ABSTRACT

The Underwater Vehicles (UVs) modelling generally uses the Newton-Euler or Lagrangian approach. The possible ways of using the Newton-Euler method are either the conventional Newton-Euler method or the Newton-Euler method using Denavit–Hartenberg (DH) parameters. In the conventional Newton-Euler method, the inertia matrix and the Coriolis and centripetal matrix are transformed into an inertial frame for vehicle control. On the other hand, Newton-Euler modelling using the DH parameter considers the vehicle motion in the inertial frame using virtual frames. Thus, the vehicle's equations of motion (EOM) are derived directly from the inertial frame without needing transformation between frames. This method is beneficial for multibody applications like UV with a manipulator. In this case, the coupling effects of the interaction between the bodies are implicit in the equations. While using the conventional Newton-Euler method, these coupling effects must be explicitly introduced in the equations, increasing the complexity. A comparison study of the two methods is done as part of the study. The equations of motion are derived using these two methods, and their relative performance is tested by simulating an UV in the same environment.

INTRODUCTION

The EOM is generally derived from the vehicle frame using the conventional Newton-Euler method. However, the trajectory tracking is intuitive when represented in the inertial frame and thus more predominantly implemented. In the trajectory tracking task, the acceleration of the vehicle is found from the control forces by solving the EOM. This acceleration is then converted to the acceleration in the inertial frame and then integrated twice to find the actual position of the vehicle in the inertial frame. This moving from one frame to another involves a lot of frame transformations, which increases the computational time and cost. One another method to do the trajectory tracking task is to transform the EOM from vehicle frame to inertial frame, which involves a lot of inverse transform operations. This problem will become much more complex when the number of states estimated increases when multibody systems such as vehicle with manipulator is used.

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