七軸機器手臂最佳化路徑規劃與防止自我碰撞之研究

Abstract

目前在工業界，六軸機器手臂占了大多數，因為六個自由度足以讓機器手臂末端點到達卡式空間中給定的位置與方向，但六軸機器手臂若是在空間中遇到障礙物，便很可能無法避障而無解，七軸機器手臂便可以利用其冗餘自由度來避開障礙物，因此七軸機器手臂還有很大的發展空間。在本研究中的七軸機器手臂，其結構與仿生機器手臂很相似，兩者差異在於本研究中的七軸機器手臂在腕部與肘部間多了一個偏移量。為了描述機器手臂末端點在卡式空間位置與各軸角度關係，利用D-H rules建立機器手臂模型，並推導其運動學模型與動力學模型，並將馬達模型與動力學模型整合在一起，推導出完整的機器手臂動態方程式。在馬達力矩受限於硬體規格的情況下，機器手臂並不能滿足所有使用者要求的軌跡命令，因為軌跡所需要的力矩可能超出馬達所能負荷的範圍；另外，在工業界，如何使機器手臂的運動時間縮短也是很重要的課題，因為運動時間越小表示機器手臂的工作效率越高；任何路徑規劃都必須滿足機器手臂防自我碰撞，一旦發生自我碰撞，機器手臂將會損壞。本研究將以上兩種問題改寫成最佳化控制問題的形式，並考慮機器手臂防自我碰撞、馬達最大輸出力矩等限制，並利用GPOPS軟體求得最佳化之路徑。但由於七軸機器手臂的動態方程式相當複雜，使得GPOPS在解問題時需要花很多時間，為了尋找更有效率的解法，本研究擬利用動態規劃法求解最佳化路徑，並以模擬方式比較動態規劃法與GPOPS軟體的解，探討解的正確性與計算的效率等問題。

In industry, six-degree-of-freedom (DOF) manipulators are most widely used, because the 3D position and orientation of the end-effector can be completely determined. However, if there exist obstacles in the work space, there may be no solutions for 6-DOF manipulators to avoid the obstacles. Seven-DOF manipulators can avoid the obstacle by exploiting the redundant DOF; therefore, they are worthy of further researches. The seven-DOF manipulator in this thesis has the similar structure to an anthropomorphic manipulator. The difference is that the manipulator in this thesis has an offset between the wrist and the elbow. To describe the relationship between the position of the end-effector of the manipulator and the angle of each joint, we built the manipulator's model by the D-H rules, and derived the kinematic model, and the dynamic model which includes motor models. The motors' torque is limited by the hardware. In such situation, trajectory commands are not always fulfilled by the manipulator because the motors cannot afford the torques required to follow the desired trajectory. In addition, it is an important issue in industry to reduce the moving time of manipulators, because moving faster means working more efficiently. Manipulators' self-collision-avoidance must be fulfilled by all the path planning methods. Once self-collision happens, manipulators will be damaged. In this thesis, we formulated two problems mentioned above as optimal control problems with the constraints of manipulators' self-collision-avoidance and maximum-motor-torque, and solved the path by using GPOPS software. However, dynamic equations of seven-DOF manipulators are very complicated, such that it spent a long time for GPOPS to solve the problem. To find a more efficient solver, we use dynamic programming, and compared the result with the solution derived by GPOPS software by means of simulations. Then we verify correctness and efficiency of both solutions.