A Simultaneous Ultrasound-Robot Calibration Approach for Dual-Robot Intervention by Solving the AXP = YCQ Problem

Robotic ultrasound-guided intervention is an effective approach to ameliorating the quality of the intervention surgery. Ultrasound-robot calibration, conducted to obtain spatial relationships among different frames, is an essential step for the ultrasound-guided robotic system. However, existing step-by-step calibration methods mainly rely on phantoms or external trackers and are prone to error accumulation and workflow complexity. In this article, a novel simultaneous ultrasound-robot calibration approach is proposed. It calibrates the ultrasound-guided dual-robot intervention system in a one-step process without resorting to any phantoms or external trackers, thereby enhancing the calibration accuracy and simplifying the workflow. Specifically, an ${\text {AXP} = \text {YCQ}}$ calibration equation is formulated to transform the calibration problem into the equation solving. For simultaneously deciding the equation’s unknowns, the Kronecker-product-based closed-form method and the Gauss–Newton iterative method based on the Lie algebra are proposed. The closed-form method offers a coarse estimation to the iterative method. Evaluation experiments are implemented to illustrate the favorable performance of the proposed approach. Furthermore, an in vitro ultrasound-guided dual-robot intervention experiment was also realized with the proposed approach and the intervention errors were 0.75 ± 0.27 mm when the calibration sample data size is 50.