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

arXiv:2610.19403v1 Announce Type: new Abstract: Discrete multi-group pipe routers place channels on a grid or coarse graph. The resulting centerlines are topologically feasible but typically contain many axis-aligned corners. For permanently occupied fluid tubes---as in additively manufactured hydraulic manifolds---those corners are undesirable: they degrade geometric fairness and, in practice, flow quality. This technical report studies the downstream geometric stage that starts from a fixed routing topology and a feasible coarse layout, and refines tubular centerlines under permanent clearance. Unlike classical robotic path smoothing, which usually fair one temporary open trajectory, our setting is a branched manifold with declared terminal usages, finite tube radii, and static cross-group occupancy. We formalize the refinement problem, highlight the multi-usage junction conflict that a single shared branch point cannot resolve, and outline a hybrid trunk-share / junction-split parameterization with soft geometric costs and hard clearance acceptance. On a multi-group suite ($8$ groups $\times$ $8$ terminals, $r{=}2$) with capsule clearance, the refine reaches full hard-accept success, $\kappa r\lesssim 1$, and about a $95\%$ relative drop in the soft objective. Physics-based pressure-drop optimization is intentionally deferred to a later PDE stage; here the objective remains geometric.

Abstract:Discrete multi-group pipe routers place channels on a grid or coarse graph. The resulting centerlines are topologically feasible but typically contain many axis-aligned corners. For permanently occupied fluid tubes---as in additively manufactured hydraulic manifolds---those corners are undesirable: they degrade geometric fairness and, in practice, flow quality. This technical report studies the downstream geometric stage that starts from a fixed routing topology and a feasible coarse layout, and refines tubular centerlines under permanent clearance. Unlike classical robotic path smoothing, which usually fair one temporary open trajectory, our setting is a branched manifold with declared terminal usages, finite tube radii, and static cross-group occupancy. We formalize the refinement problem, highlight the multi-usage junction conflict that a single shared branch point cannot resolve, and outline a hybrid trunk-share / junction-split parameterization with soft geometric costs and hard clearance acceptance. On a multi-group suite ($8$ groups $\times$ $8$ terminals, $r{=}2$) with capsule clearance, the refine reaches full hard-accept success, $\kappa r\lesssim 1$, and about a $95\%$ relative drop in the soft objective. Physics-based pressure-drop optimization is intentionally deferred to a later PDE stage; here the objective remains geometric.

Robotics (cs.RO)

arXiv:2610.19403 [cs.RO]

(or arXiv:2610.19403v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2610.19403 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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

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