Unified Gravitational and Elasto-Geometrical Calibration for an Industrial Robot Using Closed-Form Formulation

The absolute positioning accuracy of industrial robots is significant in modern manufacturing scenarios. Mainstream approaches mostly focus on calibrating kinematic and joint compliance models to compensate for position errors. However, previous elasto-geometrical calibrations typically employ a priori gravity parameters (e.g., link mass) to estimate the compliant joint deformation, which inevitably leads to a loss of accuracy. To obtain more accurate results, this paper proposes a unified gravitational and elasto-geometrical calibration method based on the closed-form expression. The proposed method establishes a unified model that integrates kinematic, joint stiffness, and gravity parameters, thereby enabling the handling of inter-model coupling characteristics. An analytic derivative of gravity torque is derived, and an improved adaptive damping Levenberg-Marquardt algorithm is utilized to accelerate calibration convergence. Finally, the position error of a serial industrial robot is reduced from 3.329 mm to 0.251 mm using the proposed method. The load generalization experiments further validate the effectiveness of the proposed method.