基於雷射指標器與位置感測器之機器手臂參數校正

Abstract

本論文探討一個由雷射指標器與影像感測器所組成的低成本的機器手臂校正裝置，將雷射指標器配置在機器手臂末端，控制機器手臂產生多個姿態將雷射光斑打在感測器取像範圍內，使用相機或影像感測器取得雷射光斑影像，分析影像找到光斑中心位置，藉由雷射光束具有良好的直線特性，可將光斑中心視為線與平面的交點，便可配合對應的手臂角度命令，進行機器手臂機構參數校正．根據配置的不同可分為雷射-平面-相機與雷射-影像感測器，前者是將雷射光斑打在平面讓相機觀察，根據針孔相機模型原理，影像誤差會隨著相機與平面之間的距離而放大，後者是將雷射光斑直接打在影像感測器上．由於雷射的直線性，可知光斑中心位置的誤差與雷射光束行進的距離無關．同時本論文也從估測參數的變異數分析中發現，當雷射光束行進的距離越遠，手臂的角度參數估測的變異數會越小，而長度參數則跟距離無關． 任何可測量手臂末端六維姿態的裝置，如相機、三次元量測儀(Coordinate Measuring Machine)、雷射追蹤儀(Laser Tracker)等等，研究者都會面臨到一個抉擇，是先計算出姿態後再校正還是使用原始資料來校正，以Eye-in-Hand方法來說，原始測量資料是棋盤格影像的角點位置，透過相機校正可得到內部參數與相機姿態，當直接使用測量資料進行參數估測者，定義為一次校正，否者就是二次校正．文獻上只提到二次校正會有誤差累積的問題，但卻沒有研究去分析或解釋其影響，本論文將從數學分析上去證明一次校正所估結果的變異數會比二次校正小．

This dissertation proposes a calibration device consisted of a laser pointer and the image sensors for manipulator kinematic calibration. The laser pointer is attached on the end-effector of a manipulator. The manipulator is operated to generate multiple laser speckles which are observed by the image sensors. The speckle image is analyzed to obtain the central location of speckle. The geometry of speckle’s center is the line-plane intersection due to the linearity of laser beam. The kinematic calibration of a manipulator is carried out using the information of the central location of speckle and the corresponding joint command. There are two configurations: Laser-Plane-Camera and Laser-Sensor. The laser pointer beams to a plane and then the camera observes the speckle in the first configuration. Due to the principle of pin-hole camera model, the position error of a speckle enlarges with increasing distance between the camera and the plane. For the second configuration, the laser pointer beams to the image sensor directly. From the linearity of laser beam, the position error of a speckle is uncorrelated to the distance of laser light traveled. Furthermore, this dissertation analyzes the variance of estimated parameter and investigates the variance of angle parameter decreases with the increasing distance of laser light traveled. However, the length parameter is uncorrelated to the distance. For any measuring instrument that can obtain the six-dimensional pose of end-effector, such as the camera, the coordinate measuring machine, the laser tracker, etc., the researcher should use the raw measurement or the estimated six-dimensional pose to calibrate the kinematics of a manipulator. For the eye-in-hand configuration, the raw measurement is the locations of corners in each checkerboard image. The researchers may implement the camera calibration first to obtain the inertial parameters and the poses of the camera. If the parameters are estimated directly from the measurements, it is called one-stage estimation. Otherwise, it is called two-stage estimation. It was previously observed that two-stage estimation has the drawback of error propagation. However, this observation has never been formally proved or generalized. In this dissertation, the statistical properties of one-stage and two-stage estimations are compared under a newly established mathematical fact that shows that the variances of estimated parameters using one-stage estimation are smaller than those using two-stage estimation under certain conditions.