Receding-Horizon Ergodic Exploration Planning using Optimal Transport Theory

This paper addresses the ergodic exploration problem based on the optimal transport theory. The ergodic exploration has been actively investigated due to its wide applicability. Most of the previous methods to realize the ergodicity in robot exploration problems are based on the Fourier basis function, which contains some technical issues. In this paper, we propose a new method to yield ergodic dynamics for a robot in a receding-horizon manner while avoiding issues stemming from the Fourier basis function. The optimal transport theory that quantifies the distance between two probability density functions is employed as a tool to measure as well as to realize ergodicity. A computationally efficient method is derived to measure the performance of the proposed algorithm. Finally, simulation results are provided for two different scenarios uniform and nonuniform distributions, to validate the proposed method.