The design and development of intelligent service mobile robots that interact with humans in daily living activities or cooperate with persons in specific tasks, requires the design of new tools that allow the understanding of human motion intentionality. We can find examples of this kind of requirements for guiding people, for meeting persons whether in indoor or outdoor environ- ments or for doing robust navigation in highly crowded spaces. In any case, the knowledge of human motion intentionality might allow to optimize the trajectory described by the robot towards a more harmonized interaction in environments typically inhabited by humans and help to find the best human-robot motion behavior. Tackling the problem by only relying on a robust navigation is not enough, although this topic has grown enormously in the few past years. Thus, the understanding of human motion in urban environments is of extreme impor- tance in order to adapt service robots to typical human environments and not in the contrary. The present Master Thesis is a study in depth of the most relevant tech- niques that tackle the problem of Human Motion Prediction (HMP). Specif- ically, this document is focused on solving the HMP in outdoor and free spaces. To this end, it has been developed a geometrical method for generating optimal trajectories based on the concatenation of cubic polynomials using the so-called Collocation method. The main drawback of the aforementioned method remains in its initialization. Regarding this issue, an initial estimated solution has also been proposed to accelerate the calculation and to guarantee convergence to a feasible solution. Results show a robust method for human motion estimation in addition to a good calculation performance, making the proposed algorithm a valid option to consider in real-time applications. Furthermore, a statistical study of a large amount of trajectories was done aiming to obtain a simple and accurate model of the basics for human motion. Once obtained a model, concretely in the shape of a probability density function, we can build a method for predicting using probabilistic methods. As a validation, both prediction methods are evaluated in a real outdoor scenario through the Edinburgh pedestrian data base [14].