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This paper addresses the autonomous robot ergodicity problem for efficientenvironment exploration. The spatial distribution as a reference is given by amixture of Gaussian and the mass generation of the robot is assumed to beskinny Gaussian. The main problem to solve is then to find out proper timingfor the robot to visit as well as leave each component-wise Gaussian for thepurpose of achieving the ergodicity. The novelty of the proposed method is thatno approximation is required for the developed method. Given the definition ofthe ergodic function, a convergence condition is derived based on the timinganalysis. Also, a formal algorithm to achieve the ergodicity is provided. Tosupport the validity of the proposed algorithm, simulation results areprovided.

On the Ergodicity of an Autonomous Robot for Efficient Environment Explorations