基於雷射光束投影之機器人手眼校正方法

Abstract

手眼系統參數的誤差直接影響機械手臂工作的表現，要讓系統具有高精準的能力，校正是一個基本且必要的步驟。此類系統的校正包含攝影機校正、手眼關係校正、工作區域空間關係校正以及機械手臂校正。本論文提供一種創新的手眼系統校正的架構，裝設雷射於機械手臂末端作用器上，將雷射投射於攝影機可視範圍中的工作平面上。自空間幾何對應關係的觀點來說，拍攝畫面中的雷射投影與機械手臂姿態之間存在一非線性關係，本論文據此關係推導出系統參數的解法。本論文提出的方法可以在攝影機無法看到機械手臂的情況下完成校正，相較於現存校正方法，此能力提供了更多的應用可能性，並且所提出的方法不需要精準製作的參考物，能以較低的成本有效校正系統參數。 本論文提出兩種使用單點雷射的手與眼與工作區域的校正方法。第一種方法在攝影機事前校正的前提下可求解手與眼與工作區域之間的三維空間關係。第二種方法合理地假設主軸點位置在畫面中心以及影像長寬比為等比，在單一工作平面姿態下可同時求得部分的攝影機內部參數；或是利用將平面擺設於不同姿態下，以雷射投射取樣，進一步地同時校正所有的攝影機內部參數。本論文亦提供使用線結構光雷射同時校正攝影機內部參數以及手與眼與工作區域關係的方法。這些校正方法皆包含兩階段處理，第一階段的閉鎖式解法利用齊性轉換式以及平行雷射線或面限制關係，將非線性關係拆解為多個線性形式。第二階段使用非線性最佳化方法能避免誤差傳遞問題，更準確地修正第一階段求得的參數。此兩階段處理可以在沒有人為提供初始參數的情況下完成校正。基於上述方法，本論文同時提出一種創新的機械手臂校正方法，在手到眼的架構下使用單點雷射投射，比對正向幾何計算的雷射光點位置與實際影像畫面的光點位置形成非線性成本函式，以最佳化解法計算機械手臂正向運動學模型參數。最後，本論文提供模擬與真實環境下的實驗結果來說明所提出方法的可行性。

Errors in the parameters of a hand-eye coordination system lead to errors in the position controlling of the robot. This makes the hand-eye calibration an essential task in robotics. A complete calibration procedure encompasses calibrations of camera, hand/eye, robot/workspace and robot kinematics. In this dissertation, the proposed methods target on calibration of an eye-to-hand system by utilizing a laser mounted on the hand to project laser beams onto a working plane. Since the collected images of laser projections must obey certain nonlinear constraints established by each hand pose and the corresponding plane-laser intersection, the solutions can be derived. Moreover, the proposed methods are effective when the eye cannot see the hand, and they eliminate the need for a precise calibration pattern or object. Two methods using a single beam laser are proposed for calibrating hand-eye-workspace relationships. In the first method, the uniqueness of the solution is guaranteed when the camera is calibrated in advance. The second method can simultaneously calibrate camera intrinsic parameters by applying several plane poses or under the assumption that the aspect ratio of the camera is known and the projected laser spot is at the center of the image. This leads to a minimal ground truth information needed which greatly reduces the cost and enhances the reliability. A procedure using a line laser module is illustrated in this dissertation for simultaneously calibrating the intrinsic parameters of a camera and the hand-eye-workspace relationships. In each method, a closed-form solution is derived by decoupling nonlinear relationships based on the homogeneous transform and parallel plane/line constraints. A nonlinear optimization, which considers all parameters simultaneously without error propagation problem, is to refine the closed-form solution. This two-stage process can be executed automatically without manual intervention. Based on the methodology described above, this dissertation further proposes a novel robot kinematic calibration method utilizing a laser pointer under an eye-to-hand configuration. The optimal solution of kinematic parameters is obtained by minimizing the laser spot position difference between the forward estimation and camera measurement. Finally, both simulations and experiments are conducted to validate these proposed approaches.