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TLDR: The dot product of two vectors are a⋅b=∣a∣∣b∣cos(θ). By checking the sign of the dot product before and after movement, you can determine if the vehicle has crossed the plane. D=(x−x0)⋅(current position – halfplane) will hold positive value.

Code Breakdown

To determine the desired track and altitude, we get GPS coordinates (latitude, longitude), altitude, then a track. Formatting is done by the sensor driver.

So when you are given an input like this:

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language	cpp

WaypointManager_Data_In input1 = {43.467998128, -80.537331184, 11, 100};

It simply means :

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WaypointManager_Data_In input = {latitude, longitude, altitude, track};

We are assuming that the flight path and home base is already initialized in this test.

Let’s look into more detail:

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auto status1 = cruisingState.pathFollow(input1, &out1);

When you go to the pathFollow function, it calls a function called ‘get_next_directions’.

This simply allows you to get the next direction using waypoint manager logic. We introduce a new array called position. We then call a function to get coordinates.

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    WaypointStatus CruisingStateManager::get_next_directions(WaypointManager_Data_In currentStatus, WaypointManager_Data_Out *Data)
    {
        // follow waypoints
        float position[3]; 
        // Gets current track
        float currentTrack = (float) currentStatus.track;
        PM::Waypoint::get_coordinates(currentStatus.longitude, currentStatus.latitude, position);
        position[2] = (float) currentStatus.altitude;

        follow_waypoints(waypointBuffer[currentIndex], position, currentTrack);

        // update return data
        update_return_data(Data);
        
        return WAYPOINT_SUCCESS;
    }

Get coordinates calls get distance. They calculate longitude and latitude relative to defined origin, and output it into position[0] and position[1]. In this case, xyCoordinates[0] and xyCoordinates[1].

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void get_coordinates(long double longitude, long double latitude, float* xyCoordinates) { // Parameters expected to be in degrees
        xyCoordinates[0] = get_distance(REFERENCE_LATITUDE, REFERENCE_LONGITUDE, REFERENCE_LATITUDE, longitude); //Calculates longitude (x coordinate) relative to defined origin (RELATIVE_LONGITUDE, RELATIVE_LATITUDE)
        xyCoordinates[1] = get_distance(REFERENCE_LATITUDE, REFERENCE_LONGITUDE, latitude, REFERENCE_LONGITUDE); //Calculates latitude (y coordinate) relative to defined origin (RELATIVE_LONGITUDE, RELATIVE_LATITUDE)
    }

As I mentioned, to convert XY coordinates, we need to calculate Haversine Formula. Why do we need Haversine formula? Because Earth is not flat and square, it is spherical. The distance between two waypoints lies along the spherical surface - This is called the great-circle distance.

Earlier I said that we receive inputs from Telemetry Manager and store it in Waypoint buffer. In our test, we have pre-defined custom data we feed to the system for the purpose of testing without using RTOS and actual board and setup. We modify the path using editFlightPath function. This will assign necessary information to the system.

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float latitudes[numPaths] = {43.47075830402289, 43.469649460242174, 43.46764349709017, 43.46430420301871, 43.461854997441996, 43.46144872072057};
    float longitudes[numPaths] = {-80.5479053969044, -80.55044911526599, -80.54172626568685, -80.54806720987989, -80.5406705046026, -80.53505945389745};
    float altitudes[numPaths] = {10, 20, 30, 33, 32, 50};

    WaypointManager_Data_In inputData;
    WaypointsCommand telemetryData;
    telemetryData.num_waypoints = numPaths;
    for (uint8_t i=0; i<numPaths; ++i) {
      telemetryData.waypoints[i] = {
        i, // waypoint_id
        i, // seq_num
        longitudes[i], // longitude
        latitudes[i], // latitude
        altitudes[i] // altitude     
      };    
    }

Now we proceed with the next line in get_next_direction function, follow_waypoint.

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void CruisingStateManager::follow_waypoints(WaypointData* currentWaypoint, float* position, float track)
    {
        if (currentWaypoint->next == nullptr) 
        { // If target waypoint is not defined
            follow_last_line_segment(currentWaypoint, position, track);
        }
        else if (currentWaypoint->next->next == nullptr) 
        { // If waypoint after target waypoint is not defined
            follow_line_segment(currentWaypoint, position, track);
        }
        else
        { // If there are two waypoints after target waypoint
            next_waypoints(currentWaypoint, position, track);
            
        }
    }

Because we have our test waypoints fed to the system, you’ll jump to next_waypoints.

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  void CruisingStateManager::next_waypoints(WaypointData* currentWaypoint, float* position, float track)
    {
        float waypointPosition[3]; 
        PM::Waypoint::get_coordinates(currentWaypoint->longitude, currentWaypoint->latitude, waypointPosition);
        waypointPosition[2] = currentWaypoint->altitude;

        // Defines target waypoint
        WaypointData * targetWaypoint = currentWaypoint->next;
        float targetCoordinates[3];
        PM::Waypoint::get_coordinates(targetWaypoint->longitude, targetWaypoint->latitude, targetCoordinates);
        targetCoordinates[2] = targetWaypoint->altitude;
       
        // Defines waypoint after target waypoint
        WaypointData* waypointAfterTarget = targetWaypoint->next;
        float waypointAfterTargetCoordinates[3];
        PM::Waypoint::get_coordinates(waypointAfterTarget->longitude, waypointAfterTarget->latitude, waypointAfterTargetCoordinates);
        waypointAfterTargetCoordinates[2] = waypointAfterTarget->altitude;

This part is pretty self explanatory, it defines current waypoint, target waypoint, and the waypoint after the target waypoint. The altitude of each waypoint, in case of input1, will be 10, 20, and 30.

We would then calculate direction to waypoint. It calculate the direction by computing the norm first, and dividing the difference between two waypoints by the norm.

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  float waypointDirection[3];
        PM::Waypoint::calculate_direction_to_waypoint(targetCoordinates, waypointPosition, waypointDirection);
        std::cout << "waypointDirection " << waypointDirection[2] <<std::endl;


        float nextWaypointDirection[3];
        PM::Waypoint::calculate_direction_to_waypoint(waypointAfterTargetCoordinates, targetCoordinates, nextWaypointDirection);
        //Before it was PM::Waypoint::calculate_direction_to_waypoint(targetCoordinates, waypointPosition, waypointDirection); Is this intended to be overwritten? I think not...

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 void calculate_direction_to_waypoint(float* nextWaypointCoordinates, float* prevWaypointCoordnates, float* waypointDirection)
    {
        float norm = sqrt(pow(nextWaypointCoordinates[0] - prevWaypointCoordnates[0],2) + pow(nextWaypointCoordinates[1] - prevWaypointCoordnates[1],2) + pow(nextWaypointCoordinates[2] - prevWaypointCoordnates[2],2));
        waypointDirection[0] = (nextWaypointCoordinates[0] - prevWaypointCoordnates[0])/norm;
        waypointDirection[1] = (nextWaypointCoordinates[1] - prevWaypointCoordnates[1])/norm;
        waypointDirection[2] = (nextWaypointCoordinates[2] - prevWaypointCoordnates[2])/norm;
    }

We now compute turning angle and tangent factor to compute half plane. Refer to orbit following for details.

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        // Required turning angle
        float turningAngle = acos(-DEG_TO_RAD(waypointDirection[0] * nextWaypointDirection[0] + waypointDirection[1] * nextWaypointDirection[1] + waypointDirection[2] * nextWaypointDirection[2]));
        // Calculates tangent factor that helps determine centre of turn 
        float tangentFactor = turnRadius/tan(turningAngle/2);

        float halfPlane[3];
        halfPlane[0] = targetCoordinates[0] - tangentFactor * waypointDirection[0];
        halfPlane[1] = targetCoordinates[1] - tangentFactor * waypointDirection[1];
        halfPlane[2] = targetCoordinates[2] - tangentFactor * waypointDirection[2];

We then compute distance to next waypoint. This function simply computes the distance between the current waypoint and next waypoint.

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distanceToNextWaypoint = PM::Waypoint::calculate_distance_to_waypoint(waypointPosition, position);

We would then receive orbit status from TM. This will decide whether we will be computing follow_straight_path or follow_orbit_path. For math, refer to the straight path and orbit path follow section. In our test case, we only follow the straight path.

The error with desired track and desired altitude was so simple yet so weird.

You just have to assign the output variables to the values.

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Python Haversine formula simulator

import math

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#Coordinates in decimal degrees (e.g. 2.89078, 12.79797)

lon1 = -80.5373
lat1 = 43.468
lon2 = -80.5479
lat2 = 43.468

R = 6371000  # radius of Earth in meters
phi_1 = math.radians(lat1)
phi_2 = math.radians(lat2)

delta_phi = math.radians(lat2 - lat1)
delta_lambda = math.radians(lon2 - lon1)

a = math.sin(delta_phi / 2.0) ** 2 + math.cos(phi_1) * math.cos(phi_2) * math.sin(delta_lambda / 2.0) ** 2

c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))

meters = R * c  # output distance in meters
km = meters / 1000.0  # output distance in kilometers

meters = round(meters, 3)
km = round(km, 3)

print(f"Distance: {meters} m")
print(f"Distance: {km} km")

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