Abstract：A new method for solving the r-circulant solution and symmetric r-circulant solution of reduced biquaternion matrix equation AX＋XB＝D is proposed in this paper. According to the properties of reduced biquaternion， the vec operator is used to uniformly transform the position of variable X to the end of the reduced biquaternion equation.Then， the reduced biquaternion matrix equation is transformed into the real matrix equation according to the real representation method of reduced biquaternion. The independent elements of the matrix are extracted by using the H-representation method of special matrix to participate in the operation， which reduces the complexity of the operation. The effectiveness of the algorithm is verified by numerical experiments. Finally， the content of this paper is applied to the hand-eye calibration method of harvesting robot.
2023, Vol. 57 
