A direct linear solution with Jacobian optimization to AX=XB for hand-eye calibration1

作者：Jianfei Mao^*; Qing Tian; Ronghua Liang

来源：WSEAS Transactions on Systems and Control, 2010, 5(7): 509-518.

• Closed form solutions
• Hand-eye calibration
• Jacobian optimization
• Jacobians
• Orthonormal
• SVD

A linear closed-form solution followed by Jacobian optimization is proposed to solve AX=XB for hand-eye calibration. Our approach does not require A,B satisfying rigid transformation rather than the classic ones based on quaternion algebra or screw rule. We firstly give the detailed proof of the optimal orthonormal estimation for an arbitrary scale matrix. With the theorem, a linear closed solution based on singular value decomposition (SVD) and the rule of optimal rotation estimation, is presented, followed by the nonlinear optimization with the proposed Jacobian recursive formula. Detailed deduction and demonstration are given based on matrix theory. Since our approach is applicable for non-rigid transformation rather than the classic ones, our technique is more flexible. Plenty of computer simulation and real data implementation indicate that: (1) In computation of initial value, our technique has higher precision and more robustness. (2) As more equations are added, initial value will converge to final value gradually, which shows it credible to regard initial value as final solution when many equations are supplied.

• 出版日期2010
• 单位浙江大学