Hopfield network application to optimal edge selection

The goal of the present work is to plan the shortest collision-free path in 3-D, when a robot is navigated to pick up some tools or to repair some parts from various locations. To accomplish this goal, the path coordinator should have the capabilities of an obstacle avoidance strategy and a traveling salesman problem strategy (TSP). The obstacle avoidance strategy is to plan the shortest collision-free path between each pair of n locations in 2-D or in 3-D. The TSP strategy is to compute a minimal system cost of a tour that is defined as a closed path navigating each location exactly once. The TSP strategy can be implemented by a neural network. The obstacle avoidance strategy in 2-D can be implemented by the V-graph algorithm. However, the V-graph algorithm is not useful in 3-D, because it cannot compute the global optimality n 3-D. Thus, the path coordinator is proposed to solve this problem, having the capabilities of selecting the optimal edges by the modified genetic algorithm and computing the optimal nodes along the optimal edges by the recursive compensation algorithm