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This paper presents an efficient method for minimum distance calculation between a robot and its environment and the implementation framework as a tool for the verification of robotic systems' safety. Collision is the most fundamental safety problem in robotic systems. Therefore, robotic system software must be verified to ensure that there are no risks of collision during development and implementation. The online distance tracker (ODT) is intended to provide minimum distances between the robots and their environments for verification of system software to inspect whether it causes a collision risk. The proposed method employs the representations of the robot and its environment with cylinders and an occupancy map. Furthermore, the bounding box approach improves the performance of the minimum distance calculation regarding computational cost. Finally, the method is applied to a realistically simulated twin of the ROKOS, which is an automated robotic inspection cell for quality control of automotive body-in-white and is actively used in the bus manufacturing industry. The simulation results demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]