Minimum-Time Dubins Airplane Inspection Tours with Visibility and Dwell Time Constraints

This paper investigates the planning of a minimum-time tour for a three-dimensional (3D) Dubins airplane model to visually inspect a series of static targets in an urban environment. The inspection tour contains path segments that continuously observe each target (without occlusion) for a predetermined dwell time. Such tours are relevant to applications in urban surveillance and infrastructure inspection. The proposed approach overcomes gaps in existing methods by simultaneously considering 3D visibility constraints, different camera models (body-fixed or gimbaled), dwell times enforced along straight segments, the inspection of multiple targets concurrently, and cost savings gained via altitude changes. The approach presented is underpinned by the computation of visibility volumes as triangular meshes, which encode admissible viewing locations, and a 3D Dubins traveling salesperson problem with overlapping neighborhoods (DTSPN). Several sampling strategies to generate vehicle configurations with feasible dwell segments are proposed and used to formulate the DTSPN graph. Additionally, a heuristic approach is proposed to improve computation time by approximating DTSPN edge costs with a lower bound. Simulation results demonstrate that using the proposed 3D methods leads to a reduction in tour cost compared to two-dimensional constant-altitude methods. A flight test experiment illustrates the practicality of the approach in a simple inspection scenario.