隨著工業4.0的發展，生產線上的模式也逐漸地發生改變，漸漸衍生出人機協作的工作模式，在人機協作模式下，人類與協作機器人相互攜手合作並且截長補短，可望帶動生產效率與彈性的提升。而有不少廠商也開始思考如何讓人類與機器人透過更好的協作方式讓彼此發揮更大的價值。但是人機協作意味著，機器人的工作空間不再穩定，隨時會有外在物體入侵到機器人的工作範圍內，此時安全問題成為了首要考量，要確認外在物體是否與機器人軌跡發生干涉，模式有分為連續碰撞檢測與離散碰撞檢測，而主要的干涉檢測方式為基於距離的Gilbert–Johnson–Keerthi (GJK)演算法，且人機協作希望再發現機器人運動軌跡會與障礙物發生干涉後，能尋找出一條新的軌跡使機器人能避開障礙物並繼續完成任務，目前主流的修正軌跡演算法有基於強化學習的神經網絡路徑規劃算法或者是Rapidly-exploring random tree (RRT)演算法，本論文提出一個基於回歸空間安全模型判斷機器人在路徑上整體安全性，替代正向運動學與干涉檢測的步驟，並藉由最佳化方法尋找修正軌跡，希望能實時的達到手臂避障軌跡規劃。

With the development of Industry 4.0, the mode of the production line has gradually changed, the concept of Human-robot collaboration (HRC), HRC has gradually derived. In HRC, humans and robots cooperate with each other, which is expected to improve production efficiency and flexibility. And many manufacturers have begun to think about how to let humans and robots play a greater value to each other. However, HRC means that the robot’s working space is no longer stable, and there will be external objects invading the robot’s working space at any time. Therefore, safety issues become the most important considerations. To confirm whether the obstacle occupy the robot's trajectory. The collision detection mode is divided into continuous collision detection (CCD) and discrete collision detection (DCD), and the main detection method is the distance-based like Gilbert–Johnson–Keerthi (GJK) algorithm. HRC also hopes to find the new trajectory which will avoid the obstacles and the robor can keep doing the task before detected the collision. The collision avoidance beforehand algorithm includes a neural network path planning algorithm based on reinforcement learning or a Rapidly-exploring random tree (RRT) algorithm. This paper proposes Obstacle Occupancy Model is used to judge the safety of robot trajectory, replacing the steps of forward kinematics and interference detection, and finding a fix trajectory through optimization methods, hoping to achieve real-time obstacle avoidance trajectory planning.

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