Simultaneous Calibration of Multicoordinates for a Dual-Robot System by Solving the AXB = YCZ Problem

Multirobot systems have shown great potential in dealing with complicated tasks that are impossible for a single robot to achieve. One essential problem encountered in cooperatively working of the multirobot systems is the unknown initial transformation relationships from hand to eye, base to base, and flange to tool. In this article, the problem of multicoordinates calibration for a dual-robot system is formulated to a matrix equation AXB = YCZ. A novel approach for simultaneously solving the unknowns in equation AXB = YCZ is proposed, which is composed of a closed form method based on the Kronecker product and an iterative method which converts the calculation of a nonlinear problem to an optimization problem of a strictly convex function. The closed form method is used to quickly obtain an initial estimation for the iterative method to improve the efficiency and accuracy of iteration. In addition, a series of conditions on the solvability of the problem are proposed to guide the operators to select appropriate robot attitudes during the calibration process. To show the feasibility and superiority of the proposed iterative method, two other calibration methods are chosen to be compared to the proposed method through simulation and practical experiments. The comparison results verify the superiority of the proposed method in accuracy, efficiency, and stability.