  This paper addresses the autonomous robot ergodicity problem for efficient
environment exploration. The spatial distribution as a reference is given by a
mixture of Gaussian and the mass generation of the robot is assumed to be
skinny Gaussian. The main problem to solve is then to find out proper timing
for the robot to visit as well as leave each component-wise Gaussian for the
purpose of achieving the ergodicity. The novelty of the proposed method is that
no approximation is required for the developed method. Given the definition of
the ergodic function, a convergence condition is derived based on the timing
analysis. Also, a formal algorithm to achieve the ergodicity is provided. To
support the validity of the proposed algorithm, simulation results are
provided.
