Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing

TL;DR

This work tackles collision avoidance in multi-axis manufacturing by learning a neural-implicit representation of the Collision Measure Field (CMF) and its derived Inaccessibility Measure Field (IMF) over the full configuration space $ig( ext{3D} imes SO(3) ig)$. A fully connected network with sinusoidal activations, 5 hidden layers of 512 units, skip connections, and a sigmoid output is trained to regress the CMF from sparse cross-section data across orientations, enabling a continuous and memory-efficient representation compared to voxel/FFT approaches. The paper introduces a multi-resolution fine-tuning strategy and demonstrates transfer learning to adapt to geometry changes with substantially reduced training time. Through single- and multi-resolution experiments on 3D parts and axisymmetric tools, the method achieves accurate IMF/CMF reconstructions, with notable gains in interpolation quality and efficient adaptation to new geometries, suggesting practical applicability to topology optimization and process planning under continuous rotational motion. Limitations include training time, angular-resolution dependencies, and the need for smarter sampling strategies; future work points to meta-learning and hashing-based encoding to further accelerate training and inference.

Abstract

One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., a part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix $O(m)$ sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution $O(n^3)$ via fast Fourier transforms (FFTs) scales as in $O(mn^3 \log n)$ in time and $O(mn^3)$ in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).

Figures (11)

• Figure 1: An illustration of the computation of the CMF and IMF for a two-dimensional tool and part. The domain of the CMF in this example is three-dimensional and can be computed for a discrete sample of orientations of the tool, while the IMF is the minimum over all such orientations.
• Figure 2: A diagram of the deep neural network architecture for representing the CMF and IMF described in Section \ref{['sec_dnn_imf_rep']}.
• Figure 3: A depiction of the part and tool used for the two-dimensional comparison.
• Figure 4: Comparison between our DNN representation of the CMF to other interpolation schemes.
• Figure 5: Tool and part geometries used in Sections \ref{['sec_sing_res']} and \ref{['sec_multi_res']}.