Field Computation Based Kernel for Vector 3D Printing

尽管增材制造被称为3D打印，但在大多数情况下，制造仍然是2.5D的方式-材料沿着沿着固定的打印方向在平面上层层堆积，限制了3DP的灵活性。当前2.5D打印实践中常见的问题是：i）材料层之间的机械强度弱，ii）难以移除的额外支撑结构，导致材料和制造时间的浪费，iii）打印模型表面上的楼梯外观。此外，这种平面制造还禁止沿沿着设计的路径（如“肌肉中的肌腱”）印刷各向异性强的材料（如碳纤维）以增强机械强度，或者禁止在弯曲表面的顶部印刷以实现先进的电/生物功能。矢量3D打印（Vector 3D Printing，Vec 3DP）是一种将材料沿沿着变化的方向进行动态挤压的打印技术。在3D打印机上添加更多的自由度（DoF）并控制其多轴运动在硬件上实现起来不那么困难。用于焊接或先进的多轴铣床的机器人手臂已经实现了这种运动。然而，尽管有一些试点工作可以产生相对简单的模型，但最先进的技术缺乏一个计算内核来有效地为具有复杂几何形状和材料分布的模型生成优化的Vec 3DP刀具路径/运动。这种计算内核的差距进一步阻碍了Vec 3DP的上游设计研究和下游应用。我的团队是世界上第一个发明自动生成可制造的弯曲3D刀具路径的技术，通过机器人系统的多轴运动来制造通用实体模型。为了确保我们在这一工程前沿的领先地位，我的目标是研究和开发一个计算内核，以实现矢量3D打印作为下一代增材制造的集成设计和制造。为Vec 3DP研究这样的内核具有以下科学挑战：1）最优解的搜索空间已经从两个流形（传统3DP的平面层或多轴CNC的给定表面）扩展到三个流形（体积）。这种从平面/曲面到体积的变化极大地增加了自由度（DoF）和问题的复杂性。2）在设计、规划和制造实现的不同阶段进行的解耦优化不能系统地解决问题。这导致在设计阶段优化的产品无法在制造阶段成功实现。这对于传统3DP和矢量3DP都是一个挑战;然而，矢量3DP具有要考虑的更复杂的制造目标/约束。3）整个流水线优化需要计算目标、约束、材料模型和其他操作相对于设计变量的导数（即，灵敏度），其中拓扑改变（例如，网格生成、B代表上的布尔运算）是不可微的。这限制了基于导数的优化器的使用，包括基于神经网络的深度学习，它依赖于反向传播中的微分。我设想，通过研究基于场的计算内核来解决Vec 3DP的设计和制造问题，可以克服所有这些挑战。

Although additive manufacturing is called 3D printing, the fabrication in most cases is still in a 2.5D way - materials are accumulated layer upon layer in planes along a fixed printing direction, restricting the flexibility of 3DP. The commonly identified problems of the current 2.5D printing practice are i) weak mechanical strength between the layers of materials, ii) additional supporting structures that are hard to remove and lead to the waste of material and fabrication time, iii) staircase appearance on the surface of printed models. Moreover, this planar fabrication also forbids printing anisotropically strong materials such as carbon fibres along designed paths like "tendons in muscles" to reinforce the mechanical strength or printing on top of curved surfaces for advanced electrical / biological functions. All restrict the fast growth of 3DP technology.These limitations can be overcome by the strategy of Vector 3D Printing (Vec3DP) that extrudes materials along dynamically varied directions. Adding more Degrees-of-Freedom (DoFs) onto the 3D printer and controlling its multi-axis motion is less difficult to implement on hardware. Robotic arms for welding or advanced multi-axis milling machines have already realised this sort of motion. However, the state-of-the-art lacks a computational kernel to effectively generate optimised toolpaths / motions of Vec3DP for models with complex geometry and material distribution although there are some pilot works that can produce relatively simple models. This gap of computational kernel further prohibits the upstream investigation of design for Vec3DP and the downstream applications for Vec3DP. My group is the first in the world that invents the technology for automatically generating manufacturable curved 3D toolpaths to fabricate a general solid model through the multi-axis motion of a robotic system. To secure our leading position at the vanguard of this engineering frontier, my ambition of this fellowship is to investigate and develop a computational kernel to enable the integrated design and manufacturing for vector 3D printing as the next generation of additive manufacturing. Investigating such a kernel for Vec3DP has the following scientific challenges:1) The search space for optimal solutions has been extended from two-manifold (planar layers for conventional 3DP or given surfaces for multi-axis CNC) into three-manifold (volume). This change from plane / surface to volume tremendously increases both the degrees-of-freedom (DoFs) and the complexity of problems.2) Decoupled optimization conducted in different phases of design, planning and manufacturing realisation cannot solve the problem systematically. This leads to a consequence that the products optimised in the design phase cannot be successfully realised in the manufacturing phase. This is a challenge for both conventional 3DP and vector 3DP; however, vector 3DP has more complicated manufacturing objectives / constraints to be considered.3) A whole pipeline optimisation needs to compute the derivatives of objectives, constraints, material models, and other operations with respect to the design variables (i.e., sensitivities), where topological changes (e.g., mesh generation, Boolean operations on B-reps) are not differentiable. This restricts the usage of derivative-based optimisers, including neural network based deep-learning that relies on differentiation in back-propagation.I envision that all these challenges can be overcome by investigating a field-based computational kernel to tackle the design and manufacturing problems for Vec3DP.