CN115097865B - Flight path planning method for multi-machine formation obstacle avoidance - Google Patents
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Abstract
The invention relates to a flight path planning method for multi-machine formation obstacle avoidance, which comprises the following steps: firstly, a single-machine three-dimensional space point quality motion model is established, then a plurality of constraint conditions are added on the basis of the motion model, and finally, an objective function which meets the motion model and the constraint conditions and reaches a target point in the shortest time of multi-machine formation is set, so that a multi-machine formation track planning model corresponding to the motion model is established; establishing an obstacle model needing to be avoided by multi-machine formation, wherein the obstacle model comprises a radar identification area model and a no-fly area model; and pre-planning a track route of the multi-machine formation obstacle avoidance of the task to be executed based on the multi-machine formation track planning model and the obstacle model.
Description
Technical Field
The invention relates to the technical field of aviation, in particular to a track planning method for multi-machine formation obstacle avoidance.
Background
With the development of aviation technology, demands for low-altitude flight are increasing, for example, a large number of unmanned aerial vehicles can be applied to industrial inspection, public security patrol, transportation and transportation, and can also be applied to various fine fields, such as insurance evidence collection, livestock monitoring, aerial photography, agricultural plant protection, police security, electric power inspection, geological exploration and mapping, disaster relief and the like. In addition, for modern warfare, low-altitude combat is also becoming more and more important and low-altitude flight techniques are being continuously studied due to the development of unmanned aerial vehicle techniques.
In the face of complex and changeable low-altitude environments, especially low-altitude battlefield environments, whether manned flight or unmanned aerial vehicle flight, the flight path planning is an important part in a flight task, and the flight path planning of the aircraft refers to planning an optimal collision-free flight path from a starting point to an end point according to one or more preset performance indexes. The advantages and disadvantages of the flight path planning method directly determine the effect of completing the low-altitude flight mission, scientific and effective flight path planning is performed in advance, and reasonable flight paths are planned, which are critical to the execution and smooth completion of the mission.
Track planning is generally divided into two types according to different modeling modes, wherein the first type is to establish algebraic motion equations based on turning angles and leg lengths, the algebraic motion equations comprise potential field methods, graph theory methods, random tree methods and the like, and the modeling modes are suitable for large-scale global planning problems; the second type is to build differential motion equation model based on overload or acceleration control quantity, and the modeling mode is closer to engineering practice and is more fit with control theory. The solution mode for the second type modeling model can be divided into a direct method and an indirect method. The principle of the direct method is that the optimal control problem is converted into a finite-dimension parameter optimization problem, and the problem is solved by a nonlinear programming method, and the defect is that the solving accuracy is not high. The indirect method comprises a pseudo-spectrum method, a mixed integer programming algorithm, a heuristic algorithm and the like, and the principle is that a flight path programming problem is regarded as an optimal control problem to be solved, but the technical problem that convergence is difficult to achieve exists.
Currently, with the rapid development of convex optimization theory, as one of typical representatives of the direct method, the convex optimization method has become an efficient and stable algorithm for solving the track planning problem. However, since the convex optimization modeling method needs to be based on linear dynamics assumption, the convex optimization method disclosed in the prior art is used for solving the second type modeling model, so that the technical problem of slow iteration convergence exists, and meanwhile, the existing track planning method using the convex optimization method has the problems of lack of planning design for obstacle avoidance, lack of flight safety planning design when tasks are executed on multiple machines, and the like.
Disclosure of Invention
In order to solve the problems, the invention provides a track planning method for multi-machine formation obstacle avoidance.
The track planning method for the multi-machine formation obstacle avoidance comprises the following steps:
firstly, a single-machine three-dimensional space point quality motion model is established, then a plurality of constraint conditions are added on the basis of the motion model, and finally, an objective function which meets the motion model and the constraint conditions and reaches a target point in the shortest time of multi-machine formation is set, so that a multi-machine formation track planning model corresponding to the motion model is established;
establishing an obstacle model needing to be avoided by multi-machine formation, wherein the obstacle model comprises a radar identification area model and a no-fly area model;
and pre-planning a track route of the multi-machine formation obstacle avoidance of the task to be executed based on the multi-machine formation track planning model and the obstacle model.
The single machine three-dimensional space point mass motion model comprises the following steps:
wherein, (x) i ,y i ,h i ) Representing three-dimensional coordinates of the aircraft i in a ground coordinate system; gamma ray i Represents the track dip angle, χ of the aircraft i i Representing the heading angle of the aircraft i; v (V) i Represents the ground speed of aircraft i; n is n x,i Indicating horizontal axial overload of aircraft i, n y,i A horizontal component representing the normal overload of aircraft i, n z,i A vertical component representing the normal overload of aircraft i; g represents the gravitational acceleration.
Wherein the constraint condition includes: initial/final state quantity constraints for aircraft i, magnitude constraints for state quantity/control quantity for aircraft i, rate of change constraints for control quantity for aircraft i, inter-aircraft collision avoidance constraints for multi-aircraft formation, and collision avoidance constraints for aircraft i with external obstacles, wherein:
the expression of the initial/final state quantity constraint of the airplane i is as follows:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; s is(s) i,0 Representing an initial state quantity, s, of an aircraft i i,f Representing the state quantity of the aircraft i reaching the target point;
the expression of the amplitude constraint of the state quantity/control quantity of the airplane i is as follows:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; s is(s) i,min Representing the minimum state quantity of the aircraft i, s i,max Representing the maximum state quantity of the aircraft i, u i,min Representing the minimum control quantity of aircraft i, u i,max Maximum control quantity of aircraft i;
the expression of the rate of change constraint of the control quantity of the aircraft i is:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning;representing the minimum control variable of aircraft i, < >>Representing the maximum control variation of the aircraft i;
the expression of the inter-machine anti-collision constraint of the multi-machine formation is as follows:
||F·[s i (t)-s j (t)]|| 2 ≥R t and i is not equal to j, t 0 ≤t≤t f (5)
Wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; matrix f= [ I 3×3 ,O 3×3 ]，I 3×3 Is a 3X3 identity matrix, O 3×3 A 0 matrix of 3X 3; r is R t Is an inter-machine safety distance matrix;
the expression of the anti-collision constraint of the airplane i and the external obstacle is as follows:
||E·s i (t)-p obs,m || 2 ≥r m ，m＝1,2...M 0 ，t 0 ≤t≤t f (6)
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; matrix e= [ I 2×2 ,O 4×4 ]，I 2×2 Is a unit matrix of 2X2, O 4×4 A 0 matrix of 4X 4; p is p obs,m Is the center coordinates of the external obstacle, r m Is a safe distance corresponding to an external obstacle, and the value of the safe distance is a self-defined value; m is M 0 The number of static threats;
in the above formulae (2) to (6), s i Representing a set of state quantities for aircraft i, u i Representing a set of control variables for aircraft i, where s i ＝(x i ,y i ,h i ,V i ,χ i ,γ i ) T ，u i ＝(n x,i ,n y,i ,n z,i ) T 。
Wherein, the multimachine formation track planning model is:
wherein s.t. formulas (1) to (6) represent constraints satisfying formulas (1) to (6) listed above.
The radar identification area model needing multi-machine formation avoidance comprises the following steps: d is greater than or equal to R r +d s Where D is the distance of the aircraft to the center point of the radar identification area, R r For the detection radius of the radar, d s Is a safety margin; and
the no-fly zone model requiring multi-machine formation avoidance comprises the following steps:
in (x) o ,y o ) Is the central coordinate of the no-fly zone, (x) i ,y i ) The flight coordinate of the aircraft is a width of a no-fly zone, b is a length of the no-fly zone, R r For the detection radius of the radar, d s For safety margin, k represents a shape parameter of which the no-fly zone is approximately polygonal, and when k=1, the no-fly zone is approximately diamond; when k=2, the no-fly zone is approximately elliptical; when k → infinity, the no-fly zone is approximately rectangular.
The method for pre-planning the track route of the multi-machine formation obstacle avoidance of the task to be executed based on the multi-machine formation track planning model and the obstacle model comprises the following steps: determining constraint conditions as initial/final state quantity constraint of the airplane i, amplitude constraint of state quantity/control quantity of the airplane i and change rate constraint of control quantity of the airplane i, wherein:
the results of the initial sequence convex optimization iteration of the initial/final state quantity constraint expression of the airplane i are as follows: s is(s) i [0]＝s i,0 ,s i [K]＝s i,f ,i＝1,2…N (9)
Wherein K is the discrete time number, s i,0 Representing an initial state quantity, s, of an aircraft i i,f Representing the state quantity of the aircraft i reaching the target point, wherein N is the number of the aircraft in the multi-aircraft formation;
the result of the initial sequence convex optimization iteration of the expression of the amplitude constraint of the state quantity/control quantity of the airplane i is as follows:
s i,min ≤s i [k]≤s i,max ，k＝0,1,…,K，i＝1,2…N (10)
U i,min ≤u i [k]≤U i,max ，k＝0,1,…,K，i＝1,2…N (11)
wherein K is the number of discrete moments, K is the kth discrete moment, and N is the number of planes in the multi-plane formation; s is(s) i,min Representing the minimum state quantity of the aircraft i, s i,max Representing the maximum state quantity of the aircraft i, U i,min Representing the minimum control quantity of aircraft i, U i,max Representing the maximum control quantity of the aircraft i;
the result of the initial sequence convex optimization iteration of the expression of the change rate constraint of the control quantity of the airplane i is as follows:
wherein K is the number of discrete moments, K is the kth discrete moment, and N is the number of planes in the multi-plane formation;representing the minimum control variable of aircraft i, < >>Representing the maximum control variation of the aircraft i;
the track route of the multi-machine formation obstacle avoidance can be obtained through the following algorithm:
is limited by
Wherein K is the number of discrete moments, K is the kth discrete moment, i is the ith aircraft, N is the number of aircraft in the multi-aircraft formation, q is the iteration number, epsilon is the convergence domain and varies with q, and when q is increased by 1, epsilon is changed into the original 1/2; Δt (delta t) 0 Is a discrete time step; equation constraint A eq ·Z＝b eq Including expression (9), wherein subscript eq represents "equation", a and b are both coefficients for expressing the constraint of the equation; inequality constraint A in ·Z≤b in Including expressions (10) to (12) in which the subscript in represents "inequality", a and b are both coefficients for expressing the constraint of the equality; mu (mu) eq Sum mu in Respectively the proportionality coefficients; z is an optimization variable comprising a discrete time step Deltat 0 Amplitude set z of state quantity and control quantity of aircraft i i ，
z i ＝(s i [0],s i [1]…s i [K],u i [0],u i [1]…u i [K]),i＝1,2…N。
Wherein, for the forbidden zone which is approximate to polygonal obstacle, the method for avoiding obstacle by multi-machine formation comprises the following steps: when the track of the aircraft accords with the following expressions (14) and (15), the track of the multi-aircraft formation is ensured to avoid the no-fly zone,
where k represents a certain time, (x) p [k],y p [k]) Is p [ k ]]Is used for the purpose of determining the coordinates of (a),is->Coordinates of (a) p ,b p ,c p ) Is p [ k ]]Linear expression coefficient of a line on which a reference edge determined from the center point of the no-fly zone is located, and flag is a value about the reference point p [ k ]]Early warning signal value d pc Is p [ k ]]A distance from a coordinate point of (c) to a center point of the no-fly zone;
where k represents a certain time, (x) p [k],y p [k]) Is p [ k ]]Is used for the purpose of determining the coordinates of (a),is->Coordinates of (a) p-1 ,b p-1 ,c p-1 ) Is->Linear expression coefficient, flag of straight line where reference edge determined by central point of no-fly zone is located * Is about datum point->Early warning signal value,/-, of (2)>Is->A distance from a coordinate point of (c) to a center point of the no-fly zone.
Wherein, still include: the multi-aircraft formation is divided into a plurality of task groups, and for the 1 st task group which flies first due to the highest priority of the tasks, the obstacle avoidance method between the aircraft of the 1 st task group is as follows:
the inter-aircraft obstacle avoidance can be achieved when the flight path of each aircraft of the mission 1 group meets the following constraints:
wherein E= [ I 2×2 ,O 4×4 ]，I 2×2 Is a unit matrix of 2X2, O 4×4 A 0 matrix of 4X 4;representing the state quantity of a reference track of the aircraft i at the moment k; />Representing the state quantity of a reference track of the airplane j at the moment k; v (V) i,max Representing the maximum flight speed of aircraft i; v (V) j,max Representing the maximum flight speed of aircraft j; Δt (delta t) 0 Is a discrete time step; r represents a safe distance in the XOY plane; r is R t Is an inter-machine safety distance matrix; η represents a correction coefficient of the inter-machine safety distance; k is the discrete time number; n is the number of aircraft in the multi-aircraft formation;
for the 2 nd to N task groups which fly successively due to the task priority, the flight path of each aircraft of each task group accords with the inter-aircraft anti-collision constraint and avoids the prior task group flying in advance according to the method of avoiding the obstacle.
Compared with the prior art, the invention has the beneficial effects that: the invention designs a pre-planned flight path which meets the kinematics rule and is more close to the actual demand, and a polygonal obstacle area which is more close to the battlefield environment and is used for simulating the no-fly area is added in the convex optimization process, so that the problem that collision with polygonal obstacle is likely to occur between flight path planning discrete points in the flight task is solved; finally, aiming at the flight safety when the multi-machine executes the tasks, particularly the collision problem possibly occurring among different task groups, a virtual polygon concept is introduced to perform the salifying treatment so as to further ensure the flight safety when the multi-machine executes the tasks, particularly the flight safety of the aircraft in each task group in the planned flight path flight.
Drawings
FIG. 1 is a flow chart of a track planning method for multi-machine formation obstacle avoidance provided by the invention;
FIG. 2 is a diagram of the positional relationship of an aircraft and a radar;
FIG. 3 is a schematic diagram of a feasible region of an approximate polygonal obstacle;
fig. 4 is a schematic illustration of the avoidance of a plurality of task groups from each other in a multi-machine formation.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the track planning method for multi-machine formation obstacle avoidance provided by the invention comprises the following steps:
s1: and establishing a multi-machine formation track planning model.
Firstly, a single-machine three-dimensional space point quality motion model is established, then a plurality of constraint conditions are added on the basis of the motion model, finally, an objective function which meets the motion model and the constraint conditions and reaches a target point in the shortest time of multi-machine formation is set, and a multi-machine formation track planning model corresponding to the objective function is established on the basis of the three conditions.
The multimachine formation track planning model is required to be built based on an aircraft motion model. Setting each aircraft of the multi-aircraft formation to be of the same model, enabling the thrust of an engine to be consistent with the direction of the flight speed, and establishing a three-dimensional space point mass motion model of a single aircraft (single aircraft) as follows:
wherein, (x) i ,y i ,h i ) Representing three-dimensional coordinates of the aircraft i in a ground coordinate system; gamma ray i Represents the track dip angle, χ of the aircraft i i Representing the heading angle of the aircraft i; v (V) i Represents the ground speed of aircraft i; n is n x,i Indicating horizontal axial overload of aircraft i, n y,i A horizontal component representing the normal overload of aircraft i, n z,i A vertical component representing the normal overload of aircraft i; g represents the gravitational acceleration.
On the basis of establishing a single-machine three-dimensional space point quality motion model, a plurality of constraint conditions are required to be considered in designing a multi-machine track planning, namely a plurality of constraint conditions are required to be added, and the constraint conditions can comprise: initial/final state quantity constraints of aircraft i, magnitude constraints of state quantity/control quantity of aircraft i, rate of change constraints of control quantity of aircraft i, inter-aircraft collision avoidance constraints of multi-aircraft formation, collision avoidance constraints of aircraft i with external obstacles, and the like, wherein:
the expression of the initial/final state quantity constraint of the airplane i is as follows:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; s is(s) i,0 Representing an initial state quantity of aircraft i，s i,f Representing the amount of state of the aircraft i reaching the target point.
The expression of the amplitude constraint of the state quantity/control quantity of the airplane i is as follows:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; s is(s) i,min Representing the minimum state quantity of the aircraft i, s i,max Representing the maximum state quantity of the aircraft i, u i,min Representing the minimum control quantity of aircraft i, u i,max Maximum control of aircraft i.
The expression of the rate of change constraint of the control quantity of the aircraft i is:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning;representing the minimum control variable of aircraft i, < >>Indicating the maximum control variation of the aircraft i.
The expression of the inter-machine anti-collision constraint of the multi-machine formation is as follows:
||F·[s i (t)-s j (t)]|| 2 ≥R t and i is not equal to j, t 0 ≤t≤t f (5)
Wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; matrix f= [ I 3×3 ,O 3×3 ]，I 3×3 Is a 3X3 identity matrix, O 3×3 0 matrix (zero matrix) which is 3X 3; r is R t The value of the inter-aircraft safety distance matrix can be a self-defined value, and the inter-aircraft safety distance matrix refers to the mutual distance between two aircraft.
The expression (5) is used for preventing the aircrafts in the multi-aircraft formation from collision with each other, and ensuring the flight safety when the multiple aircrafts execute tasks.
The expression of the anti-collision constraint of the airplane i and the external obstacle is as follows:
||E·s i (t)-p obs,m || 2 ≥r m ，m＝1,2...M 0 ，t 0 ≤t≤t f (6)
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; matrix e= [ I 2×2 ,O 4×4 ]，I 2×2 Is a unit matrix of 2X2, O 4×4 0 matrix (zero matrix) which is 4X 4; p is p obs,m Is the center coordinates of the external obstacle, r m Is a safe distance corresponding to an external obstacle, and the value of the safe distance is a self-defined value; m is M 0 The static threat is the number of detected radars, no-fly zones and the like, M 0 The value is known in advance.
In the above expressions (2) to (6), s i Representing a set of state quantities for aircraft i, u i Representing a set of control variables for aircraft i, where s i ＝(x i ,y i ,h i ,V i ,χ i ,γ i ) T ，u i ＝(n x,i ,n y,i ,n z,i ) T 。
After the three-dimensional space point quality motion model and the constraint condition of the single machine are determined, an objective function for the multi-machine formation to reach the target point is also required to be set. Different objective functions may be set depending on the task and purpose being performed. In a preferred example, for the requirement that the low-altitude flight mission is to reach the target location rapidly and accurately, a function of reaching the target point in the shortest time of the multi-machine formation can be set as the target function, so that a corresponding flight path planning model expression can be obtained, which is specifically as follows:
the flight path planning model is used for solving the shortest time for the multimachine formation to reach the target point by taking the state quantity and the control quantity as optimization variables and taking the formulas (1) - (6) as constraint conditions; wherein s.t. formulas (1) to (6) represent constraints satisfying formulas (1) to (6) listed above.
Based on the above, after a single three-dimensional space point quality motion model is established and constraint conditions are determined, a function which meets the motion model and constraint conditions and reaches a target point in the shortest time of the multi-machine formation is set as an objective function, and a multi-machine formation track planning model corresponding to the motion model is established, wherein the expression (7) is shown.
S2: and establishing an obstacle model needing to be avoided by multi-machine formation, wherein the obstacle model comprises a radar identification area model and a no-fly area model.
In the low-altitude flight process, the aircraft often encounters obstacles in an airspace, and particularly, for low-altitude battlefield environments, the aircraft often encounters obstacles such as radars, no-fly areas and the like of enemies. The method considers the commonality and the characteristics of the barriers such as the radar, the no-fly zone and the like in modeling, and simultaneously needs to reasonably simplify and refine to reduce the computational complexity. In view of this, the present invention regards the obstacle as a three-dimensional cylinder with unlimited height, so that only two-dimensional cross-sections need to be considered in modeling the obstacle.
The radar of the enemy can be similar to a circular obstacle, the coverage area of the radar can be represented by a circle with the position of the radar as the center and the detection range as the radius in the flight process, and a schematic diagram of the position relation between the plane and the radar is shown in fig. 2.
The radar identification area model requiring multi-machine formation avoidance comprises the following steps: d is greater than or equal to R r +d s Where D is the distance of the aircraft to the center point of the radar identification area, R r For the detection radius of the radar, d s Is a safety margin. Therefore, when the flying position of the airplane meets D is more than or equal to R r +d s When the aircraft is considered to be realizing obstacle avoidance to the radar.
Most of the no-fly zones encountered in the low-altitude flight process are in irregular shapes, and the no-fly zones in irregular patterns are simplified into regular patterns expressed by mathematical expressions. That is to say,
the no-fly zone model requiring multi-machine formation avoidance comprises the following steps:
in (x) o ,y o ) Is the central coordinate of the no-fly zone, (x) i ,y i ) The flight coordinate of the aircraft is a width of a no-fly zone, b is a length of the no-fly zone, R r For the detection radius of the radar, d s For safety margin, k represents a shape parameter of which the no-fly zone is approximately polygonal, and when k=1, the no-fly zone is approximately diamond; when k=2, the no-fly zone is approximately elliptical; when k → infinity, the no-fly zone is approximately rectangular.
When the flight position of the aircraft satisfies expression (8), the aircraft can be considered to realize obstacle avoidance for the no-fly zone.
S3: and pre-planning a track route of the multi-machine formation obstacle avoidance of the task to be executed based on the multi-machine formation track planning model and the obstacle model.
And integrating the multi-machine formation track planning model and the obstacle model, and resolving the multi-machine formation track planning model to obtain a multi-machine formation obstacle avoidance track route, namely, pre-planning the multi-machine formation obstacle avoidance track route of the task to be executed.
In a preferred embodiment, after determining the task to be performed, the present invention uses an initial sequence of convex optimization iterations to solve for the pre-planned track route. In the resolving process, the important guarantee is that the motion characteristics and the resolving efficiency of the aircraft are guaranteed, so that only the initial/final state quantity constraint, the amplitude constraint of the state quantity/control quantity and the change rate constraint of the control quantity of the aircraft are considered, and the inter-aircraft anti-collision constraint and the anti-collision constraint of the aircraft and external obstacles are ignored temporarily.
Based on the above, the preferred method for pre-planning the track route of the multi-machine formation obstacle avoidance to be executed task based on the multi-machine formation track planning model and the obstacle model includes: determining constraint conditions as initial/final state quantity constraint of the airplane i, amplitude constraint of state quantity/control quantity of the airplane i and change rate constraint of control quantity of the airplane i, wherein:
the results of the initial sequence convex optimization iteration of the initial/final state quantity constraint expression of the airplane i are as follows: s is(s) i [0]＝s i,0 ,s i [K]＝s i,f ，i＝1,2…N (9)
Where K is the number of discrete moments, s i,0 Representing an initial state quantity, s, of an aircraft i i,f Representing the state quantity of the aircraft i reaching the target point, N being the number of aircraft in the multi-aircraft formation. The discrete time number refers to the number of time periods in which the time period from the initial time of flight of the aircraft in the track planning to the time when the flight of the aircraft reaches the target point is discrete.
The result of the initial sequence convex optimization iteration of the expression of the amplitude constraint of the state quantity/control quantity of the airplane i is as follows:
s i,min ≤s i [k]≤s i,max ，k＝0,1,…,K，i＝1,2…N (10)
U i,min ≤u i [k]≤U i,max ，k＝0,1,…,K，i＝1,2…N (11)
wherein K is the number of discrete moments, K is the kth discrete moment, and N is the number of planes in the multi-plane formation; s is(s) i,min Representing the minimum state quantity of the aircraft i, s i,max Representing the maximum state quantity of the aircraft i, U i,min Representing the minimum control quantity of aircraft i, U i,max Representing the maximum control quantity of the aircraft i.
The result of the initial sequence convex optimization iteration of the expression of the change rate constraint of the control quantity of the airplane i is as follows:
wherein the method comprises the steps ofK is the number of discrete moments, K is the kth discrete moment, and N is the number of planes in the multi-plane formation;representing the minimum control variable of aircraft i, < >>Indicating the maximum control variation of the aircraft i.
After the new initial/final state quantity constraint expression of the airplane i, the new state quantity/control quantity amplitude constraint expression of the airplane i and the new control quantity change rate constraint expression of the airplane i are obtained through initial sequence convex optimization iteration, the multi-airplane formation obstacle avoidance track route can be obtained through solving through the following expression (13) algorithm:
wherein K is the number of discrete moments, K is the kth discrete moment, i is the ith aircraft, N is the number of aircraft in the multi-aircraft formation, q is the iteration number, epsilon is the convergence domain and changes along with q, and every time q is increased by 1, epsilon becomes 1/2 of the original value.
Δt 0 Is a discrete time step, i.e. the time period from the initial time of flight of the aircraft in the flight path planning to the time when the flight of the aircraft reaches the target point is equally divided into T time periods, each time period being Δt 0 。
Equation constraint A eq ·Z＝b eq Expression (9) is included, wherein subscript eq represents "equation", and a and b are both coefficients for expressing the constraint of the equation. Equation constraint A eq ·Z＝b eq The meaning of including expression (9) means that the equality constraint contains only expression (9).
Inequality constraint A in ·Z≤b in Including expressions (10) to (12) where the subscript in represents "inequality", a and b are both coefficients for expressing the inequality constraint. Inequality constraint A in ·Z≤b in Includes the meanings of the expressions (10) to (12)It is meant that the inequality constraint contains only formulas (10) to (12).
μ eq Sum mu in Each of which is a scaling factor, which may be a custom value.
Z is an optimization variable comprising a discrete time step Deltat 0 Amplitude set z of state quantity and control quantity of aircraft i i ，
z i ＝(s i [0],s i [1]…s i [K],u i [0],u i [1]…u i [K]),i＝1,2…N。
Expression (13) is briefly explained below.
Δt 0 Expressed in discrete time steps Δt 0 The state quantity and the control quantity after the initial sequence convex optimization iteration are taken as optimization variables to obtain a discrete time step delta t 0 I.e. the shortest total time for the multimachine formation to reach the target point is obtained.
Expression (13) indicates that the pre-planned track route is to satisfy simultaneously:
and
wherein the method comprises the steps ofΔt 0 +μ eq ·||A eq ·Z-b eq || 1 +μ in ·||max(A in ·Z-b in ,0)|| 1 The meaning of (2) is that the equality constraint and the inequality constraint are put into the objective function in the form of penalty function, and the minimum value of the objective function is calculated.
And (3) solving the expression (13) to obtain the control quantity and the state quantity of the aircraft at a plurality of discrete moments, so as to obtain a plurality of track nodes of the aircraft, thereby drawing a track route.
Thus, the preplanned track route of the multi-machine formation is obtained.
In a preferred embodiment, in a track planning scheme to achieve obstacle avoidance, the present invention classifies external obstacles into approximately circular obstacles, which are commonly known as radar detection areas, and approximately polygonal obstacles, which are known as no-fly areas as mentioned herein. For approximately circular obstacles, as long as the flight position of the aircraft satisfies D.gtoreq.R r +d s I.e. see the relevant description above in step S2.
For the no-fly zone approximating a polygonal obstacle, the constraint condition of the expression (6) of the external obstacle anti-collision constraint described in step S1 can ensure that the aircraft does not collide with the no-fly zone, but the constraint is obviously non-convex and cannot be directly used for the sequence convex optimization solution. The present invention provides in this preferred embodiment a new solution method: the external obstacle collision constraint is convexly approximated by means of a reference track, i.e. the track that was found in the last iteration.
The following is a detailed description of the feasible region diagram of the approximate polygonal obstacle shown in fig. 3.
First, a flying-restricted zone which can be approximately rectangular is obtained in advance, and thenIndicating that its four vertices are marked counterclockwise from the most west vertex as +.>Where i=1, 2,3,4. Setting a reference point +.>It is +.>Is connected to the center of the rectangle if the connection is equal to the rectangle +>If there is an intersection point on one of the edges, a warning signal flag=0 is set, the edge is defined as a reference edge, and fig. 3 shows 2 reference edges; if the connection line is rectangular->If any one of the edges has no intersection point, the early warning signal flag is set to a positive constant value, for example, the positive constant value can be 10 4 Simultaneously calculate +.>To rectangle->The distance between the centers is denoted as d pc . Secondly, according to the coordinates of two vertexes of the reference edge, a linear expression of the straight line where the reference edge is located can be obtained, the straight line divides the plane into two parts, and obviously, the two parts are convex, wherein the half plane where the reference point is located is the sub-cycle p [ k ]]Is a feasible region of (2); finally, penalizing this constraint as an inequality constraint in the sequence convex optimization model (expression (13)), using C in The expression is represented by the following formula (14), regarding C in The flag/d is used in the expression of (a) pc Is to better guide convergence. This ensures that obstacle avoidance can be achieved at discrete points, i.e. that the aircraft avoids no-fly zones at discrete track nodes.
In addition, it should be ensured that the track between discrete points (track nodes) of the track route is not identical to a rectangleThe collision takes place by combining, on the basis of the expression (14), the expression (15) listed below, in particular the combination +.>The flight safety of the flight path of the airplane among the discrete points can be ensured, namely the flight path line among the flight path nodes of the flight path route is ensured not to collide with the no-fly zoneAnd the collision can avoid the no-fly zone.
The simultaneous expressions (14) and (15) result in a feasible region of p [ k ], such as the corresponding region shown in FIG. 3, it being evident that the intersection of the two convex sets is still convex, which conforms to the principles of the sequence convex optimization solution. The track route in the feasible region can avoid the no-fly zone.
Therefore, the method for avoiding the obstacle by the multi-machine formation provided by the invention further comprises the following steps: when the track of the aircraft conforms to the following expressions (14) and (15), it can be ensured that the track of the multi-aircraft formation avoids the no-fly zone,
wherein: k represents a certain time, (x) p [k],y p [k]) Is p [ k ]]Is used for the purpose of determining the coordinates of (a),is->Coordinates of (a) p ,b p ,c p ) Is p [ k ]]Linear expression coefficient of a line on which a reference edge determined from the center point of the no-fly zone is located, and flag is a value about the reference point p [ k ]]Early warning signal value d pc Is p [ k ]]A distance from a coordinate point of (c) to a center point of the no-fly zone. />
Wherein: k represents a certain time, (x) p [k],y p [k]) Is p [ k ]]Is used for the purpose of determining the coordinates of (a),is thatCoordinates of (a) p-1 ,b p-1 ,c p-1 ) Is->Linear expression coefficient, flag of straight line where reference edge determined by central point of no-fly zone is located * Is about datum point->Early warning signal value,/-, of (2)>Is->A distance from a coordinate point of (c) to a center point of the no-fly zone.
In a preferred embodiment, the multi-machine formation is also subjected to inter-plane flight safety, i.e. possible collision problems between planes, especially when the multi-machine formation is divided into a plurality of task groups, and the possible collision problems between different task groups on the flight path for performing the tasks affect the flight safety of the multi-machine for performing the tasks.
In order to solve the flight safety problem between machines, the invention introduces the concept of virtual polygon to perform the salifying treatment so as to solve the obstacle avoidance problem between task groups. Thus, the track planning method for the multi-machine formation obstacle avoidance further comprises the following steps: dividing the multi-machine formation into a plurality of task groups, dividing different tasks into priorities of different levels, and for a 1 st task group which flies first due to the highest task priority, avoiding the obstacle among the planes of the 1 st task group as follows:
the inter-aircraft obstacle avoidance can be achieved when the flight path of each aircraft of the mission 1 group meets the following constraints:
wherein E= [ I 2×2 ,O 4×4 ]；Representing the state quantity of a reference track of the aircraft i at the moment k; />Representing the state quantity of a reference track of the airplane j at the moment k; v (V) i,max Representing the maximum flight speed of aircraft i; v (V) j,max Representing the maximum flight speed of aircraft j; Δt (delta t) 0 Is a discrete time step; r represents a safe distance in the XOY plane (i.e., a two-dimensional plane without regard to height); r is R t Is an inter-machine safety distance matrix; η represents a correction coefficient of the safe distance between machines, 1 is preferably chosen; k is the discrete time number; n is the number of aircraft in the multi-aircraft formation.
For the 2 nd to N th task groups flying sequentially due to the task priority, the flight path of each aircraft of each task group meets the inter-aircraft anti-collision constraint and avoids the prior task group flying in advance according to the method of avoiding the obstacle, namely the flight path of the aircraft meets the expressions (5), (14) and (15).
A brief description is provided below in connection with FIG. 4. As shown in FIG. 4, the task group flies to T at task 1 1 When the moment, the task group 2 is instructed to start executing the task, and when the track planning is carried out on the task group 2, the track route of the task group 1 needs to be considered, and the task group 1 is supposed to be intercepted at T 1 ～T p Marking the planned track of the time period, marking the maximum value of the abscissa of the track under the ground coordinate system, and determining four maximum points, namely: the method comprises the steps of determining a first maximum point determined by an abscissa maximum value and an ordinate minimum value, determining a second maximum point determined by an abscissa maximum value and an ordinate maximum value, determining a third maximum point determined by an abscissa minimum value and an ordinate minimum value, determining a fourth maximum point determined by an abscissa minimum value and an ordinate maximum value, and determining a rectangle according to the 4 maximum points, wherein the rectangle is called as a virtual polygon for obstacle avoidance between groups. In this way, when the mission 2 group is planned, the flight path of the mission 1 group at a certain time period is determined as a rectangular flight zone, which can be regarded as a no-fly zone, so that the mission 2 group can be avoided according to the no-fly zone described above in connection with fig. 3The track route of the group needs to satisfy expressions (14) and (15).
Compared with the prior art, the track planning method for avoiding the obstacle of the multi-machine formation provided by the invention has the advantages that the track route pre-planned by the invention is more in accordance with the kinematics rule and is closer to the actual demand, so that the airplane can effectively avoid circular obstacles such as radars and polygonal obstacles such as no-fly areas, and meanwhile, the effective obstacle avoidance among a plurality of task subgroups in the multi-machine formation can be realized in a mode of avoiding virtual polygons.
The foregoing is a further elaboration of the present invention in connection with the detailed description, and it is not intended that the invention be limited to the specific embodiments shown, but rather that a number of simple deductions or substitutions be made by one of ordinary skill in the art without departing from the spirit of the invention, should be considered as falling within the scope of the invention as defined in the appended claims.
Claims (1)
1. A flight path planning method for multi-machine formation obstacle avoidance is characterized by comprising the following steps:
firstly, a single-machine three-dimensional space point quality motion model is established, then a plurality of constraint conditions are added on the basis of the motion model, and finally, an objective function which meets the motion model and the constraint conditions and reaches a target point in the shortest time of multi-machine formation is set, so that a multi-machine formation track planning model corresponding to the motion model is established;
establishing an obstacle model needing to be avoided by multi-machine formation, wherein the obstacle model comprises a radar identification area model and a no-fly area model;
based on a multi-machine formation track planning model and an obstacle model, a track route of multi-machine formation obstacle avoidance of a task to be executed is pre-planned;
the single machine three-dimensional space point mass motion model is as follows:
wherein, (x) i ,y i ,h i ) Representing three-dimensional coordinates of the aircraft i in a ground coordinate system; gamma ray i Represents the track dip angle, χ of the aircraft i i Representing the heading angle of the aircraft i; v (V) i Represents the ground speed of aircraft i; n is n x,i Indicating horizontal axial overload of aircraft i, n y,i A horizontal component representing the normal overload of aircraft i, n z,i A vertical component representing the normal overload of aircraft i; g represents gravitational acceleration;
the constraint conditions include: initial/final state quantity constraints for aircraft i, magnitude constraints for state quantity/control quantity for aircraft i, rate of change constraints for control quantity for aircraft i, inter-aircraft collision avoidance constraints for multi-aircraft formation, and collision avoidance constraints for aircraft i with external obstacles, wherein:
the expression of the initial/final state quantity constraint of the airplane i is as follows:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; s is(s) i,0 Representing an initial state quantity, s, of an aircraft i i,f Representing the state quantity of the aircraft i reaching the target point;
the expression of the amplitude constraint of the state quantity/control quantity of the airplane i is as follows:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; s is(s) i,min Representing the minimum state quantity of the aircraft i, s i,max Representing the maximum state quantity of the aircraft i, u i,min Representing the minimum control quantity of aircraft i, u i,max Maximum control quantity of aircraft i;
the expression of the rate of change constraint of the control quantity of the aircraft i is:
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning;representing the minimum control variable of aircraft i, < >>Representing the maximum control variation of the aircraft i;
the expression of the inter-machine anti-collision constraint of the multi-machine formation is as follows:
||F·[s i (t)-s j (t)]|| 2 ≥R t and i is not equal to j, t 0 ≤t≤t f (5)
Wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; matrix f= [ I 3×3 ,O 3×3 ]，I 3×3 Is a 3X3 identity matrix, O 3×3 A 0 matrix of 3X 3; r is R t Is an inter-machine safety distance matrix;
the expression of the anti-collision constraint of the airplane i and the external obstacle is as follows:
||E·s i (t)-p obs,m || 2 ≥r m ，m＝1,2…M 0 ，t 0 ≤t≤t f (6)
wherein t is 0 Representing the initial time t of the aircraft flight in the track planning f Representing the moment when the aircraft flight reaches the target point in the track planning; matrix e= [ I 2×2 ,O 4×4 ]，I 2×2 Is a unit matrix of 2X2, O 4×4 A 0 matrix of 4X 4; p is p obs,m Is the center coordinates of the external obstacle, r m Is a safe distance corresponding to an external obstacle, and the value of the safe distance is a self-defined value; m is M 0 The number of static threats;
in the above formulae (2) to (6), s i Representing a set of state quantities for aircraft i, u i Representing a set of control variables for aircraft i, where s i ＝(x i ,y i ,h i ,V i ,χ i ,γ i ) T ，u i ＝(n x,i ,n y,i ,n z,i ) T ；
The multi-machine formation track planning model is as follows:
s.t. formulas (1) to (6) (7)
Wherein s.t. formulas (1) to (6) represent constraints satisfying formulas (1) to (6) listed above;
the radar identification area model requiring multi-machine formation avoidance comprises the following steps: d is greater than or equal to R r +d s Where D is the distance of the aircraft to the center point of the radar identification area, R r For the detection radius of the radar, d s Is a safety margin; and
the no-fly zone model requiring multi-machine formation avoidance comprises the following steps:
in (x) o ,y o ) Is the central coordinate of the no-fly zone, (x) i ,y i ) The flight coordinate of the aircraft is a width of a no-fly zone, b is a length of the no-fly zone, R r For the detection radius of the radar, d s As a safety margin, k represents a shape parameter of a polygon of the no-fly zone, and when k=1, the no-fly zone is a diamond; when k=2, the no-fly zone is elliptical; when the distance is k-infinity, the no-fly zone is rectangular;
the method for pre-planning the track route of the multi-machine formation obstacle avoidance of the task to be executed based on the multi-machine formation track planning model and the obstacle model comprises the following steps: determining constraint conditions as initial/final state quantity constraint of the airplane i, amplitude constraint of state quantity/control quantity of the airplane i and change rate constraint of control quantity of the airplane i, wherein:
the results of the initial sequence convex optimization iteration of the initial/final state quantity constraint expression of the airplane i are as follows: s is(s) i [0]＝s i,0 ,s i [K]＝s i,f ,i＝1,2…N (9)
Wherein K is the discrete time number, s i,0 Representing an initial state quantity, s, of an aircraft i i,f Representing the state quantity of the aircraft i reaching the target point, wherein N is the number of the aircraft in the multi-aircraft formation;
the result of the initial sequence convex optimization iteration of the expression of the amplitude constraint of the state quantity/control quantity of the airplane i is as follows:
s i,min ≤s i [k]≤s i,max ，k＝0,1,…,K，i＝1,2…N (10)
U i,min ≤u i [k]≤U i,max ，k＝0,1,…,K，i＝1,2…N (11)
wherein K is the number of discrete moments, K is the kth discrete moment, and N is the number of planes in the multi-plane formation; s is(s) i,min Representing the minimum state quantity of the aircraft i, s i,max Representing the maximum state quantity of the aircraft i, U i,min Representing the minimum control quantity of aircraft i, U i,max Representing the maximum control quantity of the aircraft i;
the result of the initial sequence convex optimization iteration of the expression of the change rate constraint of the control quantity of the airplane i is as follows:
wherein K is the number of discrete moments, K is the kth discrete moment, and N is the number of planes in the multi-plane formation;representing the minimum control variable of aircraft i, < >>Representing flyMaximum control variation of machine i;
the track route of the multi-machine formation obstacle avoidance can be obtained through the following algorithm:
is limited byWherein K is the number of discrete moments, K is the kth discrete moment, i is the ith aircraft, N is the number of aircraft in the multi-aircraft formation, q is the iteration number, epsilon is the convergence domain and varies with q, and when q is increased by 1, epsilon is changed into the original 1/2; Δt (delta t) 0 Is a discrete time step; equation constraint A eq ·Z＝b eq Including expression (9), wherein subscript eq represents "equation", and a and b are both coefficients for expressing inequality constraints; inequality constraint A in ·Z≤b in Including expressions (10) to (12) in which the subscript in represents "inequality", a and b are both coefficients for expressing the constraint of the equality; mu (mu) eq Sum mu in Respectively the proportionality coefficients; z is an optimization variable comprising a discrete time step Deltat 0 Amplitude set z of state quantity and control quantity of aircraft i i ，
z i ＝(s i [0],s i [1]…s i [K],u i [0],u i [1]…u i [K]),i＝1,2…N (14)
For a no-fly zone of polygonal obstacle, the method for avoiding the obstacle by the multi-machine formation comprises the following steps: when the track of the aircraft conforms to the following expressions (15) and (16), the track of the multi-aircraft formation is ensured to avoid the no-fly zone,
where k represents a certain time, (x) p [k],y p [k]) Is p [ k ]]Is used for the purpose of determining the coordinates of (a),is->Coordinates of (a) p ,b p ,c p ) Is p [ k ]]Linear expression coefficient of a line on which a reference edge determined from the center point of the no-fly zone is located, and flag is a value about the reference point p [ k ]]Early warning signal value d pc Is p [ k ]]A distance from a coordinate point of (c) to a center point of the no-fly zone;
where k represents a certain time, (x) p [k],y p [k]) Is p [ k ]]Is used for the purpose of determining the coordinates of (a),is->Coordinates of (a) p-1 ,b p-1 ,c p-1 ) Is->Linear expression coefficient, flag of straight line where reference edge determined by central point of no-fly zone is located * Is about datum point->Early warning signal value,/-, of (2)>Is->A distance from a coordinate point of (c) to a center point of the no-fly zone;
the track planning method for the multi-machine formation obstacle avoidance further comprises the following steps: the multi-aircraft formation is divided into a plurality of task groups, and for the 1 st task group which flies first due to the highest priority of the tasks, the obstacle avoidance method between the aircraft of the 1 st task group is as follows:
the inter-aircraft obstacle avoidance can be achieved when the flight path of each aircraft of the mission 1 group meets the following constraints:
wherein E= [ I 2×2 ,O 4×4 ]，I 2×2 Is a unit matrix of 2X2, O 4×4 A 0 matrix of 4X 4;representing the state quantity of a reference track of the aircraft i at the moment k; />Representing the state quantity of a reference track of the airplane j at the moment k; v (V) i,max Representing the maximum flight speed of aircraft i; v (V) j,max Representing the maximum flight speed of aircraft j; Δt (delta t) 0 Is a discrete time step; r represents a safe distance in the XOY plane; r is R t Is an inter-machine safety distance matrix; η represents a correction coefficient of the inter-machine safety distance; k is the discrete time number; n is the number of aircraft in the multi-aircraft formation;
for the 2 nd to N task groups which fly successively due to the task priority, the flight path of each aircraft of each task group accords with the inter-aircraft anti-collision constraint and avoids the prior task group flying in advance according to the method of avoiding the obstacle.
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