This paper presents a comprehensive study on the analysis of the complexity and safety of the movement of controlled objects along specified predefined routes. The focus is on a method for evaluating route complexity, which entails encoding routes into a finite number of nonoverlapping segments and applying recurrent forms to compute the spectra of dynamic parameters. This technique allows for an assessment of the difficulty level of a particular object's route. The methodology enables the identification of potential obstacles and safety hazards associated with the movement along such routes. An instance of this technique illustrated in this study through a practical example, which includes the movement of a rover on Mars. This instance demonstrates the efficacy of the proposed technique in a real-world scenario, highlighting its potential applicability in both terrestrial and extra-terrestrial navigation. The study emphasizes the significance of route complexity analysis for enhancing the reliability and security of controlled objects, which is essential for the advancement of technologies in space exploration and other areas.