Abstract
Autonomous anticollision of unmanned aerial vehicle (UAV) is one of the key technologies to realize intelligent decision-making and autonomous control, and it is of great significance to improve the flight safety and survivability of UAV in complex environment. Firstly, the UAV autonomous anticollision system configuration is constructed in this paper, and the UAV autonomous anticollision problem and related models are described. Then, the potential collision conflict prediction rules are defined, and a practical three-dimensional collision conflict prediction method is proposed. Finally, the UAV autonomous avoidance decision-making method is designed by using the optimization theory, and the corresponding simple and feasible flight control law is put forward. Numerical simulation results show that the proposed method can ensure the flight safety of UAV by relying on autonomous decision-making and control strategy, so as to realize the autonomous anticollision between a single UAV and non-cooperative dynamic obstacles in three-dimensional airspace.
1. Introduction
With the rapid development of aviation industry in various countries, UAVs have been widely used in war and civil fields, resulting in a sharp increase in the number of various combat aircraft, including UAVs, which also leads to an increasing flight density and severe flight safety situation [1, 2]. Therefore, UAV autonomous anticollision technology is one of the key technologies of UAV autonomous control technology, which is of great significance to improve the survivability of UAV in complex environment. Especially for non-cooperative dynamic obstacles, UAV autonomous anticollision system has become an urgent need [3, 4].
The research of UAV anticollision has attracted great attention of scholars at home and abroad. In terms of intelligent solution algorithm, literature [5, 6] studies genetic avoidance algorithm, adopts discrete waypoint model, and considers the error caused by aircraft speed uncertainty. This method is easy to expand to three-dimensional without increasing complexity, but the accuracy needs to be strengthened. In terms of graph theory, literature [7, 8] analyzes the complexity of multi aircraft flight collision and uses the method of establishing a Voronoi polygon to solve the anticollision problem, but it is only applicable to two-dimensional plane. Literature [9–12] uses the artificial potential field method to treat UAV and obstacles as positively and negatively charged particles respectively, so as to construct a cooperative anticollision method, but this method cannot effectively solve the anticollision problem with constraints. In solving the multi constraint anticollision problem, the model predictive control method has a good effect [13]. References [14, 15] established an anticollision control algorithm under nonlinear constraints in two-dimensional environment by comprehensively using geometric method and model predictive control method and based on the tangent principle. Literature [16] proposed a multi UAV cooperative anticollision method under nonlinear dynamic constraints by using distributed model predictive control, but the premise of this method is that all obstacles are cooperative and their states are accurately known.
Through the above analysis, it can be found that the current research on UAV anticollision mainly has the following problems: (1) most of them are aimed at cooperative obstacles, which is difficult to meet the requirements of non-cooperative anticollision and has great limitations. (2) Many methods do not consider the dynamic constraints of UAV, which is inconsistent with the actual situation. (3) The computational complexity of model predictive control method is high, which is difficult to meet the real-time requirements of the system.
Therefore, based on the optimization theory, this paper studies the autonomous anticollision control method of UAV for non-cooperative dynamic obstacles. Firstly, the dynamic obstacle autonomous anticollision problem is reasonably described, which is divided into two parts: collision prediction and autonomous avoidance. Then a three-dimensional dynamic collision prediction algorithm is proposed. On this basis, the UAV autonomous anticollision control strategy is designed. Finally, the correctness and effectiveness of the proposed method are verified by simulation experiments.
2. Preliminaries and Problem Statement
2.1. UAV Autonomous Anti-Collision System
The UAV autonomous anticollision system for non-cooperative dynamic obstacles is shown in Figure 1.
UAV detects the obstacles that may be encountered in the flight process through airborne sensors and other equipment to realize the perception of the surrounding environment. Then, based on certain rules, the collision conflict is predicted. If the collision is predicted, the autonomous anticollision strategy is started. Among them, the autonomous anticollision strategy mainly includes three parts: anticollision guidance, emergency anticollision and pre planning tracking. Its output has two forms: waypoint and maneuver command. After collision avoidance, the UAV returns to the preset route. If it does not happen, the UAV will fly normally along the preset route.
2.2. Description of UAV Autonomous Anti-Collision Problem
UAV status information is represented by an identifier, a position and a speed vector. The identifier is assumed to be unique and unchanged. That is, there will not be two different UAVs with the same identifier in the same airspace. Letters are used to represent UAV status, and bold letters represent vector parameters. For example, represents position vector and represents speed vector. When a vector variable represents a UAV, the UAV state is taken as the footmark: for example, the current position and speed vector of a UAV are represented by and respectively. Generally, the angle dividing mark represents the value on each direction axis. For example, , is the horizontal component of velocity , and .
It is assumed that the autonomous sensing function in the function of UAV autonomous anticollision system has been realized, the initial position and speed information is accurate, and the radius, position and speed vector of the intruder can be obtained. At the same time, the dynamic obstacles are represented by the sphere protection area in the coordinate system. The reserve defines a minimum safety interval between two machines, that is, a sphere with a diameter of .
In order to study the anticollision methods of UAV against dynamic obstacles, a set of basic concepts for collision prediction and avoidance methods of all dynamic obstacles are defined, and then the related research of this paper is carried out on this basis.
Definition 1 (Protected area). The protected area of UAV is defined as a point set , which meets the following requirements:where, is the position of any point in space, is a vector norm, so that also represents the position of a point in space, satisfying:(1)Non-negativity: ,(2)Zero value: if and only if ,(3)Homogeneity: ,(4)Trigonometric inequality: .The above is the abstract concept of all protected areas. In this paper, the imaginary protection area around each UAV is a sphere with a diameter of , that is, the sphere protection area of UAV is defined as a point set satisfying:Therefore, its norm is defined as:
Proposition 1. Equation (3) is a normal norm vector, which satisfies non-negativity, zero value, homogeneity and triangular inequality.
Proposition 1 makes the definition of the loss of distance and safety interval between UAVs independent of the choice of the shape of the protected area.
Definition 2 (Distance). The distance between UAV and is defined as:
Definition 3 (Loss of safety interval). The loss of safety interval between UAVs is when the protection areas of two UAVs overlap, that is:
Proposition 2. UAV and safety interval are lost if and only if:
Definition 4 (Collision conflict). The collision conflict between UAV and is that if there is a future time before exceeding time , that is, when , the distance between the two aircraft is strictly less than 1.Collision is usually determined by comparing the predicted closest interval between two unmanned aircraft with the minimum safety interval defined by the protected area.
Definition 5 (Closest interval). The closest interval between UAV and in the override time is , i.e. the minimum time , which is different for any time of :The closest interval always exists because is a continuous function and the time range is defined as a closed interval.
Definition 6 (Closest interval distance). The closest interval distance between UAV and within the override time is the distance between two UAVs at the closest interval time, i.e:Therefore, the collision conflict based on the closest interval distance can be redefined.
Proposition 3. UAV and have collision conflict if and only if .
Definition 7 (Evasion strategy). The evasion strategy is that the UAV only modifies the new state of the current speed vector. The new speed of UAV under is expressed as .
Avoidance strategies can be classified according to the interval criteria they meet. Let and be the avoidance strategies of UAV and respectively:(1)When , is a non-cooperative evasion strategy for UAV (UAV does not maneuver), if , is also a tangent evasion strategy.(2)When , and is the cooperative avoidance strategy, if , and is also the smallest avoidance strategy.(3)When , and are mutually exclusive avoidance strategies.The anticollision of UAV against dynamic obstacles can be clearly divided into three stages: the first stage is the state estimation of intruder. The second stage is conflict prediction. The potential conflict between the two aircraft will be predicted and whether the minimum interval loss will occur in their future position after a period of time (i.e. whether the UAV enters the UAV protection area). Once the conflict situation is predicted, it will enter the third stage, that is, the UAV loaded with autonomous anticollision function will take corresponding avoidance methods in time. The state estimation can adopt the similar extended Kalman filter method to obtain the estimated state of the intruder [17]. This section assumes to study the collision prediction and avoidance method of dynamic obstacles when the state of the intruder has been obtained.
3. Dynamic Obstacle Collision Prediction Rules
3.1. Two-Dimensional Dynamic Collision Conflict Prediction
Based on the basic definition of the protected area, a protected area centered on the intruder coordinate system is considered, that is, a circle with diameter . The loss of safety interval occurs at time if and only if the projection distance between the two machines at time is strictly less than (i.e. ). Assuming that and are the position and ground velocity vectors of the local machine and the intruder at time , there is:
Time has a solution if and only if:
There are two solutions , which meets . Two solutions are the start and end time of the security interval loss. By definition, if , no interval loss occurs. This two-dimensional method was proposed and applied by Bilimoria [18]. The intruder is considered to be fixed in space, and the local position and speed adopt the quantity relative to the state of the intruder, i.e. and . If a new relative speed of the local machine can make it disjoint with the inside of the intruder protection zone, the collision can be avoided. Among the infinite new velocity vector solutions to avoid collision, Bilimoria selects the velocity vector with the smallest angle with its original velocity vector as the optimal solution. As shown in Figure 2, any other solution requires a large number of changes to the ground path of the local machine, so any optimal solution is tangent to the intrusion machine protection zone. A new local path to the ground is determined every time it passes through points and . under certain constraints, it is optimal. For example, the constraint condition is that it can only turn left, and the target point is optimal. The length of the velocity vector is optional.
Bilimoria two-dimensional method can predict and avoid horizontal conflicts, but it does not consider vertical conflicts. In reference [19], the three-dimensional conflict is decomposed into horizontal and vertical conflicts, so that the collision conflict can be predicted and avoided independently, and then the solutions in all directions are combined to obtain three-dimensional maneuver. Although this method is simple, it is difficult to prove its correctness. Based on Bilimoria’s two-dimensional horizontal conflict prediction and avoidance method, a real three-dimensional collision prediction and avoidance method for dynamic obstacles is proposed.
3.2. Collision Prediction Rules for 3D Dynamic Obstacles
Based on the two-dimensional dynamic obstacle collision prediction rules, a new three-dimensional dynamic obstacle collision prediction rule is proposed to realize three-dimensional collision prediction. Assuming that and represent UAV and intrusion UAV respectively, and the intrusion UAV is a non-cooperative obstacle, the autonomous anticollision problem studied in this paper can be regarded as that the UAV first predicts the collision conflict with the intrusion UAV , and then adopts the autonomous anticollision strategy to complete anticollision. The flight diagram of the two is shown in Figure 3.
Assuming that is the smallest possible interval between and , after a certain period of time, the expression of becomes:
Theorem 1. Both UAV and intruder UAV (a sphere with radius ) fly at a constant speed, and the speed is and respectively. The two UAVs collide, if and only if the following formula is true:where, .
Proof. Let be the plane of vectors and . The plane intersects the sphere to determine a circle with radius , as shown in Figure 3. In Figure 4, also considering this plane, the particle collides with the sphere with radius if and only if the particle is assumed to collide with the assumed stationary circle in plane at constant velocity . Considering the right unit vectors and , the following expression can be obtained:The following lemma can be applied in the plane (For the proof, see Reference [20]).
Lemma 1. If a point and a circle move at a constant speed and the initial conditions are satisfied:Then they will be in conflict, and the above conditions are necessary and sufficient for the occurrence of conflict.
The condition indicates that the UAV is approaching. In order to prove (13), first prove the following equivalent equation:And because , we have:It can be obtained from equations (16) and (17): .
This completes the proof.
4. Autonomous anticollision strategy based on optimization
Figure 5 shows the geometric diagram describing the anticollision between two non-cooperative UAVs in the three-dimensional inertial reference coordinate system. It is assumed that the UAV model equipped with airborne autonomous anticollision system is represented by a particle with velocity , while the other intruder is assumed to be a sphere with a half diameter of the protection area and a velocity of .
Then the UAV autonomous anticollision strategy for non-cooperative dynamic obstacles can be described as the following optimization problem: Find the solution that enables the UAV to independently avoid the invading UAV and minimize the deviation from the preset route.
The UAV position vector is expressed as: , and the intruder UAV position vector is expressed as: . can be calculated from by:
Assuming that is the position vector calculated according to the desired speed , the deviation value is:
The goal is to minimize the deviation value under the constraints of UAV itself. The problem is expressed as follows:where, , which represents the collision prevention between UAV and invading UAV , the second and third constraints are dynamic constraints, and represents the velocity delay constant.
In order to solve the problem expressed by equation (20) using the analytical method, the above problem can be simplified to:
The first constraint is:
Meanwhile, we have: and .
Then equation (22) continues to be:
It can be proved that , is the smallest, and the result is . Since (tangent to the reserve), equation (22) is satisfied. At this point, equation (20) becomes:
An analytical solution can be obtained for this new problem, which is proved in the form of geometric description as follows.
It is necessary to find the minimum and apply it to the velocity vector so that the new velocity vector is tangent to the protected area. The unit vector of is expressed as . In the plane constructed by the unit vectors and , minimizing can be applied to the orthogonal projection of on : the modulus of any vector is greater than , as is shown in Figure 6. Then, , .
In order to find the minimum value of , first solve , which is tangent to the reserve and expressed by the minimum angle . Therefore, circle is the intersection of the cone with angle to the -axis and the protected area, as shown in Figure 7.
For any point on circle , as is shown in Figure 8, determines a vector tangent to the reserve. However, on is the only point to ensure the minimum of (i.e. the minimum of ). Because , the analytical expression of must be found in plane .
If angles and have the same sign, then is the smallest. It is divided into the following two cases: and (1) (General) The minimization form of can be obtained from Figure 9 by:Equation (25) is the global optimal solution of general problem (20) under assumptions.(2) (Special) This unity depends on the relationship between and . At this time, plane is not defined singly, but must be selected from a group of plane bundles in the same direction as ..
4.1. Design Principle of Reserve
In order to consider the dynamic constraints, the radius R of the reserve can be expanded. In this paper, the expanded reserve is selected as , where (according to the American FAA accident standard). can be designed as a conservative estimate of all possible maneuvers that the intruder can perform in time . If and have the same performance, such as and , even if is a pursuer, and the protection area with radius is enough to ensure anticollision (the relative distance between the two aircraft is always greater than ).
Because the radius of the reserve is properly designed with , if and have the same performance, it can ensure that the minimum distance between the two aircraft is always greater than , and even if is the pursuer, the initial relative distance is greater than a critical distance. However, in some cases, still enters the reserve with radius . In this case, the tangent solution (25) cannot be used because there is no tangent passing through a point in the sphere and tangent to the sphere with radius .
Therefore, when is located in the protection zone with radius , another strategy can be selected: in this case, the speed vector required for the UAV autopilot is defined as shown in Figure 10. The adopted strategy provides a powerful control maneuver to quickly move the UAV out of the protected area with radius , and then continue to apply the tangent solution (25).
4.2. Anti-collision Control Command under UAV Dynamic Constraints
It is assumed that the current speed direction of the UAV is the direction of and the modified anticollision speed direction is the direction of . Let be the roll angle of the UAV and be the pitch angle of the UAV, then equations (26) and (27) are the anti-anticollision guidance control commands generated under the boundary constraints of the UAV:where, is the UAV maneuver time delay constant. During the simulation, make .(1)Horizontal Maneuver In the horizontal plane, the line of sight inclination angle of the UAV is:where, is the horizontal component of velocity. Therefore, the roll angle of UAV is regarded as input. Make the maximum roll angle , so that the maximum longitudinal inclination changes in 1 second:where, is the gravitational acceleration constant. The horizontal maneuver logic is shown in Table 1.(2)Vertical Maneuver The desired pitch angle can be expressed as: The vertical maneuver logic is shown in Table 2.
5. Simulation and Analysis
It is assumed that the initial position, speed and target position information of two UAVs (UAV1 and UAV2) are shown in Table 3, where UAV2 is our UAV and UAV1 is a non-cooperative obstacle. During the flight, it is predicted that the two opportunities will collide, UAV2 will take corresponding evasion maneuver, and UAV1 will fly in a straight line. The obtained simulation curve is shown in Figures 11(a)–11(d).
(a)
(b)
(c)
(d)
From the simulation results, Figure 11(a) shows the flight trajectory of the two aircraft. The flight routes of UAV1 and UAV2 do not intersect. The dotted line in Figure 11(b) represents the ideal anticollision interval, and the solid line represents the real-time interval during the actual flight of the two aircraft. It can be seen that UAV2 has completed the autonomous anticollision with UAV1. Figure 11(c) shows the UAV2 roll angle command, and Figure 11(d) shows the UAV2 pitch angle speed command, both of which are within the limit range.
To make a Monte Carlo simulation with 500 times, we find that the average running time of the method proposed in the paper is 20 ms, which has a great advantage on the existed anticollision method, such as the MPC algorithm in Ref. [13].
Therefore, the simulation results show that the proposed method can ensure the autonomous anticollision between UAV and non-cooperative obstacles.
6. Conclusions
Aiming at the non-cooperative anticollision problem in three-dimensional airspace, this paper studies the autonomous anticollision decision and control method of UAV based on optimization theory. The autonomous anticollision problem of UAV is described and divided into two stages: prediction and avoidance, which provides a model basis for decision-making and control design. Based on the two-dimensional dynamic collision conflict prediction, a three-dimensional collision conflict prediction method is proposed to predict the collision between aircraft and effectively realize the environmental airspace cognition. By using the optimization theory, the autonomous anticollision decision and control method of UAV is designed. The simulation results show that the proposed method is effective in the three-dimensional airspace non-cooperative anticollision problem, and can greatly improve the flight safety of UAV. The research makes a contribution to the autonomous anticollision domain, and results of this paper can be applied to the design of UAV decision and control system. The next research focus is on the cooperative anticollision decision and control of multi-UAVs or UAV cluster.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare no conflicts of interest.
Acknowledgments
The author acknowledges funding received from the following science foundations: National Natural Science Foundation of China (No. 62101590, 62176214), The Natural Science Foundation of Shaanxi Province, China (2020JQ-481, 2019JQ-014).