Autonomous Underwater Vehicles Identification through a Kernel Regressor

A kernel regressor to estimate a six-degree-of-fredoom non linear model of an autonomous underwater vehicle is proposed. Although this estimator assumes that the model coefficients are linear combinations of basis functions, it circumvents the problem of specifying the basis functions by using the kernel trick. The Gaussian radial basis function is the chosen kernel, with the Kernel matrix being regularized by its principal components. The variance of the Gaussian radial basis function and the number of principal components are hyper-parameters to be determined by the minimisation of a final prediction error criterion and using the training data. A simulated autonomous underwater vehicle is proposed was used as case study.

I. Introduction

Autonomous Underwater Vehicles (AUV) have been successfully used in various applications, such as oceanographic surveys [3], [7], [8], [15], bathymetric measurements [4], [8], [15], [17] and underwater maintenance activities [6]. Hence, deriving accurate dynamic models for these vehicles is of prime importance for their maneuvering prediction and control, that is a difficult task due to the nonlinear cross-coupled hydrodynamics forces affecting the various body elements and possible mechanical interaction with surrounding structures. The most common are six-degree-of-fredoom (6 DoF) models based on Newtonian-Lagrange mechanics first principles [13]. In some maneuvers, such as diving or motion in waves, the AUV may be described by a linear time invariant (LTI) model [9], [12]. Therefore, LTI time-domain and frequency-domain system identification algorithms have been proposed to estimate these models. Due to the complexity of the 6 DoF models, most system identification approaches do not estimate the full model. In [1], the authors split the 6 DoF model into several simplified sub-models such as the longitudinal dynamic model or the surge dynamic model. Gibson and Stilwell estimate damping models only by assuming that the other parameters are known [5]. Ross et al. split the AUV into longitudinal and lateral subsystems and identify each of these models using tests in a pool with the AUV attached with four springs, and the vehicle positions measured by a camera. The velocities and accelerations were determined by FIR derivative filters and the model parameters were found by a Least-Squares estimator [10]. Feng et al. estimate the AUV model in a zig-zag diving motion using a Least-Squares Support Vector Machine (LSVM) with a Linear Kernel [16], where the linear and rotational velocities are assumed to be known. Pepijn et al propose a method to identify the hydrodynamic damping with neural networks [14]. In [11] the damping viscous coefficients are included in the state vector of the 6 DoF model and estimated using either the Extended Kalman Filter or the Unscented Kalman filter.