Introduces and developed a novel computational approach for efficiently calculating the navigation of infinite multi-dimensional spaces using a improved algorithm named Bellande Step function within a infinite multi-dimensional model-integrated framework. By optimizing and advancing the step function, the method addresses challenges in infinite-dimensional random point generation and nearest node calculation in in an existing tree while moving from the nearest node towards a random point by a step size collision free, allowing movement towards target nodes within defined distance constraints to be added as node to the tree. Leveraging this type of approach, efficiently compute the next step towards a target node for infinite-dimensions, ensuring accurate movement while reducing collisions with adhering to specified distance limits set by the user. The integration of infinite dimensional space modeling enhances the process of the step function while increasing the capabilities, accuracy, adaptability, effectiveness and computational efficiency. The results underscore the robustness and scalability of this approach, showcasing its potential applications in robotics and other fields related to robotics, and complex systems modeling. This integration of the Bellande Step function with model-integrated infinite dimensional space represents a significant advancement in the computational efficiency, precision, accuracy of Infinite multi-dimensional node calculations.