Kinematic calibration via 3D reconstruction in constrained measurement volume: Application to serial manipulators with miniaturized end-effectors

High-precision kinematic calibration for manipulators with miniaturized end-effectors (such as surgical forceps and microneedles) remains challenging due to conventional measurement systems’ limitations in applicability, accuracy, and measurement volume. These constraints demand additional tool center point calibration after kinematic calibration, increasing system complexity and associated costs. In this work, a novel kinematic calibration method is proposed for serial manipulators to solve these challenges, employing a three-dimensional reconstruction system with a limited measurement volume (10.24 mm × 10.24 mm × 7.68 mm) to capture three-dimensional end-effector images for precise positioning, thereby eliminating additional tool center point calibration. To address measurement volume constraints, multiple measurement frames are employed to expand the measurement coverage across the manipulator’s workspace. End-effector positions measured from these frames construct an error model via the product of exponentials formula, with a novel algorithm identifying high-dimensional parameters induced by these frames. Validation was performed through simulations and comparative experiments on a six-degree-of-freedom manipulator equipped with a miniaturized end-effector. The results demonstrate that the proposed method achieves higher positioning accuracy compared to the conventional baseline (laser tracker combined with tool center point calibration), confirming the method’s effectiveness for the high-precision calibration of manipulators with miniaturized end-effectors.