Simultaneous robot-world and hand-eye calibration by the alternative linear programming.

• The hand-eye calibration is reconsidered as minimizing two kinematic loops' errors. • The alternative linear programming is introduced to solve the calibration. • The semi-convex constraint is also proposed for the construction of cost function. • Two formulations of calibration are presented: homogeneous matrix, dual quaternion. A typical hand-eye robot system has two related kinematic loops, which proper functioning requires the accurate determination of robot-world (RW) and hand-eye (HY) transformations in them. Insofar as HY calibration can resolve only the issues related to HY transformation, this study is focused on the joint treatment of the RW&HY transformations, which process is referred to as simultaneous RW&HY calibration. An alternative linear programming is adopted for the construction of semi-convex objective functions via two algorithms. These involve the homogeneous matrix and dual quaternion parameterizations, respectively. Their feasibility was further tested using simulated and real experimental datasets and compared to the results obtained via two available methods (NL and LMI). The results obtained strongly suggest that the homogeneous matrix parametrization (ALP1) had better performance than the dual quaternion one (ALP2). Meanwhile, both of them yielded the good optimal calibration solutions instead of local minima ones. Therefore, both formulations provide new insights into the behavior and complexity of the simultaneous RW&HY calibration. [ABSTRACT FROM AUTHOR]