利用常見物體形狀作機器人公式化定位

Abstract

本論文提出利用常見物體決定機器人位置公式解的三種新方法。第一種方法是利用任 意具有一已知多邊形頂面及一垂直比頂面的側面之多面體作機器人定位。第二種方法 在有系統地利用多面體上已知相對位置直線的任意組合作機器人定位。第三種方法則 利用任意具有已知曲線的平面及一垂直此平面的側面之曲面體作機器人定位。因為在 此三方法中所用的物體在室內外皆常見到，使得本論文所提方法較其它利用特殊設計 標的作定位之方法更適用於一般應用。而且本研究所用標的具有多樣性，使本論文所 提方法可在不同環境中使用。 本論文使用一簡易的數學模式，分別在所提三種方法中推導出一類似共線點交叉比的 性質、一有利於將束限方程式線性化的性質、及數個有關座標轉換的等次性質。這些 性質可降低機器人定位的困難度，進而使公式解得以推導出來。此一特性使得本論文 所提方法較其它需要重複計算的定位方法更適用於需要快速計算的應用。 本論文所提三方法利用影像處理及數值分析技巧，分別萃取出多面體表面轉角的投影 特徵、多面體表面直線的投影特徵、及曲面體表面曲片的投影特徵。然后利用這些特 徵所提供的資訊，計算出架設在機器人上相機的方向及位置參數。實驗數據顯示此三 方法的定位錯誤率皆低於 5% ，足以證實此三方法確實可行。

In this dissertation, three analytic approaches to robot location by common object pes are proposed. In the first approach, robot locations are determined by the use of polyhedral object that has a known polygon-shaped top and a lateral planar surface perpendicular to the top. Proposed in the second approach is a systematic analysis of robot location determination using various combinations of multiple edge on polyhedral objects with known relative locations. And in the third approach, to locations are determined using any curved object that has a planar surface taining a known curve and a lateral curved surface perpendicular to the planar face. Objects used in the three approaches are seen frequently both in indoor and in door environments. This merit makes the proposed approaches more flexible for lateral applications than other approaches using specially-designed marks. And the lety of the marks usable by the approaches enhances the applicability of the approaches to different environments. Moreover, a convenient mathematical model is used, based on which a property lar to that of cross ratios of collinear points, a property useful for linearizing constraint equations, and several homogeneity properties of coordinate transformation can be derived respectively in the three approaches. These properties reduce the difficulty of solving the robot location problem, resulting in the possibility of deriving analytic solutions. This merit makes the proposed approaches more useful for fast computation than other approaches requiring iterative computation. In these approaches, from a monocular image of an object used for robot location, image processing and numerical analysis techniques are applied to extract respectively in the three approaches the projection characteristics of the polyhedral corners on the object top surface, those of the lines on the polyhedral object, and those of the surface patches on the curved object. The orientation and the position parameters of a cameramounted robot are then determined accordingly. Experimental results with low location error percentages for all the three approaches prove the feasibility of the proposed approaches.