, the forward dynamics equations can be reorganized as algebraic equations and solved by the numerical iterative estimation algorithm. Simulations of a 6-DOF serial robot are performed to verify the accuracy of the proposed algorithms.