10. Missions and geometry

Where did it go?

An AUTO mission is a list of numbered items, usually waypoints (latitude, longitude, altitude). The ground station uploads them, the autopilot flies them in order and reports MISSION_ITEM_REACHED as it gets to each one.

AnaTele rebuilds the uploaded plan from the log's own messages. Then, for each waypoint, it checks whether the drone actually got there.

The simulated mission is a takeoff to 10 m, four waypoints and a return-to-launch. In the nominal flight every waypoint is reported reached. In the motor-failure flight:

Item	Status	Nearest recorded position
WP2–WP4	reported_complete	0.97, 0.97, 0.70 m
WP5	geometry_consistent_with_completion	0.32 m, but no "reached" report before the crash
RTL	completion_not_observed	(not a positional item)

Distance on a sphere

GPS gives latitude and longitude in degrees, but we need metres. On a sphere of radius \(R\), the shortest distance between two points is along the surface. The haversine formula gives it:

\[ h = \sin^2\!\frac{\Delta\varphi}{2} + \cos\varphi_1 \cos\varphi_2 \sin^2\!\frac{\Delta\lambda}{2}, \qquad d = 2R \arcsin\sqrt{h} \]

with \(\varphi\) = latitude, \(\lambda\) = longitude (in radians) and \(R = 6\,371\,008.8\) m (the mean Earth radius).

Over a few kilometres the flat-earth shortcut is accurate to millimetres, far smaller than GPS error. AnaTele uses haversine anyway because it's correct everywhere, including long survey flights and high latitudes.

When does a waypoint count as reached?

ArduPilot treats a waypoint as reached when the drone is within WP_RADIUS_M (2 m in the simulation). GPS has its own uncertainty, so AnaTele allows

\[ d_\text{nearest} \le \texttt{WP\_RADIUS\_M} + h_\text{acc} \]

where \(h_\text{acc}\) is the GPS horizontal accuracy at that moment. Passing this test is labelled consistent with completion, not completed: being close isn't proof.

Drawing the path

The 3D replay in the desktop app draws the flown path with the waypoints. To keep drawing fast it uses at most 6,000 points, keeping every k-th sample with \(k = \lceil n / 6000 \rceil\):

Note

Thinning only affects the picture. Every rule, statistic and distance above uses every sample.