SYSTEM IDENTIFICATION OF AN UNINHABITED SURFACE VEHICLE
Date
2024
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Abstract
Uninhabited Surface Vehicles (USVs) require a robust and capable Guidance, Navigation, and Control (GNC) system to operate effectively. GNC requires a model of the USV’s dynamics for state estimation, control, and other applications. Data-driven modeling, the process of determining practical models from data, is a re-emerging method and active field of research for modeling system dynamics. The purpose of this research is to explore the use of PySINDy, an open-source Python module that implements the Sparse Identification of Nonlinear Dynamics (SINDy) data-driven system identification method, to generate a generalizable and interpretable model of a Wave Adaptive Modular Vessel (WAM-V). PySINDy is equipped with tools to simplify the modeling process, such as a library class to initialize a matrix of nonlinear terms for SINDy to create models from, a fit function that incorporates control inputs and time series data to infer a model from, and a score function that evaluates the model’s performance against validation data using ?2 as the scoring metric. First, existing examples of PySINDy’s capabilities are explored and demonstrate that the algorithm can produce the underlying model of a numerically simulated Lorenz system with: no noise (?2=1.00), with an external force acting on the system (?2=0.99), with “low” and “high” level noise (R5% ?????2=0.99; R60% ?????2=0.78), and with filtered low and high noise (?5% ?????2=1.00; ?60% ?????2=0.99). These test cases illustrate SINDy’s ability to generate effective models in various circumstances expected by a real system as indicated by the high ?2 values. Second, with a baseline understanding of SINDy’s capabilities, Blanke’s simplified version of Norrbin’s second-order nonlinear model, suggested as a representative maneuvering model for simulation in Fossen1, is utilized to simulate the dynamics of a WAM-V. Like the Lorenz system case studies, simulated data with low- and high-level noises are filtered and used to generate models which score ?5% ?????2=0.81 and ?75% ?????2=0.78 indicating SINDy’s capability to generate effective models for a potentially representative USV and confirm that straight-line and turning circle maneuvers provide enough data variety to sufficiently capture the system’s behavior. Third, and finally, the same procedure is replicated in a real-world experiment by recording and subsequently estimating the full state data of a WAM-V at Sand Island in calm water (i.e. no waves - wind and current disturbances were present). SINDy generated a second-order nonlinear cross-coupled modulus model with a model score of ?2=0.28. Due to the low validation score, the time-constant of the generated model, which is approximately 14s, is estimated by analyzing the model’s rise time from a step input and the quality of the model is also validated by its ability to predict the state of the system over 3 time-constants (i.e. 36 s). This time horizon was applied to create a sliding window on the validation dataset with 0-36 s, 12-48 s, and 24-60 s windows where the initial conditions of the model are updated at the beginning of each time window and results in an ?2 score of 0.32, 0.28, and 0.29 respectively.
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Mechanical engineering, Robotics, SINDy, System Identficiation, USV
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120 pages
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