Christoph Hartmann | Searcharxiv

arXiv2025

A Unified Framework for Automated Assembly Sequence and Production Line Planning using Graph-based Optimization

This paper presents PyCAALP (Python-based Computer-Aided Assembly Line Planning), a framework for automated Assembly Sequence Planning (ASP) and Production Line Planning (PLP), employing a graph-based approach to model components and joints within production modules. The framework integrates kinematic boundary conditions, such as potential part collisions, to guarantee the feasibility of automated assembly planning. The developed algorithm computes all feasible production sequences, integrating modules for detecting spatial relationships and formulating geometric constraints. The algorithm incorporates additional attributes, including handling feasibility, tolerance matching, and joint compatibility, to manage the high combinatorial complexity inherent in assembly sequence generation. Heuristics, such as Single-Piece Flow assembly and geometrical constraint enforcement, are utilized to further refine the solution space, facilitating more efficient planning for complex assemblies. The PLP stage is formulated as a Mixed-Integer Program (MIP), balancing the total times of a fixed number of manufacturing stations. To keep the MIP tractable for complex assemblies, a deterministic path-guided reduction solves it on a subgraph assembled from complete, high-quality assembly paths, which preserves feasibility by construction and reproduces the full-graph optimum, exactly or near-exactly, at a small fraction of the directed graph and with speedups of up to three orders of magnitude. Furthermore, the framework enables customization of engineering constraints and supports a flexible trade-off between ASP and PLP. The open-source nature of the framework, available at https://github.com/TUM-utg/PyCAALP, promotes further collaboration and adoption in both industrial and production research applications.

cs.RO↗

arXiv2014

Besov regularity of solutions to the p-Poisson equation

In this paper, we study the regularity of solutions to the $p$-Poisson equation for all $1<p<\infty$. In particular, we are interested in smoothness estimates in the adaptivity scale $ B^\sigma_{\tau}(L_{\tau}(\Omega))$, $1/\tau = \sigma/d+1/p$, of Besov spaces. The regularity in this scale determines the order of approximation that can be achieved by adaptive and other nonlinear approximation methods. It turns out that, especially for solutions to $p$-Poisson equations with homogeneous Dirichlet boundary conditions on bounded polygonal domains, the Besov regularity is significantly higher than the Sobolev regularity which justifies the use of adaptive algorithms. This type of results is obtained by combining local H\"older with global Sobolev estimates. In particular, we prove that intersections of locally weighted H\"older spaces and Sobolev spaces can be continuously embedded into the specific scale of Besov spaces we are interested in. The proof of this embedding result is based on wavelet characterizations of Besov spaces.

math.NA↗