This paper investigates path planning strategies for additive manufacturing processes such as powder bed fusion. The state of the art mainly studies trajectories based on existing patterns. Parametric optimization on these patterns and allocating them to the object areas are the main strategies. We propose in this work a more systematic optimization approach without any a priori restriction on the trajectories. The typical optimization problem is to melt the desired structure, without over-heating (to avoid thermally induced residual stresses) and possibly with a minimal path length. The state equation is the heat equation with a source term depending on the scanning path. First, in a steady-state context, shape optimization tools are applied to trajectories. Second, for time-dependent problems, an optimal control method is considered instead. In both cases, gradient-type algorithms are deduced and tested on 2-D examples. Numerical results are discussed, leading to a better understanding of the problem and thus to short- and long-term perspectives.

本文研究了诸如粉末床熔合等增材制造过程的路径规划策略。现有技术主要基于现有模式来研究轨迹。主要策略是对这些模式进行参数优化并将其分配给对象区域。我们在这项工作中提出了一种更系统的优化方法，对轨迹没有先验限制。典型的优化问题是要熔化所需的结构，而不会过热（避免热引起的残余应力），并且可能具有最小的路径长度。状态方程是热方程，其源项取决于扫描路径。首先，在稳态环境中，将形状优化工具应用于轨迹。其次，对于与时间有关的问题，可以考虑采用一种最佳控制方法。在这两种情况下，都可以推导梯度类型算法并在2D实例上进行测试。讨论了数值结果，从而使人们对问题有了更好的理解，从而形成了短期和长期的观点。