Objective: Robotic technology is being developed to increase productivity and alleviate wasted time. The trajectories of motion which these robots operate on are determined by matrix algorithms within the controller of the robots. This report contains a detailed analysis of the optimal-path finding algorithm which can be integrated with a robotic manipulator. Using a two-dimensional model, an algorithm was written to input the coordinates of an infinite number of objects, the destination, and the location of the robot. The program calculates and optimizes the path required to pick up the objects and position them at the desired location in an optimal fashion. Utilizing the Graphics Kernal System (GKS), the path was then animated to visually demonstrate that the selected order to pick the objects was in fact the optimal one. The final aspect of the project involved the integration of the path-finding algorithm with a PUMA 500 series robot. A successful optimal path-finding program was developed and implemented with the GKS software. By translating the program into the PUMA robot language, VAL-II, the algorithm was utilized in a practical and easily adaptable manner.