Constructing complete graph and implement of TSP in the multi-objects path planning

Traveling salesman problem (TSP) is one of the unsolved problems nowadays that carry significant value to the transportation work in the complete graph. There are some good approximation algorithms that can provide an approximate solution. Here, we propose a method of extending the conventional Traveling salesman problem to construct plans for multi-objects which we may encounter frequently in real world. With the traveling of the vehicle, the optimal path generated from single path planner can be used to decrease the cost of tour. As the condition of environment has influence on optimal result of path, we propose a way of transferring from the grid-based real world to topological map first of all, and then we acquire the complete graph from it. With the process of update, the complete map is going to be updated and provides a more precise answer to the optimization. Throughout the simulation, such a method of producing optimal path for multi-objects based on TSP algorithms works well and reduces the cost of path phenomenally. We also find that the correct foundation of complete graph is important for the outcomes of the path from experiments.