# An Outline of Fused Deposition Modeling: System Models and Control Strategies
## 1 Introduction  
Additive Manufacturing is a process that, unlike conventional machining, fabricates an object by continuously stacking material in the form of layers rather than removing it from a block [1]. Initially born for rapid prototyping purposes, AM quickly shifted towards mass production thanks to its elevated versatility, reduction in material waste and ability to manufacture geometries that are otherwise impossible to obtain. However, the advantages above come with some limitations, such as low throughput, high uncertainties and sensitivity to defects. Different AM technologies have emerged to process different materials, including polymers [2], metals [3], ceramics [4] and concrete [5]. Amongst them, the most mature ones are known as (i) Fused Deposition Modeling (FDM), (ii) Powder Bed Fusion (PBF), Stereolithography (SLA), (iii) Direct Energy Deposition (DED) and (iv) Laminated Object Manufacturing (LOM). In this work, the focus is on FDM, which is specialized in plastic materials and composites, making this technology extremely pervasive in a wide range of sectors. In general, the FDM process comprises the following subroutines [6]. * path planning;  
* motion control;
* extrusion control. The offline phase is a preliminary step that takes place during simulation, in which dedicated software elaborates on the digital model (e.g., CAD) of the part with the aim of planning the optimal building trajectory based on specific factors, such as accuracy or build time. Given the nature of AM, some of these variables are inversely proportional to each other, which makes finding the optimal trajectory a multi-variable optimization problem with several trade-offs. In practice, this problem is dealt with by solving the sub-routines known as slicing and path planning. The reader is referred to [7] for a dedicated review of slicing and path planning strategies, which are briefly summarized in the following. The slicing operation consists of determining the layer-wise partition of the part to be fabricated. Based on the application and on the machinery available, the layers can be planar or non-planar, and their height can be constant or adaptive. Planar layers allow the end-effector (EE) to keep a fixed orientation, hence enabling the implementation of simple configurations, such as gantries. Conversely, non-planar layers require the use of an EE with additional degrees of freedom. Path planning consists of defining the ideal sequence of poses the EE needs to follow (usually represented as B-splines or Bezier curves) in order to build the part. There exist numerous path planning algorithms depending on the feature they aim to optimize, e.g., accuracy, build time or surface roughness. The online phase represents the realization of the trajectory planned and is responsible for the correct execution of motion and extrusion. Current industrial robots can achieve accuracy and repeatability tolerances that exceed the requirements for most FDM applications. Therefore, the motion system is not discussed in this work since it is a negligible source of error with respect to the extrusion one  
Extrusion is defined as the process of enforcing the flow of a semi-solid material through pressure and heat. In FDM, the raw material, which is usually powder, pellet or filament of solid polymers, is compressed and heated until reaching the melting temperature; then, it melts inside the extruder and is extruded through the nozzle as a viscous fluid. The block constituted by the extruder and the nozzle is also called the printing head, and it coincides with the EE of the printer. Outside the nozzle, the geometrical arrangement of the extrudate and the ability to maintain the shape obtained until solidification are the final and most important aspects of extrusion and are both determined primarily by the composition of the material [8]. The complex extrusion dynamics makes model-based approaches inconvenient, causing engineers to resort to experience and qualitative observations.