Topology-Preserving Multi-Usage Pipe Centerline Refinement under Permanent Tubular Occupancy

Additive manufacturing (AM) enables compact hydraulic components whose internal fluid channels can follow free-form 3D paths rather than conventionally drilled holes. A representative case is multi-group channel layout in rotary direct-drive servo valves: once a channel is placed it permanently occupies volume, so later channels must clear earlier geometry--unlike classical multi-agent pathfinding (MAPF), where agents free space after moving. We study this setting as multi-group pipe routing under permanent geometric occupancy. Our contributions are a problem formalization with geometric dual-witness conflicts, a constructive 3D benchmark (two corridor generators x two obstacle painters, controlled difficulty, feasibility witnesses), and baseline results for CBS, PBS, and priority planning adapted to this coupling. We evaluate by success rate under a fixed time budget. PlaneSlice hard instances clearly rank CBS above PBS and PP, while easier cells validate the pipeline. The goal is a reproducible problem definition, suite, and classical baselines--not a new optimal MAPF algorithm.

Design for manufacturing plays a critical role in advanced aeroengine development, where complex components necessitate careful consideration of manufacturability. However, current practices in pipe routing remain largely decoupled from down-stream manufacturing, leading to labor-intensive, trial-and-error iterations to achieve manufacturable designs. To address this problem, this study proposes the Frenet-based pipe routing optimization (FPRO) framework, a manufacturability knowledge-integrated reinforcement learning approach for free-form pipe design in aeroengines. FPRO formulates the routing problem as a boundary value problem in the Frenet frame. In this framework, the pipe path is represented by curvature and torsion profiles, which are generated using cubic Hermite interpolation. To integrate design and manufacturing, domain-specific manufacturing knowledge is embedded as constraints on the permissible ranges of curvature and torsion. The path optimization is performed using the proximal policy optimization algorithm with stochastic exploration and a stage-guided reward mechanism. A unified mapping formulation then translates the optimized path into motion trajectories for the bending die, enabling direct fabrication on a six-axis free-bending machine. Experimental results demonstrate that FPRO consistently generates collision-free, manufacturable paths with smoother geometric profiles compared to Cartesian-based methods. It also achieves faster convergence and superior performance in terminal alignment, path length, obstacle avoidance, and manufacturability compared to state-of-the-art reinforcement learning baselines. Real-world validation confirms the close geometric correspondence between the manufactured pipe and its digital design, validating the practical feasibility of FPRO.

Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often computationally intractable beyond a very small swarm size. In this paper, we propose Flow-Opt, a learning-based approach towards improving the computational tractability of centralized multi-robot trajectory optimization. Specifically, we reduce the problem to first learning a generative model to sample different candidate trajectories and then using a learned Safety-Filter(SF) to ensure fast inference-time constraint satisfaction. We propose a flow-matching model with a diffusion transformer (DiT) augmented with permutation invariant robot position and map encoders as the generative model. We develop a custom solver for our SF and equip it with a neural network that predicts context-specific initialization. The initialization network is trained in a self-supervised manner, taking advantage of the differentiability of the SF solver. We advance the state-of-the-art in the following respects. First, we show that we can generate trajectories of tens of robots in cluttered environments in a few tens of milliseconds. This is several times faster than existing centralized optimization approaches. Moreover, our approach also generates smoother trajectories orders of magnitude faster than competing baselines based on diffusion models. Second, each component of our approach can be batched, allowing us to solve a few tens of problem instances in a fraction of a second. We believe this is a first such result; no existing approach provides such capabilities. Finally, our approach can generate a diverse set of trajectories between a given set of start and goal locations, which can capture different collision-avoidance behaviors.