In this paper, a multi-agent motion planner is developed for nonlinear Gaussian systems using a combination of probabilistic approaches and a rapidly exploring random tree (RRT) algorithm. A closed-loop model consisting of a controller and estimation loops is used to predict future distributions to manage the level of uncertainty in the path planner. The closed-loop model assumes the existence of a feedback control law that drives the actual system towards a nominal system. This ensures the uncertainty in the evolution does not grow significantly and the tracking errors are bounded. To trade conservatism with the risk of infeasibility and failure, we use probabilistic constraints to limit the probability of constraint violation. The probability of leaving the configuration space is included by using a chance constraint approach and the probability of closeness between two agents is imposed using an overlapping coefficient approach. We augment these approaches with the RRT algorithm to develop a robust path planner. Conflict among agents is resolved using a priority-based technique. Numerical results are presented to demonstrate the effectiveness of the planner.