Supplementary Material to Ref. [1]. We consider the problem of a drone having to traverse a given terrain, such that traversing the terrain exposes the drone to certain risks (e.g., concentration of chemicals, severe thunderstorm wind gusts or any disturbing weather phenomena.) The goal of the drone is to navigate the terrain while minimizing the amount of risk. We develop a model for quantifying the exposure to a risk factor in a circular zone model. We propose two main strategies based on either rectilinear or curvilinear trajectories. We validate the work using numeric simulations.
Drone, collision avoidance, obstacle avoidance, zone avoidance, risk evaluation, risk mitigation.
We address the following problem. Consider a drone having to traverse (fly over) a given terrain. While traversing the terrain, the drone is exposed to a risk related to the geographical locations of a factor. For example, a relative risk can be estimated as a function of the 2D density of a population of individuals or as a function of 3D concentration of chemicals or disturbing weather phenomena. The goal of the drone is to navigate the terrain so as to find a path of minimum risk.
We develop a metric for quantifying the exposure to a risk factor in a circular zone model. We develop new zone avoidance strategies for drones traversing terrains comprising several risky zones while following either a rectilinear (i.e., straighline) trajectory or a curvilinear (i.e., not straighline) trajectory
Figure 1 depicts the idea. It depicts a drone traversing a zone with a rectilinear trajectory from A (entrance) to B (exit) at distance h from the source point p. The shaded area represents the total amount of exposure to risk by the drone.
Figure 1. A drone is traversing a zone with a rectilinear trajectory from A (entrance) to B (exit) at distance h from the source point p. The shaded area represents the total amount of exposure to risk by the drone.
We focus on simulations and experimental results. We consider the problem of how to navigate a domain while at the same time minimizing the amount of risk that a flying drone is exposed to while flying a curvilinear trajectory. We use and extend SwarmLab [2], a MATLAB simulation environment for swarms of drones implementing existing object collision algorithms, such as those by Olfati-Saber and Murray [3] and Vasarhelyi et al. [4].
The SwarmLab simulation environment provides physical properties associated to either quadcopters or fixed-wing drones (based on software implementation of the models in [5], [6]), including mass, aerodynamics and control pa- rameters; path planning variables represented by a series of waypoints (e.g., starting position S and intermediate waypoints in rectangular terrains); and graphic tools to plot state variables associated to the drones and obstacles.
We extended the original SwarmLab simulation environment in order to represent and visualize risky zones (i.e., non-solid cylindrical obstacles placed in the environment), as well the trajectory traversing algorithms, adapting the obstacle avoidance schemes in Refs. [3], [4], and their implementation in Swarmlab, to allow drones applying new curvilinear trajectory strategies. What we do is to adapt the potential functions, by assuming that solid obstacles are now non-solid zones, hence relaxing the threshold potential schemes in the original work. The idea is as follows. Drones, modeled in Swarmlab as mobile agents, can pass through what were originally considered to be obstacles, but minimizing now the overlap, and combining both rectilinear and curvilinear itineraries, trough a series of intermediate waypoints, in addition to source start position S and target exit position T. Figure 2 depicts the idea by using three intermediate waypoints, where the drone changes direction.
Figure 2. Example of a SwarmLab trajectory combining rectilinear (a,d) and curvilinear (b,d) trajectories. Intermediate waypoints w1, w2, and w3 represent the trajectory moments in which the drone (represented by the red disc) changes the rectilinear reference, associated to red solid lines in (a) and (b), to circular references, i.e., red solid circles in (b) and (d).
Monte Carlo simulation results implemented with our extended version of Swarmlab allows us to track and compare the amount of cumulative risk levels vs. battery consumption of drones using either rectilinear or curvilinear trajectories. Simulations use randomized configurations with regard to zone sparsity and overlaps (cf. for instance results plotted in Figures 3, 4, 5, and 6). We validate that curvilinear trajectories minimize the risk, at the cost of increasing the battery consumption.
Figure 3. (a,b,c) Rectilinear drone simulation at three different time intervals. (d) Simulation results in terms of distance (top) and risk (bottom) levels.
Figure 4. (a,b,c) Curvilinear drone simulation at three different time intervals. (d) Simulation results in terms of distance (top) and risk (bottom) levels
Figure 5. Simulation results using the new features of our modified SwarmLab simulation environment [2]. (a) Rectilinear single drone simulation. (b,c,d) Curvilinear trajectory simulations (following curvilinear references adapted from the collision avoidance algorithms in [3,4] with, respectively, one, ten and twenty drones. (e) Simulation results for rectilinear trajectory simulations. (f) Simulation results for curvilinear trajectory simulations.
Figure 6. Click over the picture to see some videocaptures associated with our extended SwarmLab environment for risky zone avoidance.
We have considered the problem of drones traversing terrains that may expose them to certain risks, e.g., disturbing weather phenomena. The goal of our work is to provide means to the drone to navigate the terrain while minimizing the amount of risk. We have developed a model for quantifying the exposure to a risk factor in a circular zone model; and proposed two main strategies to evaluate the level of risk reduction: either rectilinear or curvilinear trajectories. We have validated the work by extending SwarmLab [2], a MATLAB simulation environment for swarms of drones. We have shown that curvilinear trajectories minimize the risk, at the cost of increasing the battery consumption.
Work partially supported by the Natural Sciences and Engineering Research Council of Canada.
If using this code for research purposes, please cite:
[1] M. Barbeau, J. Garcia-Alfaro, E. Kranakis. "Risky Zone Avoidance Strategies for Drones", 34th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), 2021.
@inproceedings{barbeau2021ccece2021,
title={{Risky Zone Avoidance Strategies for Drones}},
author={Barbeau, Michel and Garcia-Alfaro, Joaquin and Kranakis, Evangelos},
booktitle={34th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE)},
pages={},
year={2021},
month={ },
publisher={IEEE},
doi = {},
url = {},
}
[2] E. Soria, F. Schiano, and D. Floreano, Swarmlab: a matlab drone swarm simulator, 2020. Available on-line at: https://github.com/lis-epfl/swarmlab
[3] R. Olfati-Saber and R. M. Murray, Distributed cooperative control of multiple vehicle formations using structural potential functions, in IFAC world congress, vol. 15, no. 1. Barcelona, Spain, 2002, pp. 242–248.
[4] G. Vasarhelyi, C. Vira ́gh, G. Somorjai, T. Nepusz, A. E. Eiben, and T. Vicsek, Optimized flocking of autonomous drones in confined environments, Science Robotics, vol. 3, no. 20, 2018.
[5] S. Bouabdallah and R. Siegwart, Full control of a quadrotor, in 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems. Ieee, 2007, pp. 153–158.
[6] R. W. Beard and T. W. McLain, Small unmanned aircraft: Theory and practice. Princeton university press, 2012.
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