Path Planning and Collision Risk Management Strategy for MultiUAV Systems in 3D Environments
Abstract
:1. Introduction
 Respect the geometry of the environment.
 Ensure a safe distance of the vehicle with respect to objects.
 Minimize the risk of collisions.
 Provide a route that is navigable by the vehicle, i.e., that respects its kinematic restrictions.
 Detect possible collision threats.
 Analyze the actual collision probability and define decision criteria.
 Implement the collision avoidance algorithm.
2. Description of the Approach
2.1. Representation and Description of the Environment
2.2. Trajectory Planning Using Fast Marching Square
 It is a complete planning algorithm, i.e., it always finds the solution to the problem, if it exists.
 It completely eliminates the problem of local minima. A local minimum would imply that such point would be assigned a lower $T\left(\rho \right)$ than neighboring points closer to the wave source, which is impossible considering that $F\left(\rho \right)\ge 0\phantom{\rule{0.222222em}{0ex}}\forall \rho $.
 The trajectory obtained between two points in space is the optimal in both time and distance. In the case of FM2, a smooth and safe trajectory is obtained, which remains sufficiently optimal.
 It is an algorithm of linear complexity order O(n), where n represents the total number of points of the considered mesh, which makes it computationally faster than other planning algorithms whose complexity order is, for instance, exponential (e.g., the A* algorithm) or asymptotic (e.g., the RRT algorithm).
2.3. Collision Risk Management by Vehicle Velocity Control
 Which vehicle is found flying behind the other, in the case both are flying in the same direction.
 Which vehicle is found flying nearer to the closest point between their trajectories, in the case both are flying in opposite directions.
Algorithm 1 Routine of the complete developed strategy 

Algorithm 2 Trajectory planning using Fast Marching Square 

Algorithm 3 Distance check function to ensure a safe takeoff 

Algorithm 4 Conflict management stage function 

3. Results
 For each mission completed by each vehicle, the length of the trajectories corresponding to the outbound and return missions is registered.
 The number of totally completed missions performed by the set of drones is recorded.
 In addition to the previous collected measure, the number of missions completed by each vehicle is recorded.
 List of conflicts. For each conflict that has occurred throughout the whole execution, a series of measures is analyzed: pair of drones that have participated in the conflict, duration of the conflict and smallest distance given between both vehicles (both in the xy plane and in the zaxis).
 Number of conflicts occurred for the set of drones.
 Characteristic mission time measures. For each mission completed by each vehicle individually, eight measurements are recorded: time spent waiting in depot to start outbound mission, time spent stopped in flight due to conflicts in outbound mission, total duration of outbound mission, number of conflicts encountered in outbound mission, time spent waiting at the goal point to begin return mission, time spent stopped in flight due to conflicts in return mission, duration of return mission and number of conflicts in return mission.
 Other time measures. The time required for each iteration run is also recorded. The time spent in the routine responsible for moving the drones and updating their trajectories is also taken into account.The aim of these measurements is to calculate the real computation time of the algorithm iterative loop, discarding as much as possible the time spent in calculation processes that belong to the simulation itself and are not an essential part of the path planning and collision avoidance stages.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Angle Ranges  $({45}^{\circ},{45}^{\circ}]$  $({45}^{\circ},{135}^{\circ}]$  $({135}^{\circ},{225}^{\circ}]$  $({225}^{\circ},{315}^{\circ}]$ 

Flight Level  9  15  21  27 
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López, B.; Muñoz, J.; Quevedo, F.; Monje, C.A.; Garrido, S.; Moreno, L.E. Path Planning and Collision Risk Management Strategy for MultiUAV Systems in 3D Environments. Sensors 2021, 21, 4414. https://doi.org/10.3390/s21134414
López B, Muñoz J, Quevedo F, Monje CA, Garrido S, Moreno LE. Path Planning and Collision Risk Management Strategy for MultiUAV Systems in 3D Environments. Sensors. 2021; 21(13):4414. https://doi.org/10.3390/s21134414
Chicago/Turabian StyleLópez, Blanca, Javier Muñoz, Fernando Quevedo, Concepción A. Monje, Santiago Garrido, and Luis E. Moreno. 2021. "Path Planning and Collision Risk Management Strategy for MultiUAV Systems in 3D Environments" Sensors 21, no. 13: 4414. https://doi.org/10.3390/s21134414