This article presents outcomes of a stochastic optimization technique for trajectories of spacecraft exploring the rings of Saturn. Despite data obtained by Cassini and Voyager on their missions to Saturn, many questions regarding the formation and dynamics of Saturn's rings and planetary rings in general remain unanswered. Sending traditional large spacecraft prove to be problematic as collisions and the probability of mission failure increase dramatically in the dynamically dense region of space within planetary rings. Because of this, a swarm of small unmanned probes with decentralized communication structures and research instruments distributed amongst the swarm can provide a possible solution. In this paper, the practicality of such a swarm mission is investigated through a stochastic model of the mission trajectory dynamics with the goal of minimizing fuel consumption across the entire swarm while avoiding collisions between swarm agents and dynamic rigid body ring particles. Known probability distributions of ring particle dynamical variables (velocity, rotation rate, size) are used to define random variable parameters in a system of differential equations defined by artificial potential fields describing the swarm dynamics. Using a Monte Carlo method, the stochastic optimization problem is solved yielding probabilities of various possible swarm trajectories with the lowest fuel consumption and probability of mission completion without collisions. These optimal parameters can then be onboarded to a swarm of spacecraft allowing them to explore the rings of Saturn following optimal trajectories.