Surface Inspection via Hitting Sets and Multi-goal Motion Planning

This paper develops an approach that enables an aerial vehicle to carry out 3D surface inspections. Given a 3D environment with a set of objects that need to be inspected, and an inspection quality 0 < α < 1, the objective is to compute a set of waypoints whose joint visibility ratio is at least α and a dynamically-feasible and collision-free trajectory that enables the aerial vehicle to reach all the waypoints. The approach seeks to minimize the number of the waypoints and the overall distance traveled by the aerial vehicle. A superset of the waypoints is first generated by using random sampling or approximations of the medial axis via skeletonization algorithms. To reduce the number of the waypoints, the approach applies a visibility filtering mechanism based on a computation of a hitting set via Monte-Carlo search over an axisaligned bounding box obstacle tree. After generating the waypoints, a multi-goal motion planning approach is applied to compute a collision-free and dynamicallyfeasible trajectory that visits all the waypoints while seeking to minimize the distance traveled. Experimental results in simulation with complex 3D models where the aerial vehicle carries out outside and inside inspection tasks demonstrate the effectiveness of the approach.