This paper presents a camera node placement optimization system for motion analysis during soldering tasks. We formulate the problem as a Mixed-Integer Linear Programming (MILP) that jointly enforces (i) imaging coverage over all joint and time pairs, (ii) positional uniqueness (at most one camera per candidate location) and (iii) network connectivity under capacity-constrained wireless mesh links. To address column explosion from position \(\times \) orientation discretization, we adopt column generation with Restricted Master Problem (RMP) and Pricing, while visibility is computed only for a clustered set of representative timestamps \(\tilde{T}\) and later verified on the full set T. Communication constraints are separated via Benders decomposition considering master handles coverage, positional uniqueness, and accumulated cuts, while the subproblem verifies connectivity and returns feasibility/optimality cuts. We consider warm-start Branch-and-Bound (B&B) to round the RMP solution to a feasible integer solution. In simulations, our method consistently achieved full coverage and network connectivity. The integration of column generation, Benders decomposition, and warm-start B&B enabled practical solution even with large candidate sets.

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A Camera Placement Optimization System for Motion Analysis Considering Posture Changes During Soldering Work

  • Kyohei Wakabayashi,
  • Tetsuya Oda,
  • Leonard Barolli

摘要

This paper presents a camera node placement optimization system for motion analysis during soldering tasks. We formulate the problem as a Mixed-Integer Linear Programming (MILP) that jointly enforces (i) imaging coverage over all joint and time pairs, (ii) positional uniqueness (at most one camera per candidate location) and (iii) network connectivity under capacity-constrained wireless mesh links. To address column explosion from position \(\times \) orientation discretization, we adopt column generation with Restricted Master Problem (RMP) and Pricing, while visibility is computed only for a clustered set of representative timestamps \(\tilde{T}\) and later verified on the full set T. Communication constraints are separated via Benders decomposition considering master handles coverage, positional uniqueness, and accumulated cuts, while the subproblem verifies connectivity and returns feasibility/optimality cuts. We consider warm-start Branch-and-Bound (B&B) to round the RMP solution to a feasible integer solution. In simulations, our method consistently achieved full coverage and network connectivity. The integration of column generation, Benders decomposition, and warm-start B&B enabled practical solution even with large candidate sets.