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Multi-agent systems for quadcopters

  • * Corresponding author: M. Chyba

    * Corresponding author: M. Chyba 
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  • Unmanned Aerial Vehicles (UAVs) have been increasingly used in the context of remote sensing missions such as target search and tracking, mapping, or surveillance monitoring. In the first part of our paper we consider agent dynamics, network topologies, and collective behaviors. The objective is to enable multiple UAVs to collaborate toward a common goal, as one would find in a remote sensing setting. An agreement protocol is carried out by the multi-agents using local information, and without external user input. The second part of the paper focuses on the equations of motion for a specific type of UAV, the quadcopter, and expresses them as an affine nonlinear control system. Finally, we illustrate our work with a simulation of an agreement protocol for dynamically sound quadcopters augmenting the particle graph theoretic approach with orientation and a proper dynamics for quadcopters.

    Mathematics Subject Classification: Primary: 70E60; 93A14; Secondary: 70E55.


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  • Figure 1.  Rendezvous Missions with Unweighted Network. Displays two different communication network scenarios for a 4-agent rendezvous mission. Agreement positions coincide but trajectories differ

    Figure 2.  Comparison of the $ x, y, z $-motions for agent 1 for the scenarios of Fig. 1 corresponding to rendezvous missions with Unweighted Network

    Figure 3.  Comparison between trajectories on rendezvous missions with unweighted and weighted networks. The solid curves represents the trajectories for the unweighted network and the dashed ones for the weighted network. The two scenarios converge to the same agreement value

    Figure 4.  Comparison of the $ x, y, z $-motions for agent 1 for the rendezvous missions displayed in Figure 3. Observe that each component converges much more rapidly for the weighted network, corresponding to the difference in their $ \lambda_2 $ values: $ 13.060>1 $

    Figure 5.  Rendezvous missions comparing and unweighted network (solid curves) to a time-varying weighted one (dashed curves). They both agree on the consensus joint value. The points where the dashed curves diverge from the solid ones correspond to the addition of edges

    Figure 6.  Comparison of the $ x, y, z $-motions for agent 1 for the rendezvous mission of Figure 5. The components of the trajectory corresponding to the time-varying network clearly converge more rapidly

    Figure 7.  A quadcopter rising straight up, then yawing while hovering, then flying straight along the body $ x $-axis. Top: position in space. Bottom: orientation angles over time

    Figure 8.  The controls used to produce the motion in Figure 7. Top: angular velocities of each of the four motors over time. Bottom: total thrust over time

    Figure 9.  Three drones start at position $ (0, 0, 0) $, $ (0, 9, 0) $ and $ (15, 9, 0) $ with initial yaw angles $ 0 $, $ -\pi/4 $, and $ \pi/2 $. Their trajectories to the rendezvous position are shown

    Figure 10.  The yaw $ \psi $ over time for each drone. Total flight times differ for each drone

    Figure 11.  The controls used to produce the motions in Figures 9 and 10. We show the four motor speeds and total thrust for each drone as functions of time

    Figure 12.  Comparison of two methods of motion planning. Dashed curves include dynamics; solid curves do not. Left: $ x $-coordinate over time. Right: $ y $-coordinate over time

    Table 1.  Parameters used in simulations

    Constant Symbol Value
    drone mass $ m $ 0.468
    drone inertia $ J $ diag($ (3.8278, 3.8288, 7.6566)\cdot10^{-3} $)
    rotor inertia $ J_r $ diag$ (0, 0, 2.8385\cdot 10^{-5}) $
    distance to rotor $ d $ 0.25
    thrust coefficient $ K_r $ $ 2.9842\cdot 10^{-5} $
    translational drag $ C_D $ $ (5.5670, 5.5670, 6.3540)\cdot10^{-4} $
    rotational drag $ C_{\tau} $ $ (5.5670, 5.5670, 6.3540)\cdot 10^{-4} $
    propeller drag $ K_d $ $ 3.2320\cdot 10^{-7} $
     | Show Table
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