This work aims at providing a new reliable (asymptotic) optimal motion planner, named BoxRRT*, which can guarantee a safe path to an unknown initial mobile robot localisation. Our proposed motion planner is build upon: i) methods which use stochastic sampling to discretise the configuration space, e.g., Rapidly-exploring Random Tree, which can guarantee (asymptotic) optimality of the solution, e.g., optimal RRT (a.k.a RRT*) and ii) modern and new tools for the guaranteed numerical integration based on Runge-Kutta methods.