Leveraging Fixed-Parameter Tractability for Robot Inspection Planning

TL;DR

This work formalizes inspection planning as Graph Inspection, an edge-weighted, vertex-micolored graph problem that generalizes TSP and captures backtracking and cycles in robot workflows. It introduces two exact solvers, DP-IPA (a dynamic-programming, FPT algorithm with complexity depending on the number of POIs) and ILP-IPA (a flow-based ILP formulation), and develops practical scalability techniques including color reduction, partitioning, and walk-merging. The methods are evaluated on two robotics tasks (bridge inspection with a UAV and surgical inspection with a medical robot), where ILP-IPA achieves near-perfect or perfect coverage and DP-IPA offers robust weight reductions on larger graphs, outperforming the prior state of the art IRIS-CLI in several settings. The study also provides a principled framework for combining multiple solved walks into a single plan, enabling scalable deployment in real-world inspection scenarios and offering a path toward broader adoption in autonomous robotics planning.

Abstract

Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and efficiently perform such an inspection is an extremely difficult algorithmic challenge. In this work we consider an abstraction of the inspection planning problem which we term Graph Inspection. We give two exact algorithms for this problem, using dynamic programming and integer linear programming. We analyze the performance of these methods, and present multiple approaches to achieve scalability. We demonstrate significant improvement both in path weight and inspection coverage over a state-of-the-art approach on two robotics tasks in simulation, a bridge inspection task by a UAV and a surgical inspection task using a medical robot.

Figures (15)

• Figure 1: Inspection planning, in contrast to traditional motion planning, may necessitate leveraging cycles and backtracking on graphs embedded in the robot's configuration space. This necessitates computing a walk (rather than a path) on a graph. (A) A quadrotor, while inspecting a bridge for potential structural defects, may need to circle around obstacles, (B) leveraging a cycle in its c-space graph (teal). (C) A medical endoscopic robot (black) may need to move into and then out of an anatomical cavity to, e.g., visualize the underside of a patient's gallbladder (green), (D) requiring backtracking in its c-space graph (teal).
• Figure 2: ILP-IPA, an ILP for the Graph Inspection problem.
• Figure 3: An illustration of the partition-and-merge framework. The color set in the original graph (left) is reduced to $2$ color sets $\mathcal{C}_1$ and $\mathcal{C}_2$, each of which contains $2$ colors (middle). For each color set, we find an optimal walk collecting all colors in the set, resulting in the blue and red walks. Those walks are merged into the green walk, collecting the same colors in the color-reduced graph (right).
• Figure 4: Selected results of color partitioning experiment on datasets CRISP1000 and DRONE1000 with $k \in \{10, 20\}$. Each data point represents a solution computed using DP-IPA and ExactMerge. For each combination of color reduction method and partitioning strategy, we highlight the solutions with maximum coverage (rightward arrow) and with minimum weight (downward arrow).
• Figure 5: Overview of our experiment pipeline.

Theorems & Definitions (17)

• theorem thmcountertheorem
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