Research ArticleCOLLECTIVE BEHAVIOR

Optimized flocking of autonomous drones in confined environments

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Science Robotics  18 Jul 2018:
Vol. 3, Issue 20, eaat3536
DOI: 10.1126/scirobotics.aat3536
  • Fig. 1 Comparing previous simulation work with current study.

    Sample timelines of two order parameters (right, velocity correlation at top and normalized velocity magnitude at bottom) from our previous work (40) (algorithm A) and our novel flocking model (algorithm B). Trajectories corresponding to the gray sections of the timelines are shown for both models on the left, with color mapped to time. Corresponding motion can be seen in movies S1 and S2. Algorithm B performs much better and has a lower transient time. We used the following interaction parameter set for algorithm A: Cfrict = 30 m2, Embedded Image m, Embedded Image m, and prep = 1 s−1 [for details on parameters, see (40)]. For algorithm B, we used the optimized parameter set for vflock = 4 m/s. Using an average from 10 simulations with the same parameter setup, the order parameters averaged over time were Embedded Image and Embedded Image m/s for algorithm A and Embedded Image and Embedded Image m/s for algorithm B.

  • Fig. 2 Distribution of the number of collisions and the average closest-neighbor distance as a function of communication range and delay.

    Every bin is the average of 20 simulations with the optimized parameter setup for a flocking speed of 32 m/s. As can be seen, safe flocking can be achieved with small enough delay (<1 s) and large enough communication range (>240 m) for this setup.

  • Fig. 3 Order parameters as a function of time for different vflock values during real experiments with 30 drones.

    ϕcorr is the cluster-dependent velocity correlation, ϕvel/vflock is the average normalized velocity, and Embedded Image represents the average of the closest neighbors, whereas min(rij) is the minimum of the closest neighbors. The depicted region corresponds to the middle 5 min of Fig. 4. There are two typical, mostly stable behaviors in a square-shaped arena without obstacles: (A) shows mostly linear motion along the main diagonals with a cyclic expansion and shrinking of the flock (cyclic red and orange curves) and sudden turns at corners (blue and green curves dropping to zero), whereas (C) shows circular motion within the boundaries (nearly constant order parameters at all times). (B) The repetitive, trivial patterns were broken and became livelier due to obstacles in the way. Correspondingly, velocity correlation and average velocity magnitude drops, whereas minimal interagent distance remains the same, showing the stability of the flight even in this obstructed case.

  • Fig. 4 Multidrone flight trajectories and corresponding order parameters.

    Ten-minute trajectory sections of 30 drones in the horizontal plane for (A) 4 m/s, (B) 6 m/s and (C) 8 m/s flights, representing a selection of typical flight patterns. Blue squares show the boundaries of the virtual arena. (A) The trajectories show diagonal linear motion of the flock, bouncing back from the right-angled corners. Trajectory colors represent speed in the horizontal plane, whereas a random single trajectory is highlighted in gray scale. (B) The motion is still locally correlated, but the obstacles (red shapes) induce a very rich dynamic pattern, resembling lively flocks of birds or other animals. (C) The trajectories show a highly correlated close-to-circular flight. Colors and line styles are mapped to individual drones here; black dots show terminal positions of drones. (D) Comparison of the three qualitatively different behaviors of (A) to (C) with the timeline of a dedicated order parameter: the average normalized velocity, expressed in local angle polar coordinates (ϕLAP).

  • Fig. 5 Long-exposure photo of a flight with multiple drones. [Credit: Zsolt Bézsenyi]
  • Fig. 6 Visual explanation of the interaction terms.

    The blue line depicts repulsion between agents as a function of interagent distance. The green line is the maximum allowed velocity difference between agents as a function of interagent distance. The velocity alignment term is proportional to the difference between this and the actual velocity difference between agents (red dashed line). All exemplary parameter values are in SI units.

  • Fig. 7 Three different types of transfer functions with a codomain of [0,1].

    A global single-objective fitness value can be defined as the multiplication of several partial fitness functions based on these transfer functions.

  • Fig. 8 Probability distribution of the communication outages as a function of distance.

    The database was gathered from a 5-min section of a general flight with 32 drones in a remote open-air setting. Each drone logged a 5-Hz sampling of the elapsed time since the reception of the last status packet from all other drones. This value [we call it timeout for simplicity but it actually also contains a small (<0.2 s) processing delay] was matched later with the position of the drones recorded accurately by each drone onboard. The distribution shows logs from all drones (1,349,490 data points in total), and it is normalized for each row (distance) separately. Color indicates timeout probability in each bin for a given distance. Average timeouts with SD and with the number of data points are indicated on the right for 50-m distance binning, whereas the black line on the plot indicates average and SD of timeout for each distance bin of 10 m. Database is very sparse and thus less accurate above 150 m, but as a general tendency, communication is most stable between close-by drones, whereas outages were more frequent and longer with increasing distance.

  • robotics.sciencemag.org/cgi/content/full/3/20/eaat3536/DC1

    Movie S1. Simulation of the old flocking model (algorithm A) with 100 agents.

    Movie S2. Simulation of the new flocking model (algorithm B) after evolutionary optimization with 100 agents.

    Movie S3. Simulation of flocking for different speeds (4 to 32 m/s), flock sizes (30 to 1000 agents), and scenarios.

    Movie S4. Flight log visualization of 30 drones at 4 m/s in a diagonal flight pattern.

    Movie S5. Flight log visualization of 30 drones at 6 m/s with obstacles.

    Movie S6. Flight log visualization of 30 drones at 8 m/s in a circular flight pattern.

    Movie S7. Summarizing documentary with simulation, flight log visualization, and footage on real flights.

    Table S1. Optimized model parameter values and working ranges in simulation.

    Table S2. Statistic evaluation of optimized simulations.

    Table S3. Explanation of flocking model parameters.

    Table S4. Model parameter values used on real drones.

    Table S5. Environmental parameters of the realistic setup.

    Table S6. Parameter settings of the evolutionary optimization.

  • Supplementary Materials

    The PDF file includes:

    • Legends for movies S1 to S7
    • Table S1. Optimized model parameter values and working ranges in simulation.
    • Table S2. Statistic evaluation of optimized simulations.
    • Table S3. Explanation of flocking model parameters.
    • Table S4. Model parameter values used on real drones.
    • Table S5. Environmental parameters of the realistic setup.
    • Table S6. Parameter settings of the evolutionary optimization.

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Simulation of the old flocking model (algorithm A) with 100 agents.
    • Movie S2 (.avi format). Simulation of the new flocking model (algorithm B) after evolutionary optimization with 100 agents.
    • Movie S3 (.mp4 format). Simulation of flocking for different speeds (4 to 32 m/s), flock sizes (30 to 1000 agents), and scenarios.
    • Movie S4 (.avi format). Flight log visualization of 30 drones at 4 m/s in a diagonal flight pattern.
    • Movie S5 (.avi format). Flight log visualization of 30 drones at 6 m/s with obstacles.
    • Movie S6 (.avi format). Flight log visualization of 30 drones at 8 m/s in a circular flight pattern.
    • Movie S7 (.mp4 format). Summarizing documentary with simulation, flight log visualization, and footage on real flights.

    Files in this Data Supplement:

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