Single-query path planning is still an open research field. A very promising approach is the use of Rapidly-exploring Random Trees (RRTs). In this approach two RRTs are constructed, one starting from the initial configuration and one from the goal configuration. In comparison with other approaches, this methodology is very efficient in high-dimensional configuration spaces.However, a naive implementation of this approach results in reliability problems: For the construction of an RRT, only discrete configurations are tested for feasibility, while continuous transitions between configurations are not. Furthermore, numerical computations are performed in a floating point arithmetic without accounting for round-off errors. In this work an advanced algorithm will be presented that incorporates interval analysis to eliminate these problems and yield reliable results.