視覺引導機器人以手眼校正實現路徑追蹤

Abstract

機械手臂在工業製造，醫療機器人中扮演重要角色，以致於提升效率和品質。 然而製造誤差導致加工物件的數學模型和預料的不一致。於是引入視覺引導的系統實現手臂和工作區域定位以改善靈活性和穩健性，讓手眼校正變成重要的課題。 此論文提出三個改善之手眼校正演算法，三者皆勝過其原始的演算法。除此之外，本論文亦提出二維及三維加工路徑追蹤的演算法。第一個校正方法是分離型克羅內克積法，先用克羅內克積算出矩陣旋轉部分再用最小平方法算出位移，可以降低位移的誤差。第二個是改良型四元數法，此方法將旋轉矩陣轉換單位四元數去解校正的參數。避免旋轉矩陣轉換單位四元數的不穩定性。第三個方法是全姿態高斯牛頓法，透過高斯牛頓優化和克羅內克積，可以修正所有校正參數。 另一方面，論文也提出兩種路經追蹤演算法。第一個方法是基於邊緣偵測的二維路徑追蹤，透過邊緣偵測找到初始路徑，再經過一系列影像處理，將最終路徑點轉於手臂座標。第二個方法基於三維重建偵測三維路徑。先透過多張影像找出物體的輪廓再用最近迭代點法找出對應的點並用三角化重建出完整的輪廓。當獲得完整的路徑資訊後，再使用路徑簡化演算法生成機械手臂運動命令。 在本論文除了模擬，亦針對很多實際情境測試手眼校正的演算法，對眼對手架構、眼在手架構、立體相機架構及校正時的影像品質等情況進行實驗。 除此之外，本文亦提供三種檢驗的方法，也就是影像投影，TCP校正和三角定位誤差，都不需要使用昂貴器材便能檢測精準度。在所有的實驗中提出的方法透過此檢驗方法呈現準確率皆比其原本論文的效果好。另一方面，透過手臂中的編碼器和單眼相機，可以對加工物體定位並偵測其加工路徑及追蹤。並且對追蹤時的手臂速度進行分析。不論模擬和實驗都能呈現良好結果。

In the industrial manufacture and surgical systems, a robotic arm plays an important role to enhance the production efficiency and quality. However, because the manufacturing error and the homogeneity between the processing object and its mathematical model are dissatisfied, a visual-guided robotic arm system is introduced to realize the positioning between the robotic arm and the workspace to improve the flexibility and robustness. This makes hand-eye calibration an essential task in robotics. This thesis presents three hand-eye calibration methods and all of them outperform the original algorithms. Moreover, the approaches to path tracking including 2-D and 3-D processing paths are proposed. The first calibration method is named the separate Kronecker product method, which uses Kronecker product to identify rotation matrices. Translation vectors are refined again to reduce the translational drift. The second method is the modified quaternion product method. This proposed algorithm uses the unit quaternion to represent the rotation matrix and avoid the uncertainty that transform from the rotation matrix to the unit quaternion. The third method is called full-pose Gauss-Newton method. The proposed algorithm uses Gauss-Newton method and Kronecker product to refine all calibration parameters. For path tracking, two path detection methods are discussed. The first method is edge-based 2-D path detection. Edge detection is used to obtain the initial processing path, and the detected path is transformed from image frame to the robotic base frame. The second method is reconstruction-based 3-D path detection. Many contours of the object in the images are matched by ICP algorithm and 3-D path can be reconstructed by triangulation. After 3-D information of the path is obtained, path simplification is implemented so that the robotic arm can receive these command and track paths. In this thesis, proposed hand-eye calibration algorithms are implemented in various scenes, including eye-to-hand configuration, eye-in-hand configuration, stereo camera configuration and calibration with various image qualities. Furthermore, three methods are described to verify the calibration accuracy. All of them are image projection, TCP calibration and triangulation localization error, and it is not necessary to use the costly apparatus to compute errors. In all calibration experiments, solutions by proposed algorithms are better in all checking methods. For both 2-D and 3-D path detection, the monocular camera and encoders in the robotic arm are used to localize the object and track the processing path and speeds of robotic arm are analyzed. Both simulations and real experiments show the superiority of our algorithms.