Accurate calibration of the robot hand-eye (X) and robot-world (Y) relationships is extremely important for visually-guided robotic systems, and is usually symbolized by the AX=YB equation. The existing methodologies always calibrate the X and Y matrices using the separation of the rotational and translational components, causing the error propagation and accumulation. While the simultaneous calibration solves the derived linear matrix equation by the SVD (Singular Value Decomposition) based approach, which produces unreliable results depending on the smallest singular value of the regression matrix. To this end, the work contained herein proposes a novel and generic calibration methodology for solving the AX=YB problem using the LMI-SDP (Linear Matrix Inequality and Semi-definite Programming) optimization. In this approach, the linear form of the calibration equation is retrieved by means of the Kronecker product, and formulated as an optimization problem involving the unknown variable matrices X and Y with convex constraints, in which the simultaneous solution is obtained via the LMI-SDP techniques. The results procured via the simulation analysis, accounting for the presence of noise levels and different data pairs, as well as the calibration experiments, are compared to those produced using the classical iterative method and DQ (Dual Quaternion)-based approach, thereby verifying the accuracy and efficacy of the proposed method. Note to Practitioners—The motivation behind this work stems from the simultaneous calibration issues pertaining to robot-eye and robot-workpiece coordinate relationships, that are present in vision-guided robotic systems. Considering the inaccuracy and robustness deficiencies of the existing methodologies, due to the separated calibration of the rotational and translational components, this paper proposes a generic and efficient calibration methodology to deal with the AX=YB problem, using the Kronecker product and the LMI-SDP optimization. Simulation analysis reveals that the proposed algorithms exhibit robustness under different noise levels and data pairs. Moreover, the practicability of the algorithm has also been verified via practical experiments. The average errors with 16 sets of calibration data can reach 0.0056rad in the rotational component, and 0.2529mm in the translational component. The proposed methodology can be extended to the practical applications of the coordinate calibration involving the multi-robot systems with visual sensors.

This paper studies the synthesis of high-dimensional datasets with differential privacy (DP). The state-of-the-art solution addresses this problem by first generating a set M of noisy low-dimensional marginals of the input data D , and then use them to approximate the data distribution in D for synthetic data generation. However, it imposes several constraints on M that considerably limits the choices of marginals. This makes it difficult to capture all important correlations among attributes, which in turn degrades the quality of the resulting synthetic data. To address the above deficiency, we propose PrivMRF, a method that (i) also utilizes a set M of low-dimensional marginals for synthesizing high-dimensional data with DP, but (ii) provides a high degree of flexibility in the choices of marginals. The key idea of PrivMRF is to select an appropriate M to construct a Markov random field (MRF) that models the correlations among the attributes in the input data, and then use the MRF for data synthesis. Experimental results on four benchmark datasets show that PrivMRF consistently outperforms the state of the art in terms of the accuracy of counting queries and classification tasks conducted on the synthetic data generated.