Stochastic Collection and Replenishment : Objective Functions

This paper introduces two objective functions for computing the expected cost in the Stochastic Collection and Replenishment (SCAR) scenario. In the SCAR scenario, multiple user agents have a limited supply of a resource that they either use or collect, depending on the scenario. To enable persistent autonomy, dedicated replenishment agents travel to the user agents and replenish or collect their supply of the resource, thus allowing them to operate indefinitely in the field. Of the two objective functions, one uses a Monte Carlo method, while the other uses a significantly faster analytical method. Approximations to multiplication, division and inversion of Gaussian distributed variables are used to facilitate propagation of probability distributions in the analytical method when Gaussian distributed parameters are used. The analytical objective function is shown to have greater than 99% comparison accuracy when compared with the Monte Carlo objective function while achieving speed gains of several orders of magnitude.