The ongoing evolution of 3D printing in architecture signifies its shift from merely a prototyping tool to a mainstream fabrication technique. With the capacity to achieve enhanced structural performance while minimizing material waste, 3D printing promotes sustainability and efficient resource usage. Unlike traditional methods, which remove excess material to achieve desired shapes, 3D printing provides precision in material distribution. This innovation can emulate nature’s structural efficiencies, as seen in palm trees and cancellous bone tissues, both of which adapt to specific loading patterns. 

While the prevalent layer-based 3D printing has limitations, particularly for large-scale cellular structures, spatial 3D printing, especially using the robotic fused deposition modeling (FDM) method, emerges as a more practical alternative. Notable advancements in this realm include a) 3D-printed sandwich wall with optimized internal structure (Kwon, H 2019), b) Branch C-FabTechnology for the production of lightweight facade panels (Branch Technology, 2023), and c). Free-Oriented Additive Manufacturing printing in the + Z direction for the production of thermoplastic lattice and cellular structures (Ladron de Guevara, M 2019)., all of which advocate spatial 3D printing for its efficiency and geometric versatility. 

The core of this research proposal focuses on optimizing FDM spatial 3D printing for construction parts with internal cellular structures. The study uses Finite Element Analysis (FEA) to guide material deposition based on stress values. The research further delves into the influence of cellular geometry, emphasizing the importance of individual cell details in dictating overall mechanical properties. By integrating Spatial Subdivision methods with Eulerian principles, the study aims to create structures suited for continuous printing. 

Lastly, the research tackles the challenge of developing a continuous robotic 3D-printed toolpath. Using graph search algorithms, the goal is to devise an effective toolpath strategy that prioritizes continuity, collision avoidance, and geometric considerations. The final objective is to implement state-space planning algorithms to generate a continuous toolpath, considering robotic orientation, structural constraints, and collision prevention. 

Anticipated results include innovations in graded density extrusion for spatial extrusion, with prototypes to test these methods. This initiative not only propels the capabilities of 3D printing in architecture but also promises adaptability for unique geometries, paving the way for groundbreaking digital fabrication tools in the future.