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Fig. 2: a) The figure depicts the three main planar angle of incidence constraints on all three sides of the triangle. For a finite number of such constraints the incidence angle is only enforced approximately. The red line (and n+) demarks a sample orientation for a possible additional planar constraint at a corner. Minimum (green plane) and maximum (red plane) distance constraints are similar planar constraints on the sampling area. These constraints bound the sampling space, where g can be chosen, on all sides (gray area). b) The vertical camera angle constraints with the relevant corners of the triangle in red are depicted in the upper part, while beneath the partition of the space for convexification is depicted.

Figure 2 a) The figure depicts the three main planar angle of incidence constraints on all three sides of the triangle. For a finite number of such constraints the incidence angle is only enforced approximately. The red line (and n+) demarks a sample orientation for a possible additional planar constraint at a corner. Minimum (green plane) and maximum (red plane) distance constraints are similar planar constraints on the sampling area. These constraints bound the sampling space, where g can be chosen, on all sides (gray area). b) The vertical camera angle constraints with the relevant corners of the triangle in red are depicted in the upper part, while beneath the partition of the space for convexification is depicted.

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Structural Inspection Path Planning via Iterative Viewpoint Resampling with Application to Aerial Robotics
Structural Inspection Path Planning via Iterative Viewpoint Resampling with Application to Aerial Robotics
Fig. 1: Indicative inspection 3D reconstruction results using the proposed structural inspection planner and a rotorcraft as well as a fixed-wing UAV equipped with camera sensors. Andreas Bircher, Kostas Alexis, Michael Burri, Philipp Oettershagen, Sammy Omari, Thomas Mantel and Roland Siegwart!
Fig. 1: Indicative inspection 3D reconstruction results using the proposed structural inspection planner and a rotorcraft as well as a fixed-wing UAV equipped with camera sensors. Andreas Bircher, Kostas Alexis, Michael Burri, Philipp Oettershagen, Sammy Omari, Thomas Mantel and Roland Siegwart!
For the computed optimal position, the heading is oP Id according to the criterion minyx = (we 1 wry? / da. + pk} — ak)" /ds, st. Visible(g*,~*), where Visible(g*, ") means that from the given configuration, g® and w*, the whole triangle is Sisible. dp and ds are the Euclidean distances from g” to on 1 and ae | respectively. For simple sensor setups ssublishing the boundaries on w* The resulting convex optimization problem is given be- low. Its structure as a Quadratic Program (QP) with linear constraints allows the use of an efficient solver [6].
For the computed optimal position, the heading is oP Id according to the criterion minyx = (we 1 wry? / da. + pk} — ak)" /ds, st. Visible(g*,~*), where Visible(g*, ") means that from the given configuration, g® and w*, the whole triangle is Sisible. dp and ds are the Euclidean distances from g” to on 1 and ae | respectively. For simple sensor setups ssublishing the boundaries on w* The resulting convex optimization problem is given be- low. Its structure as a Quadratic Program (QP) with linear constraints allows the use of an efficient solver [6].
TABLE I: Scalable Inspection Scenario
TABLE I: Scalable Inspection Scenario
follows d? = qq. To avoid the insertion of unnecessary circles, the distance between the viewpoints has to be large enough according to their heading, the direction to the next viewpoint and r,,i,. The bounds on that distance l;, i = {p,s} are derived geometrically and evaluated using numerical algorithms. The distance criterions are therefore (gk — gh")? (gh — gh") > 1,2, ¢ = {p, 8} which are non- convex. To convexify, the criterions are linearized around the old viewpoint. This adaptation is conservative by the In contrast to the case of rotorcraft UAVs, where only the distance is minimized in the viewpoint position sampling step, the fixed-wing UAV sampler also aims to align the viewpoints on a as straight line as possible. This effectively avoids too many curly path segments and thus, together with the distance minimization tends to reduce the path length. The addition in the objective is therefore to minimize the squared distance d? to the straight line between the neighbouring viewpoints. Using its direction vector b, the distance is calculated as follows:
follows d? = qq. To avoid the insertion of unnecessary circles, the distance between the viewpoints has to be large enough according to their heading, the direction to the next viewpoint and r,,i,. The bounds on that distance l;, i = {p,s} are derived geometrically and evaluated using numerical algorithms. The distance criterions are therefore (gk — gh")? (gh — gh") > 1,2, ¢ = {p, 8} which are non- convex. To convexify, the criterions are linearized around the old viewpoint. This adaptation is conservative by the In contrast to the case of rotorcraft UAVs, where only the distance is minimized in the viewpoint position sampling step, the fixed-wing UAV sampler also aims to align the viewpoints on a as straight line as possible. This effectively avoids too many curly path segments and thus, together with the distance minimization tends to reduce the path length. The addition in the objective is therefore to minimize the squared distance d? to the straight line between the neighbouring viewpoints. Using its direction vector b, the distance is calculated as follows:
The criterion of Equation (7) is inverted for the heading computation and applied as long as a feasible solution is found. The proposed approach also works efficiently in case of obstacles up to some complexity by dividing the sampling space in convex pieces that are evaluated individually. In our implementation obstacles are approximated with cuboids. Wrapping all up in a single QP-formulation and adding the two slack variables €, and €, with constant C’ to allow occasional violation of the minimal distance criterion:
The criterion of Equation (7) is inverted for the heading computation and applied as long as a feasible solution is found. The proposed approach also works efficiently in case of obstacles up to some complexity by dividing the sampling space in convex pieces that are evaluated individually. In our implementation obstacles are approximated with cuboids. Wrapping all up in a single QP-formulation and adding the two slack variables €, and €, with constant C’ to allow occasional violation of the minimal distance criterion:
Fig. 4: Correlation of the number of viewpoints for both systems with the computational time consumption. The time consumption curve is given individually for different components of the algo- rithm. Fig. 3: Illustration of the triangular pattern that is used in different resolutions for the following analysis of the algorithm’s character- istics. Overlayed in brown is a naive sweeping path with a certain base line (in this case the same as the triangle edge length).
Fig. 4: Correlation of the number of viewpoints for both systems with the computational time consumption. The time consumption curve is given individually for different components of the algo- rithm. Fig. 3: Illustration of the triangular pattern that is used in different resolutions for the following analysis of the algorithm’s character- istics. Overlayed in brown is a naive sweeping path with a certain base line (in this case the same as the triangle edge length).
Fig. 5: Figure 5a depicts the relative time consumption of different parts of the algorithm, while Figure 5b shows the cost of the computed paths for different amount of facets, corresponding to varying mesh resolution.
Fig. 5: Figure 5a depicts the relative time consumption of different parts of the algorithm, while Figure 5b shows the cost of the computed paths for different amount of facets, corresponding to varying mesh resolution.
Fig. 6: Improvement of the path cost over the course of 25 iterations for 100, 144 and 256 facets. The left top figure depicts a run without heuristics and one with the heuristic on the viewpoint neighbours (running for the first 10 iterations) and the heuristic on the viewpoint yaw (running for the first 15 iterations). As shown, for the fixed-wing UAV case a less smooth path improvement procedure takes place after the first iterations due to the additional complexity introduced by the nonholonomic constraints.
Fig. 6: Improvement of the path cost over the course of 25 iterations for 100, 144 and 256 facets. The left top figure depicts a run without heuristics and one with the heuristic on the viewpoint neighbours (running for the first 10 iterations) and the heuristic on the viewpoint yaw (running for the first 15 iterations). As shown, for the fixed-wing UAV case a less smooth path improvement procedure takes place after the first iterations due to the additional complexity introduced by the nonholonomic constraints.
TABLE II: Beijing Tower Inspection Scenario
TABLE II: Beijing Tower Inspection Scenario
Fig. 7: Large scale structure to be inspected: The 405m high Central Radio & TV Tower in Beijing. The mesh used to compute the path contains 1701 triangular facets. After a computation time of 92s the cost for the inspection is 2997.44s with a maximal speed of 2m/s and a maximal yaw rate of 0.5rad/s. The red point denotes, start— and end-point of the inspection. in the experimental studies presented in subsections VI-B and VI-C.
Fig. 7: Large scale structure to be inspected: The 405m high Central Radio & TV Tower in Beijing. The mesh used to compute the path contains 1701 triangular facets. After a computation time of 92s the cost for the inspection is 2997.44s with a maximal speed of 2m/s and a maximal yaw rate of 0.5rad/s. The red point denotes, start— and end-point of the inspection. in the experimental studies presented in subsections VI-B and VI-C.
TABLE III: Rotorcraft UAV Inspection Scenario
TABLE III: Rotorcraft UAV Inspection Scenario
TABLE IV: Marche-en—Famenne Inspection Scenario
TABLE IV: Marche-en—Famenne Inspection Scenario
Fig. 9: Experimental study of the inspection of a trolley. The preliminary, terrestrial images—based, 3D reconstruction of the inspection structure is depicted and was used to derive a simplified mesh that was then employed by the inspection path planner to compute the inspection path shown in the Figure. The path cost is 151.44s for Umax = 0.25m/s and ymax = 0.5rad/s . planner, a path that guarantees complete coverage is derived and has a total length of 151.44s. Reconstruction results derived using pose—annotated (position and rotations) image sequences from one of the VI—Sensor cameras and the Pix4D software indicate excellent 3D reconstruction results, a fact that further increases confidence on the practical applicability of the proposed algorithm. The reference path and the recorded flight response along with the reconstruction results are shown in Figure 9. The arrows indicate the reference viewpoints proposed by the inspection planner.
Fig. 9: Experimental study of the inspection of a trolley. The preliminary, terrestrial images—based, 3D reconstruction of the inspection structure is depicted and was used to derive a simplified mesh that was then employed by the inspection path planner to compute the inspection path shown in the Figure. The path cost is 151.44s for Umax = 0.25m/s and ymax = 0.5rad/s . planner, a path that guarantees complete coverage is derived and has a total length of 151.44s. Reconstruction results derived using pose—annotated (position and rotations) image sequences from one of the VI—Sensor cameras and the Pix4D software indicate excellent 3D reconstruction results, a fact that further increases confidence on the practical applicability of the proposed algorithm. The reference path and the recorded flight response along with the reconstruction results are shown in Figure 9. The arrows indicate the reference viewpoints proposed by the inspection planner.
Fig. 8: The Firefly UAV equipped with the VI-Sensor.
Fig. 8: The Firefly UAV equipped with the VI-Sensor.
Fig. 10: The AtlantikSolar UAV with the sensor pod attached to its wings and further photos of the sensor pod, the solar cells and an instant of the hand—launching. lab. The particular platform, AtlantikSolar [20], is a 5.6m wingspan, 7.5kg, solar-powered vehicle with robust state— estimation capabilities [22], automatic trajectory tracking control [19] and further integrates a) an advanced sensor pod with a monocular version of the aforementioned VI—Sensor with the Aptina MT9V034 camera mounted at a 50° front— down oblique view and every image is fully pose—annotated as well as b) a GPS-tagged Sony HDR-AS100VW camera. Figure 10 depicts the UAV as well as the sensor pod.
Fig. 10: The AtlantikSolar UAV with the sensor pod attached to its wings and further photos of the sensor pod, the solar cells and an instant of the hand—launching. lab. The particular platform, AtlantikSolar [20], is a 5.6m wingspan, 7.5kg, solar-powered vehicle with robust state— estimation capabilities [22], automatic trajectory tracking control [19] and further integrates a) an advanced sensor pod with a monocular version of the aforementioned VI—Sensor with the Aptina MT9V034 camera mounted at a 50° front— down oblique view and every image is fully pose—annotated as well as b) a GPS-tagged Sony HDR-AS100VW camera. Figure 10 depicts the UAV as well as the sensor pod.
Fig. 11: Inspection path and point—cloud for 3D reconstruction pur- poses using the front-down mounted view grayscale camera of the VI-Sensor onboard AtlantikSolar. Blue line represents the reference path, green circles are used to indicate the actual waypoints loaded to the autopilot and red is used for the vehicle response. The planner commands the vehicle to navigate such that the camera covers the whole desired area marked with dashed cyan line. A UTM31N coordinate system is employed.
Fig. 11: Inspection path and point—cloud for 3D reconstruction pur- poses using the front-down mounted view grayscale camera of the VI-Sensor onboard AtlantikSolar. Blue line represents the reference path, green circles are used to indicate the actual waypoints loaded to the autopilot and red is used for the vehicle response. The planner commands the vehicle to navigate such that the camera covers the whole desired area marked with dashed cyan line. A UTM31N coordinate system is employed.
Fig. 12: Inspection path and 3D reconstruction results using the nadir mounted Sony HDR-AS100VW onboard AtlantikSolar. Blue line represents the reference path, green circles are used to indicate the actual waypoints loaded to the autopilot and red is used for the vehicle response. The planner commands the vehicle to navigate such that the camera covers the whole desired area marked with dashed cyan line. A UTM31N coordinate system is employed.
Fig. 12: Inspection path and 3D reconstruction results using the nadir mounted Sony HDR-AS100VW onboard AtlantikSolar. Blue line represents the reference path, green circles are used to indicate the actual waypoints loaded to the autopilot and red is used for the vehicle response. The planner commands the vehicle to navigate such that the camera covers the whole desired area marked with dashed cyan line. A UTM31N coordinate system is employed.