Vision-guided robotic pick-and-place with variable focal length optics: mathematical modelling, illumination optimisation, and sub-millimetre accuracy assessment

The application of robot-based visual pick-and-place technology entails the simultaneous optimization of optics and lighting systems to ensure sub-millimetre accuracy for high throughput flexible manufacturing processes. This paper explores the development, mathematical modeling, and practical application of a unified framework of a robotic manipulator with a modular machine vision system using interchangeable C-mount lenses over a focal length of 3–35 mm. An analytical model is formulated for the field of view, depth of focus, resolution, and radial distortion of optics. The performance of six lighting modes, namely ambient, low intensity ring LED, high intensity ring LED, dome diffuse, coaxial, and structured light, is compared based on detection ratio, Michelson contrast ratio, and positional error for 4,200 samples. The combined optical-photometric model for performance optimization regarding both focal length and illumination under variable operating conditions is presented. The hand-eye calibration procedure based on the Tsai-Lenz method results in a reprojection error of 0.12 pixels. The RMS error propagation model predicts a total positional uncertainty of 0.450 mm, which compares closely with the experimentally measured value, the 0.090 mm difference being well within the ± 0.19 mm (1σ) positional precision of the system. The optimum (f = 25 mm, structured illumination) yields an accuracy of 0.54 mm in position and 0.76° in orientation, with a precision of ± 0.19 mm (1σ) and a success rate of 98.7% in a validation run of 1,200 placements at the optimal configuration, outperforming the four benchmarked techniques considered in this study.