本論文旨在運用微分運動學實現數值法逆向運動學，並結合影像回授控制具特殊結構、機械臂幾何參數量測不易之六軸機械臂，能移動到與理想目標位置及姿態，差距在一定誤差內的工作點。為了驗證數值法逆運動學的可行性及讓誤差集中於機械臂幾何參數的測量，首先將二維碼張貼在目標物上進行位置及姿態檢測，接著藉由透視投影轉換求得之相機與機械臂基座標系間的齊次轉換矩陣將目標位置及姿態轉換至機械臂座標系下，最終藉由數值法逆運動學計算出機械臂各關節所需之移動量，並確保在沒有超出關節角度限制下驅動機械臂。此外，為了提升本論文使用之六軸機械臂的實用性，在確認數值法運動學可實際運用於機械臂後，本論文利用YOLO v5對目標物進行角點偵測，並透過後處理求出目標位置及姿態來取代須將二維碼張貼於物體上之限制。最終我們設定數值法逆運動學演算法的位置及姿態誤差分別在收斂至0.5(cm)及0.01(rad)內時停止數值疊代，並應用至實際六軸機械臂中查看其成效。

This thesis aims to use differential kinematics to implement numerical inverse kinematics and control the manipulator with a specific structure or its DH parameters can’t be easily measured by image feedback. The manipulator is moved to a point within a certain error from the ideal target position and pose. To verify the feasibility of numerical inverse kinematics and to focus the error on the measurement of DH parameters, the ArUco is first posted on the object for position and pose detection. Second, the target position and pose from the camera coordinate is converted to the manipulator coordinate by the homogeneous transformation matrix between them. Last, the amount of movement of each joint is calculated by using numerical inverse kinematics without exceeding the limitation of each joint angle when driving the robot arm. In addition, to enhance the practicality of the manipulator, YOLO v5 is used to perform corner detection of the object and calculate its position and pose by post-processing to replace the ArUco which was posted on the object. Consequently, the numerical inverse kinematic algorithm stops iterating when the position and pose errors converged within 0.5(cm) and 0.01(rad) respectively, then is applied to the actual 6-axis manipulator to observe its effectiveness.

[1] J. Denavit, R. S. Hartenberg, "A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices, "1955.
[2] A. Aristidou, J. Lasenby, Y. Chrysanthou, and A. Shamir," Inverse Kinematics Techniques in Computer Graphics: A Survey," COMPUTER GRAPHICS forum, vol.37, issue 6, pp.35-58, 2018.
[3] Bruno Siciliano, Lorenzo Sciavicco, Luigi Villani, and Giuseppe Oriolo," Robotics: Modelling, Planning, and Control," 2008.
[4] L. Sciavicco, B. Siciliano, “Coordinate transformation: A Solution Algorithm for One Class of Robots,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 16, pp. 550-559, 1986.
[5] R.Campa, K.Camarillo, and L.Arias," Kinematic Modeling and Control of Robot Manipulators via Unit Quaternions: Application to a Spherical Wrist," in Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, CA, USA, December 13-15, 2006, pp. 6474-6479.
[6] Tiantian Yu1, Daqing Wang and Lifu Gao," Singularity Avoidance for Manipulators with Spherical Wrists Using the Approximate Damped Reciprocal Algorithm," in International Journal of Advanced Robotic Systems, MarchApril 2021, pp.1-9.
[7] R.Campa and H. de la Torre," Pose Control of Robot Manipulators Using Different Orientation Representations: A Comparative Review," in 2009 America-n Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA, June 10-12, 2009, pp.2855-2860.
[8] C. Natale, Interaction Control of Robot Manipulators: Six Degrees–of–freedom Tasks, Springer, Germany, 2003.
[9] Zhengyou Zhang," Flexible Camera Calibration By Viewing a Plane From Unknown Orientations," in Proceedings of the Seventh IEEE International Conference on Computer Vision, 1999, vol. 1, pp.666-673.
[10] R.Y. Tsai and R.K. Lenz, “A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration”, IEEE Trans. Robotics and
Automarion, vol. 5, pp. 345-358, 1989.
[11] M. Kaur, S. Sondhi, and V. K. Yanumula," Kinematics Analysis and Jacobian Calculation for Six Degrees of Freedom Robotic Arm," in 2020 IEEE 17th India Council International Conference (INDICON), December 2020.
[12] A.Ehrlich," The Inverse Jacobian Control Method Applied to a Four Degree of
Freedom Confined Space Robot," University of Washington, 2016.
[13] Stefan Schaal. Jacobian Methods for Inverse Kinematics and Planning Slides from Stefan Schaal The Inverse Kinematics Problem, 2006.
[14] Sung-Kyun Kim, Ji-Hun Bae, Yonghwan Oh, and Doik Kim," 7-DOF Redundant Manipulator Control Using Quaternion Feedback based on Virtual Spring-Damper Hypothesis," in The 5th International Conference on the Advanced Mechatronics(ICAM2010), 2010, pp.87-92.
[15] S. R. Buss, J.S. Kim," Selectively Damped Least Squares for Inverse Kinematics," Journal of Graphics Tools, vol.10, 2005, pp.37-49.
[16] S. Caldera, A.Rassau and Douglas Chai," Review of Deep Learning Methods in Robotic Grasp Detection," Multimodal Technologies and Interaction, September 2018.
[17] 施慶隆、李文猶, 機電整合與控制-多軸運動設計與應用,第三版,全華書局股份有限公司,2015.