metrics

UAV formation performance and inter-UAV distance metrics

Since R2024b

Syntax

[performance,distance] = metrics(trajectoryEnsemble)

Description

[performance,distance] = metrics(trajectoryEnsemble) returns the performance and inter-UAV distance metrics of a UAV formation that you specify as a trajectory ensemble.

Examples

Visualize and Obtain Performance Metrics of UAV Formation

Specify the number of UAVs in a UAV formation, and create the timestamps for the UAV trajectories.

% Number of UAVs in the formation
numUAV = 4;

% Timestamps
time = [0; 1];

Specify the position of each UAV in ENU frame in meters at 0 and 1 seconds

uav1_position = [1 0 10;
                1 0 10.5];
uav2_position = [0.5 0.8 10;
                0.5 1.8 11];
uav3_position = [1.5 1 10;
                1.5 1.8 11];
uav4_position = [2 0 10;
                1.5 0 10.5];

Specify the velocity of each UAV in ENU frame in m/s at 0 and 1 seconds

uav1_velocity = [0 0 0.5; 
                1 0 0];
uav2_velocity = [0 1 1;
                1 0 0];
uav3_velocity = [0 1 1;
                1 0 0];
uav4_velocity = [0 0 0.5;
                1 0 0];

Store the trajectory of each UAV in a timetable, and store the timetables in a cell array.

trajData1=timetable(seconds(time),uav1_position,uav1_velocity,VariableNames={'Position','Velocity'});
trajData2=timetable(seconds(time),uav2_position,uav2_velocity,VariableNames={'Position','Velocity'});
trajData3=timetable(seconds(time),uav3_position,uav3_velocity,VariableNames={'Position','Velocity'});
trajData4=timetable(seconds(time),uav4_position,uav4_velocity,VariableNames={'Position','Velocity'});

Create a UAV trajectory ensemble object. Specify the safety radius as 0.25 meters, a maximum connectivity range of 1.5 meters, and a maximum number of neighbors of 5.

trajectoryEnsemble = uavFormationMetrics({trajData1,trajData2,trajData3,trajData4},SafetyRadius=0.25,ConnectivityRange=1.5,...
    MaxNumNeighbors=5);

Obtain the perfomance and distance metrics of the UAV formation.

[perfMetrics,distMetrics] = metrics(trajectoryEnsemble);

Plot the formation performance metrics

stackedplot(perfMetrics)
grid on
title("Formation Performance Metrics")

Plot the distance performance metrics

stackedplot(distMetrics)
grid on
title("Distance Metrics")

Obtain the UAV formation information.

info = formationInfo(trajectoryEnsemble);

Plot the UAV formation at the initial time step

% Create edge label for UAV distance at 0 seconds
edgeLabel0 = info.FormationGraph{1}.Edges.Weight;

% Plot the formation at 0 seconds
plot(info.FormationGraph{1},EdgeLabel=edgeLabel0, ...
    XData=info.PositionX(1,:),YData=info.PositionY(1,:), ...
    ZData=info.PositionZ(1,:));

% Add title labels to each axis
title("UAV Formation at t = 0 seconds")
xlabel("East")
ylabel("North")
zlabel("Up")

Plot the UAV formation after movement at t = 1 second. In this time, some UAVs are out of the connectivity range and form 2 connected subgroups.

% Create edge label for UAV distance at 1 second
edgeLabel1 = info.FormationGraph{2}.Edges.Weight;

% Plot the formation at 1 second
plot(info.FormationGraph{2},EdgeLabel=edgeLabel1, ...
    XData=info.PositionX(2,:),YData=info.PositionY(1,:), ...
    ZData=info.PositionZ(2,:)); 

% Add labels to each axis
title("UAV Formation at t = 1 second")
xlabel("East")
ylabel("North")
zlabel("Up")

Obtain the inter-UAV distance for all UAV pairs in the formation at t = 1 second.

info.InterUAVDistance{2}

ans=6×2 table
    UAVPair    Distance
    _______    ________

    1    2      1.9339 
    1    3      1.9339 
    1    4         0.5 
    2    3           1 
    2    4       2.119 
    3    4      1.8682 

Input Arguments

trajectoryEnsemble — UAV trajectory ensemble

uavFormationMetrics object

UAV trajectory ensemble, specified as a uavFormationMetrics object.

Output Arguments

performance — UAV formation performance metrics

timetable

UAV formation performance metrics, returned as a timetable with the following variables:

• Safety — UAV formation safety on a scale from 0 to 1, with lower values indicating greater risk of collision. A collision occurs when the safety radius of one UAV intersects with that of any other UAV.

• Order — Uniformity of UAV formation flight on a scale of -1 to 1, with lower values indicating the UAVs flying in different directions and higher values indicating more uniform directions. In order for the function to output this metric, your input trajectory must contain velocity data.

• Connectivity —Connection among UAVs within the formation on a scale from 0 to 1, where higher values indicate a greater number of UAVs are interconnected. UAVs are connected if they are within connectivity range of one another.

• Union — Measures the scatter of UAVs on a scale from 0 to 1, where lower scores signify more widely scattered UAVs, and higher scores reflect a tighter formation.

For more details on the performance metrics, see UAV Formation Performance Metrics

distance — UAV formation distance metrics

timetable

UAV formation inter-UAV distance metrics in meters, returned as a timetable with the following variables:

• Min — minimum separation distance between UAVs in the formation

• Average — average separation distance between UAVs in the formation

• Max — maximum separation distance between UAVs in the formation

More About

UAV Formation Performance Metrics

This function uses the following metrics [1] to assess the UAV formation performance

• Safety

  Safety measures the risk of collisions between UAVs in the formation, expressed as:

  $${\varphi }_s=1-\frac{n_{ag}}{N\left(N-1\right)}$$

  where N is the number of UAV in the formation, and n_ag denotes the number of collisions between UAV in the formation, expressed as:

  $$n_{ag}=\left|\left\{\left(i,j\right)s.t.j\ne i\wedge d_{ij}<2r_{ag}\right\}\right|$$

  where d_ij denotes the distance between any pair of UAV in the formation, and r_ag denotes the UAV safety radius that you set when creating the uavFormationMetrics object.

  

• Order

  Order measures the correlation of UAV velocity in the formation, expressed as:

  $${\varphi }_o=\frac{1}{N}{\displaystyle \sum _i{\eta }_i}$$

  Where

  $${\eta }_i=\{\begin{array}{l}{\displaystyle {\sum }_{j\in N_i}\frac{1}{\left|N_i\right|}\frac{v_i.v_j}{\Vert v_i\Vert \Vert v_j\Vert },if\left|N_i\right|>0}\\ 1,otherwise\end{array}$$

  The terms in the equation are as follows.

  • N — The total number of UAV in the formation

  • N_i — Connected neighbors of UAV i

  • v_i — Velocity vector of UAV i

  • v_j — Velocity vector of j^th neighbor of UAV i

  

• Connectivity

  Connectivity metric is derived from algebraic connectivity of the UAV formation graph, expressed as:

  $${\varphi }_c=\frac{{\lambda }_2}{N}$$

  where N is the number of UAV in the formation, and λ₂ denotes the second smallest eigenvalue of the Laplacian matrix of the formation graph

  

• Union

  Union metric is derived from the number of independent subgroups of the formation, expressed as:

  $${\varphi }_c=1-\frac{n_c-1}{N-1}$$

  where N is the number of UAV in the formation, andn_c denotes the number of connected UAV subgroups in the formation.

  

References

[1] E. Soria, F. Schiano and D. Floreano, "The Influence of Limited Visual Sensing on the Reynolds Flocking Algorithm," 2019 Third IEEE International Conference on Robotic Computing (IRC), Naples, Italy, 2019.

Version History

Introduced in R2024b