Integration of Sensor Data and Mathematical Modeling of Underwater Robot Behavior Using a Digital Twin

Introduction. Control of underwater robotic complexes (URC) is complicated by factors, such as inertia, stochastic disturbances, and lack of navigation infrastructure. Existing approaches to modeling and predicting URS behavior are known for their weak or absent integration of data from real sensors in real time. By eliminating this gap in integrated solutions, it is possible to combine physical models, digital twins, and visualization. A promising tool for overcoming the above limitations is a digital twin (DT), which provides an accurate digital representation of an object through the integration of data from physical sensors and mathematical models. The objective of the presented study is to develop a method for predicting the dynamics of the URC using a digital twin to improve the efficiency of autonomous control. Materials and Methods. The basis of the study was the development of a mathematical model of the motion of an underwater robotic complex. It included differential kinematics, modeling of environmental resistance, and rotation dynamics. The following sensors were used to collect and process data: incremental encoders, a three-axis accelerometer, and a gyroscope. A proportional-integral differentiating (PID) controller was applied to control the motion along each axis. The Unity Game Environment was used to visualize and test the model. It created a digital twin module with the ability to display the system state in real time. The Arduino IDE platform was used as software for low-level programming, as well as MATLAB and Python for data analysis and graphing. Results. To verify the model, experiments were conducted on a physical model. They were compared to the simulation of the object's behavior in a virtual environment. Graphs of discrepancies between physical and simulated trajectories were presented. Statistical metrics characterizing the accuracy of the digital twin were calculated. The maximum deviation in coordinates did not exceed 5.3 mm, the average angular deviation was 3.5°. This confirmed the reliability and practical applicability of the proposed model in autonomous control of a robotic complex. It was also found that the average error along X — 3.11 mm, along Y — 2.92 mm. The average error in angle Z — 1.8°. The response time was less than 10 ms. The stability of the digital twin to minor fluctuations in the data was provided by smoothing the input data, the stability of the system regulator, and adaptation of the model to the calibration values at the start of each cycle. Discussion and Conclusion. Digital twins are suitable for predictive control and monitoring of an object under uncertainty. The proposed approach can be scaled for various types of robotic systems operating in aggressive and poorly predictable environments. Further research in this area may involve the introduction of adaptive and neural network control methods.