A new method to plan guaranteed to be safe paths in an uncertain environment , with an uncertain initial and final configuration space, while avoiding static obstacles is presented. First, two improved versions of the previously proposed BoxRRT algorithm are presented: both with a better integration scheme and one of them with the control input selected according to a desired objective, and not randomly, as in the original formulation. Second, a new motion planner, called towards BoxRRT*, based on optimal Rapidly-exploring Random Trees algorithm and using interval analysis is introduced. Finally, each of the described algorithms are evaluated on a numerical example. Results show that our algorithms make it possible to find shorter reliable paths with less iterations.