Abstract
In this paper, we propose a triangulation based function approximation model for agent positioning problem in the dynamic environments. In many problems of the real-world multi-agent/robot domain, a position of each agent is an important factor to affect agents' performance. Because the real-world problem is generally dynamic, a suitable position for each agent should be determined according to the current status of the environment. First, we formalized this issue as a function approximation that maps from state variables to a desirable position of each agent, and proposed a function approximation model using Delaunay triangulation. This method is simple, fast and accurate, so that it can be implemented for real-time and scalable problems. In our previous works, our model showed very high approximation accuracy and good generalization capability for two-dimensional input. However, two-dimensional input is insufficient for more generic problems. Therefore, we extend our previous model so that multi-dimensional input can be taken. The extended model forms tree structure that each node represents a local input space. This structure enables us to maintain the multi-dimensional input space flexibly. The previous model is directly used in each local input space. Therefore, each local input space keeps high accuracy and generalization capability. We implemented the extended model and performed the experiments to evaluate its performance. The result shows our extended model can take the multi-dimensional input adequately.
