This paper considers the inverse kinematics problem of a robotic arm applying minimum mean square error with variance-based control. The proposed algorithm achieves optimal results by minimizing the average error, even when considering variance calculations. Its performance is comparable to that of the algorithm that utilizes optimally tuned singular value decomposition (SVD). The calculated variance values are added to the diagonal terms of the matrix as in the damped least squares method in the inverse matrix operation. This indicates that optimal performance can be achieved even when a Moore-Penrose pseudo-inverse matrix is employed instead of SVD. The effectiveness of the proposed method is validated with seven-degree-of-freedom (7-DoF) (1 rail + 6-DoF arm) and 6-DoF robots. By introducing practical error control methods, this paper contributes to enhancing the overall comprehension of error-related algorithms.

Current pipelinable dividers require very large lookup tables. We propose a cost-effective pipelinable divider that uses a modified Taylor-series expansion and has a smaller lookup table than other pipelinable dividers. The proposed divider requires about 27 percent less area than the pipelinable divider based on normal Taylor-series expansion in single precision.