Scalable Inspection Planning via Flow-based Mixed Integer Linear Programming

Inspection planning seeks a minimum-length collision-free robot tour that observes a given set of points of interest (POIs). Sampling-based methods reduce this continuous problem to a graph inspection planning (GIP) problem over a discrete roadmap, which is then solved using combinatorial solvers. Dense roadmaps capture diverse inspection viewpoints and motion shortcuts, and thus admit higher-quality solutions, but they induce large combinatorial search spaces on which state-of-the-art GIP solvers struggle to find good solutions within practical time budgets. Roadmap sparsification---restructuring a dense roadmap into a compact representation that preserves connectivity and path lengths---can alleviate this burden. However, existing sparsification approaches are either agnostic to the underlying inspection task, or strive to ensure coverage of the POIs without accounting for the quality of the resulting inspection plan. We present Inspection-SPARS, which is, to our knowledge, the first inspection-roadmap sparsifier with POI coverage and path-quality guarantees relative to the dense roadmap. To this end, we generalize the SPARS framework, a popular task-agnostic sparsifier, from purely geometric criteria to task-oriented ones, introducing an inspection-aware vertex admission mechanism that treats POI coverage as a first-class sparsification criterion alongside connectivity and path quality. Experiments in realistic 3D environments show that Inspection-SPARS reduces vertex and edge counts by 4-8x while preserving coverage, allowing the GIP solver to compute tours up to 25% shorter than with the dense roadmap or state-of-the-art inspection roadmap. More broadly, Inspection-SPARS shows that sparsification can be made task-aware without sacrificing guarantees on solution quality.

We present a complete, GPU-resident pipeline for multi-robot 3D inspection of underwater structures. Given a triangle mesh and a fleet of $K$ robots, each carrying a short-range, limited field-of-view camera, the pipeline computes 6-DOF trajectories that jointly cover a target fraction of the surface while minimizing a linearly interpolated makespan/total-cost objective. The joint problem is NP-hard, so we decompose it into five core stages - candidate viewpoint generation, visibility computation, set cover, min-max vehicle routing solved as a mixed integer program (MIP) with lifted Miller-Tucker-Zemlin subtour elimination, and priority-based multi-agent path finding with continuous-time inter-robot conflict checking - flanked by mesh loading and surface sampling as preprocessing and by trajectory smoothing as postprocessing. Our contributions are: an end-to-end GPU-accelerated integration of the five stages, with its kernel design documented; a GPU batch adaptation of Lien's $\varepsilon$-visibility with four custom CUDA kernels; a $β$-aware per-vehicle tour upper bound derived from the interpolated objective, supplementing the Desrochers-Laporte coefficient lift with forbidden-pair cuts; a 4D space-time extension of Zhou and Zeng's GPU parallel-frontier A*; and an experimental evaluation on 14 meshes (up to $7.2$M faces) that ablates the routing cuts and the parallel-frontier search, audits collision freedom and waypoint attainment after trajectory smoothing, and measures the end-to-end gap against analytical and LP-relaxation lower bounds. Code and raw results are publicly available.

This work investigates the use of flow-based connectivity maintenance constraints in mixed-integer linear programming (MILP) trajectory planning and decision-making models for networked multi-agent systems (MAS). We integrate flow-based encodings for standard and k-hop connectivity into MILP multi-vehicle maneuvering models that are widely used alongside receding horizon planning strategies. Their necessity and sufficiency is demonstrated, guaranteeing full coverage of potential network topologies. The flow formulation for standard connectivity decreases the growth of the required inequality constraints from exponential to polynomial w.r.t. the size of the MAS when compared to the state-of-the-art subtour elimination (SEC) method. The flow-based k-hop connectivity constraints decrease the number of required binary variables and decouple its growth from the number of hops. However, the impact of these formulations in performance is not straightforward due to the introduction of a substantial number of continuous flow optimization variables and, in the case of k-hop connectivity, additional inequality constraints. We investigate this trade-off through a statistical evaluation of costs and optimization times using a conventional branch-and-bound commercial solver and trials performed with randomized environments for increasingly larger MAS. The results show that the flow formulation outperforms SEC in standard connectivity problems, enabling the solutions to be computed for larger MAS considering the imposed optimization time limit. The reduction in number of binary variables enabled by the k-hop flow formulations decreases the theoretical worst-case number of iterations required by the branch-and-bound algorithm to compute the global optimal solution. Our results show that this advantage did not translate into improvements in the average performance when compared to the baseline.