自主式水下機器人使用多方向推進器在三維空間之動態定位控制器設計

Abstract

自主式水下機器人的動態定位能力一直是大多數任務在執行時的基礎，藉由穩定地定位在某個指定點，其餘的任務才得以順利執行，因此動態定位能力通常被視為機器人的指標性能之一。以往的船隻或載具大多專注在平面定位，然而本文為了實現三維空間的動態定位能力，特別研發了一具”多方向推進器”，以增加機器人的性能，使其具備在三維空間中的定位能力。這種多方向推進器具有三軸旋轉的特性，所以可以將其推力分布到半圓球表面的任一位置，相較於傳統的固定式推進器只能提供一種方向，此機構具有靈活操控的優勢。由於新型機構的幫助，此機器人能夠在搭載兩個推進器的情況下就擁有六個自由度。為了瞭解六個自由度的特性，我們首先用牛頓第二運動定理及尤拉旋轉方程式推導出機器人的動態模型，以便完整地描述其動作。當中，特別參考了垂直起降戰鬥機的模型，因為其可旋轉的噴射引擎和本文的機構具有極大相似處；而兩個推進器的相互運動則是藉由角動量守恆定律進行推導。在控制的過程中，縱移、橫移、起伏及偏航四個自由度將被控制，而滾轉及俯仰則可藉由回復力矩的設計和硬體重心的配置使其自然穩定，不需加以控制。四個自由度的控制律是根據動態模型和比例-積分-微分控制器而設計。之後，推力分配系統可以根據模型計算的結果將推力分配到適當的方向，而這個系統是根據摩爾偽逆轉換所設計，因為如何分配推力通常可視為求解數學最佳化的問題，而此方法能夠提供唯一的最佳化解。在整個控制技的設計過程裡，虛擬控制的概念也被引用其中，因為它可以用虛擬控制訊號的概念提供我們更直觀的參數表示方式；另外，感測器所提供的資訊也可當作回饋的輸入讓機器人隨時接受最新狀態，包含深度、姿態、推進器位置、電腦視覺(單眼視覺)計算的空間位置。最後，本文整合機器人的動態模型、比例-積分-微分控制器、感測器回饋、電腦視覺、推力分配系統而形成一個閉迴路實時控制的三維動態定位控制器。

Autonomous Underwater Vehicle (AUV), or so called underwater robot, is an intelligent machine possesses computer, IMU, depth sensor, camera and other sensors built to automatically conduct many submarine tasks. In this paper, a novel design of propulsion system consisting of two “multi-directional” thrusters is developed for an AUV. Each thruster is able to provide three-axis rotation; that is, assigning thrust in any direction by rotating thruster. Therefore, it allows the AUV a very agile maneuverability and the 6 degrees of freedom with the minimum number of thrusters. Meanwhile, designing a dynamic positioning controller for the AUV to automatically locate at an assigned point in three-dimensional space is another key issue in this paper. To design the controller, firstly the dynamic model is derived via Newton’s second law and Euler’s rotation equations; the instantaneous moments resulted by relative motions of two thrusters are analyzed by the law of conservation of angular momentum. Besides, the vertical take-off and landing aircraft is also referred to formulate the thruster parts of dynamic model, for their propulsion system have similar mechanism. Secondly, four of the six degrees of freedom which are surge, sway, heave and yaw are controlled during the dynamic positioning while pitch and roll are neglected because their motions can be small under the restoring moment by a suitable arrangement of hardware. The four control laws are designed according to the dynamic model and PID control theory; besides, the three-dimensional control task is separated into depth control (heave) and planar control (surge, sway, yaw). Thirdly, to lead the AUV to the assigned position, the total thrusts generated by two thrusters need to be distributed into appropriate directions. The way to distribute thrusts can be seen as a mathematical optimization, and the method of Moore–Penrose pseudoinverse is adopted to solve the problem, for it provides the only one solution which is the best approximation among all possible solutions in least squares sense. During the process, the concept of pseudo control that is virtual control unit is also incorporated to provide an intuitive and understandable representation for control parameters. Finally, the AUV is controlled in real-time and the sensors’ information are used as feedback through detecting a set of landmarks by monocular vision.