This paper presents Modified Artificial Potential Field (MAPF) approach application for decentralized formation control of multiple Unmanned Aerial Vehicles (UAVs) flying through dynamic environment. MAPF is based on Formation Potential Field (FPF) and it allows preventing mid-air collisions within defined security zone around multiple UAVs. This technique combines issue resolution connected with oscillation effects produced by potential fields, UAV fixed-wing type specification with the respect to application in the dynamic environment. Based on measured ranges between Remotely Piloted Aircraft (RPA) and obstacles (buildings, restricted areas), attraction and repulsion forces are formulated and are converted to aircraft flight control commands via rudder, aileron trims and engine throttle. The simulation results are used to validate and verify a given approach of real application, provision of optimal, collision-free, and safety flight path between initial UAVs positions and destination area.
Unmanned Aerial Vehicles (UAVs) are the remotely piloted aircraft (RPA), automation
levels of such vehicles vary from those that are fully piloted from a remote location to
fully automated. These ‘pilotless’ aircraft are developed for a big variety of
applications, such as surveillance, rescue, border control, agricultural production support, etc.
UAVs’ world legal acceptance is connected with their integration into the existing
aviation system without negatively affecting manned aviation and infrastructure, such as
mid-air collisions (MACs) – that is the main challenge today [
UAVs are usually used in remote and dangerous areas, especially fixed-wing that
have a high speed and heavy payload in comparison to rotary wing UAVs type. The
complexity appears because of the UAVs’ size is becoming smaller and as a result their
weight is becoming lighter. Therefore, taking into account these properties, UAVs have
not the ability of carrying heavy sensors such as Light Identification Detection and
Ranging (LIDAR) [
In addition to camera’s lightweight and the lower power consumption, the cameras are able to provide detailed environmental information Therefore, they are considered as the important sensors mounted on the small UAVs. The following obstacle avoidance sensors are being used in the RPAs, e.g.: - Stereo Vision; - Ultrasonic (Sonar); - Time-of-Flight; - Infrared; - Monocular Vision.
Another issue is connected with the path planning, which consists of defining a set
of paths, parameterized by time in order to accomplish a mission determined by
waypoints respecting flight specifications limits of both the UAV and the environment [
The collision avoidance algorithms applied to UAVs operation can be divided into
5 main groups [
2) Evolutionary Algorithm Approach; 3) Grid-based Approach; 4) Mixed Integer Linear Programming Approach; 5) Artificial Potential Field Approach.
The artificial potential field method (APF) is an approach of generating trajectories
online. It enables UAVs to navigate in a real condition environment with static and
dynamic obstacles by avoiding them. It is widespread due to its mathematical,
algorithmic simplicity and not computationally expensive [
The first approach proposed for collision avoidance based on artificial potential field
(APF) application was developed by Khatib [
P. Vadakkepat, K. Chen Tan and W. Ming-Liang [
H. Yin, L. L. Cam, U. Roy [
The global purpose of this research is to create an algorithm that guarantees safe flight generation and collisions avoidance for autonomous UAVs operation without human controlling within a limited airspace.
The main requirement is to handle collisions with fixed-wing UAVs that move at a constant speed (cruise speed, Vcruise) because of low energy consumption.
The effectiveness will be evaluated as a possibility to avoid potential collisions and conflicts, at maximum turn rate with correspondent velocity value (Vturn), occurred on the way and guarantee destination zone achievement. Potential collision is characterized by inner protection zone (rmin) intersection with an obstacle and conflict – outer protection zone (rmax) (Fig. 1). The sizes will be represented in a timely manner, for small UAV (with a weight that does not exceed 20 kg) it may be tmin=5 and tmax=10 seconds correspondently.
= = × × ; ; (1) (2) These values satisfy next conditions: minimum number of collisions and maneuvers, UAV-to-UAV communication network latency, packet loss, obstacles detection range, unique UAV flight specifications depending on size or payload. outer circle characterized by cruise speed The algorithm tests will be done using a simulator, which has such advantages: to allow finding the maximum number of UAVs safely operates in limited airspace, to model ideal conditions without unforeseen environmental factors and, in opposite side, with weather or technical factors influences. The main issues are connected with wireless communication between UAVs in a group. For this case, there is a lot of technologies for short-range line-of-sight (LoS) links deployment, which are flexibly configured and can be installed fast. The important criteria, which influence on communication link type, are data exchange rate, physical size and energy consumption. In general, UAVs supposed to be used in remote areas without a ground control station coverage, for example, in cases of severe shadowing by urban or mountains terrain, or communication infrastructure damages by natural disasters.
Artificial Potential Field method is more preferable for the solution of such issues as collision avoidance and formation control, because it is relatively simple for implementation, more efficient, fast and accurate. It assumes destination area or waypoints signed as positive charges and other dynamic objects (UAVs or obstacles) in the space as negative charges. An optimal flight path is found by calculating a total force from the attraction force of UAVs towards their destination and repulsion force away from other obstacles presented in the area (Fig. 2). However, the traditional APF usually has problems connected with local minimums in the potential field, which generate limitations such as (Fig. 3):
In this paper, an online (global) path-planning algorithm based on a modified APF approach is proposed for the control of UAVs swarm in dynamic environment, which causes constant collision avoidance with buildings, UAVs coordinates and position calculation errors based on Global Navigation Satellite System (GNSS), Inertial Navigation System (INS) and visual/radio sensors. The modification of the APF is for generating the shortest and safest path for the UAVs. Simulations are used to verify the proposed approach using MATLAB.
The Artificial Potential Field is one of the classical path planning approaches that is used for global and local path planning in the dynamic or static environments. The concept about APF is to find a mathematical function to represent attraction and repulsion forces acting UAVs and destination area both forces are generated by mathematical functions that are represented graphically by high and low areas in the simulated space.
We model the UAVs as negatively charged particles and destination area as a positively charged (Fig. 4). A repulsion force often dominates over the attraction force in scenarios containing multiple UAVs causing the vehicles to never reach their destination area. Mathematical formulation of approach assumes a numerical value in each point in space and time, and whose gradient represents forces (3).
= × + + (1 − ) × −; (3) where Ftotal is a total force acting on one UAV, F+ – is an attraction force, F- – is a repulsion force, ξ is an attraction force weighting coefficient (0 < ξ < 2) which ensures attraction force domination under repulsion in order to guarantee UAV flight towards destination area (Fig. 5). Oscillation effect referred to traditional effect is eliminated by changing circle to elliptical artificial potential field around UAV with the same area. It increases in a size toward the heading of UAV, indicating a flight direction (Fig. 1).
Additionally, the deadlock problem solution is presented, where at least two UAVs
are approaching each other head-on with destinations directly behind each other, since
UAVs cannot turn sharply or come to a complete stop to resolve this issue one UAV
turn to the left or right due to the action of artificial vortex repulsion field (Fig 6). In
some cases this principle is applied for collision avoidance with static obstacles [
Formation Control of Multiple Autonomous Fixed-Wing
Unmanned Aerial Vehicles Simulation
It is assumed that there are six UAVs, two obstacles and one destination zone for a
group. The aim is to plan an optimal collision-free path for the group, in case of multiple
UAVs application in a dynamic environment, where due to signal delay, multipath and
close obstacle location present an error of UAV coordinates definition and cooperation
in a group. The protection zone radius is equal to minimum value and remains a
constant during flight. The main peculiarity of such approach in comparison to others [
UAV movement can be described by kinematic equation system: where, i=1, 2, …, n is the index of multiple UAV, xi, yi – coordinates of the i-th UAV, Vi – is a flight-path velocity vector of the i-th UAV, φi – is the course angle characterizing the direction of the velocity vector to the destination zone.
The UAV coordinates can be calculated as a resultant force acting on i-th UAV provided by destination zone, obstacles and other UAVs: where, mi – is a mass of the i-th UAV
Attraction F+ and repulsion F- forces can be calculated as: ̈ = 1 ∑ ≠
̈ = 1 ∑ ≠ + + − − ; − − ; + = − =
;
кр ; α ϵ {2, 3, …}; β ϵ {3, 4, …}; rij = √(xi − xj)2 + (yi − yj)2; where, G – is a gravitational constant and rij – is a distance between UAV,
In order to provide the UAV movement to the destination zone, it is necessary that
its attraction force should be greater than total attraction force formulated by obstacles
and other UAVs [
The heading angle φ can be estimated as a relation of attraction and repulsion force influence on the UAV movement with correspondent coordinates.
( ) = ( ̇ ̇ ) = ( ( )− ( −1)); ( )− ( −1) where, k – is the integration step of the equation system. (4) (5) (6) (7) (8) (9) (10) (11) Fig. 8. Experiment 1. Flight trajectory of 6-th UAVs in a group with constant radius of protection zone The formation control problem of UAVs group in static and dynamic environment consists of three main problems: plan, control and form a UAVs formation in a group at their initial positions; group motion from initial position to destination; collisions avoidance during the flight (Fig. 8). The zone around obstacles has double radius value and in case of its penetration, the UAV security zone will be increased in accordance to Fig. 1, where radius is inversely proportional to the distance between UAV and the nearest obstacle edge point of contour, because obstacles can have rather different shapes.
The results of simulation depict applicability of MAPF regarding UAVs operation in the real world with static obstacles. Experiment 2 (Fig. 9) has expensed less time to reach the destination area in comparison to Experiment 1, where UAVs trajectories, in some cases, drawing obstacle shapes. In Experiment 2 (Fig. 10) UAVs start collision avoidance maneuvers earlier and characterized by potential collisions absence. The UAV motion in a dynamic environment is connected with potential conflicts presence with dynamic objects like UAV that has another speed value, shape, onboard equipment, so they can’t be compatible for position data interchange performance. In this case, UAV should be able detect any dynamic obstacles operatively, calculate ranges and motion parameters. The traditional APF is characterized by dead lock problem and the solution provided by artificial vortex fields (Fig. 6) that act only around obstacles and do not make an impact on a global potential function. In order to check this Experiment 3 (Fig. 11) and Experiment 4 (Fig. 12) have been done. The main difference between them is an application of varying security zone radius. Experiment 3 shows a flight performance of two vehicles and their destination zones. In Fig. 11(b) the flight path is optimal with less time consumption and slight maneuvers. a) b) Proposed MAPF has showed the best result in case of UAVs group motion in dynamic environment based on time consumption and number of flight maneuvers corresponding to lower energy consumption, it is the main issue characterized UAV operation (Fig. 12). In this paper, the Modified Artificial Potential Field has been proposed to control a group of autonomous UAVs to achieve the destination zone and maintain a given formation while avoiding collisions with static and dynamic obstacles. Unlike other centralized UAV formation control methods, the MAPF method does not require a high computational capability and the flying trajectory can be modified in real time when an unexpected obstacle has been detected.
The MAPF approach is based on application of artificial vortex fields around obstacles and varying protection zone radius of UAVs. It allows for significant scalability to hundreds or thousands of autonomous UAVs provide enough airspace for a safe operation in a dynamic environment with non homogeneous vehicles types.