Real-time states estimation of a farm tractor using dynamic mode decomposition

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ORIGINAL ARTICLE

Real‑time states estimation of a farm tractor using dynamic mode decomposition Hao Wang1   · Noboru Noguchi2 Received: 13 June 2020 / Accepted: 26 October 2020 © The Author(s) 2020

Abstract We present a pure data-driven method to estimate vehicle dynamics from the measurements of sideslip and yaw rate in the use of GPS and inertial navigation system. The GPS and INS configuration provides vehicle position, velocity vector, vehicle orientation, and yaw rate observations. A new dynamic mode decomposition with control (DMDc) method denoises the state observations by adopting the total least-squares algorithm. The total least-squares DMD with control (tlsDMDc) helps discover the underlying dynamics with the time-dependent observations of states and external control. The experiments of a simulated linear dynamic model with synthetic Gaussian noise illustrate that the solutions of tlsDMDc are more accurate than the standard DMDc to characterize underlying dynamics with imperfect measurements. We additionally investigate how the algorithm performs on vehicle motion deduction and sensor bias correction. It has been shown that the tlsDMDcbased state estimator with the couple of GPS and inertial sensor measurements provides accurate and robust observation in the presence of model error and measurement noise. Keywords  System identification · Machine learning control · Total least squares · Regression model · Vehicle dynamics

Introduction The automation of agricultural machinery is considered to be one of the most efficient ways of improving productivity and quality of farming. Research and development are focused on developing full autonomy, with the ultimate goal of designing unmanned vehicles or field robots for farming work (Han et al. 2018). To keep an accurate and stable path tracking performance, significant research progress has been made in vehicle control techniques, including navigation sensors, vehicle models, and steering controllers. There is abundant work on designing path tracking controllers, such as the geometric approach, the kinematic control laws, the optimal control, robust control and model predictive control (MPC), and so on (Backman et al. 2012; Li et al. 2016). Most controller designs often begin with vehicle * Hao Wang [email protected] 1



Beijing Research Center of Intelligent Equipment for Agriculture, Beijing Academy of Agriculture and Forestry Sciences, Beijing 100097, China



Research Faculty of Agriculture, Hokkaido University, Sapporo, Hokkaido 065‑8589, Japan

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modeling. The pure pursuit and its extension velocity independent controllers with a simple kinematic model, under nonholonomic constraints, control the motion of a vehicle reasonably well at low speed ( (n + l) . Therefore, only the first n + l columns of V are computed and(Σ is (n + l)-by-(n ) + l) . The computational complexity is O (n + l)2 (m − 1)  . For large-dimensional systems where n ≫ 1 , it has significant complexity because X ′ will be a very big matrix. In this case, additional SVD is require