A method and device for quickly generating an obstacle avoidance trajectory of an aircraft

Abstract

The present invention provides a method and device for quickly generating an obstacle avoidance trajectory of an aircraft, belonging to the technical field of aircraft path planning. Among them, the method includes: constructing an optimization problem for the obstacle avoidance trajectory of the aircraft according to the kinematic model and dynamic model of the aircraft, where the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft, and the objective function is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function; by constructing a flight trajectory equation represented by a polynomial, converting the obstacle avoidance constraint into an obstacle avoidance performance index function and adding it to the comprehensive performance index, simplifying the time performance index function, the overload integral performance index function, and the obstacle avoidance performance index function, and solving to obtain the optimization result of the obstacle avoidance trajectory. The present invention can transform the obstacle avoidance trajectory planning problem into an unconstrained and analytically solvable optimization problem, and improve the solution speed under the condition of ensuring the obstacle avoidance effect and calculation accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft path planning, and particularly provides a method and device for quickly generating an obstacle avoidance trajectory of an aircraft. Background Art

[0002] During the flight of an aircraft, it faces complex and changeable geographical environments, harsh weather conditions, and threats and influences from numerous ground and air facilities. The seemingly calm flight process is actually full of dangers. The efficiency and accuracy of manually formulating flight plans can no longer meet diverse flight requirements. Under such circumstances, trajectory planning has emerged. Trajectory planning is beneficial to improving the flight safety and flight quality of the aircraft and better meeting the requirements of established tasks. A faster online real-time trajectory planning method can further help the aircraft cope with more and more complex flight scenarios, broaden the capabilities of the aircraft, and maximize the use value of the aircraft.

[0003] However, traditional obstacle avoidance trajectory planning algorithms, considering multiple constraint limitations during the flight of the aircraft, usually transform the obstacle avoidance problem into a constrained non-linear optimization problem for solution. The solution speed is slow, and it is difficult to guarantee the accuracy and stability of the solution, making it difficult to be used for real-time trajectory planning. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the existing technologies and provide a method and device for quickly generating an obstacle avoidance trajectory of an aircraft. The present invention can transform a complex obstacle avoidance trajectory planning problem into an unconstrained and analytically solvable optimization problem, greatly improving the solution speed under the conditions of ensuring the obstacle avoidance effect and calculation accuracy, making real-time online trajectory planning possible.

[0005] The first aspect embodiment of the present invention provides a method for quickly generating an obstacle avoidance trajectory of an aircraft, including:

[0006] Constructing a kinematic model and a dynamic model of the aircraft;

[0007] According to the kinematic model and the dynamic model, constructing an obstacle avoidance trajectory optimization problem of the aircraft; the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft; the objective function of the optimization problem is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function;

[0008] By constructing a flight trajectory equation represented by a polynomial, transforming the obstacle avoidance constraint into an obstacle avoidance performance index function in the form of a penalty function and adding it to the comprehensive performance index; simplifying the time performance index function, the overload integral performance index function, and the obstacle avoidance performance index function respectively, and solving the optimization problem by iteratively calculating the analytical gradient to obtain the optimization result of the obstacle avoidance trajectory;

[0009] Among them, the expressions of the time performance index function and the overload integral performance index function are as follows:

[0010]

[0011] Among them, J T and J N are the time performance index function and the overload integral performance index function respectively, representing the completion time of the entire planned trajectory and the total overload consumed by the aircraft during the process of completing the planned trajectory; N f is the overload of the aircraft when it reaches the target position; t f is the planned end time; v is the constant speed of the aircraft, θ is the yaw angle, the abscissa of the real-time position of the aircraft is x, and the acceleration is a c ; g is the acceleration due to gravity; N is the lateral overload of the aircraft

[0012] The expressions of time T and overload N are as follows respectively:

[0013]

[0014] Then the expression of the comprehensive performance index J total is as follows:

[0015] J total = ω T J T + ω N J N (7)

[0016] Among them, ω T is the weighting coefficient corresponding to J T ; ω N is the weighting coefficient corresponding to J N ; both ω T and ω N are greater than 0.

[0017] In a specific embodiment of the present invention, the expression of the kinematic model is as follows:

[0018]

[0019] Among them, v is the constant speed of the aircraft, θ is the yaw angle, the abscissa of the real-time position of the aircraft is x, the ordinate is y, and the acceleration is a c ; and They are respectively the derivative of the abscissa of the real-time position of the aircraft with respect to time, the derivative of the ordinate of the real-time position of the aircraft with respect to time, and the derivative of the yaw angle of the real-time position of the aircraft with respect to time; the reference coordinate system of the kinematic model is a follow-up coordinate system, the X-axis of the follow-up coordinate system points from the initial position of the trajectory planning to the target position, the Y-axis of the follow-up coordinate system changes with the position of the aircraft, so that the current position of the aircraft is always on the Y-axis, and the initial origin of the follow-up coordinate system is the initial position of the trajectory planning;

[0020] The expression of the dynamic model is as follows:

[0021] a c = Ng (2)

[0022] where, N is the lateral overload of the aircraft, and g is the acceleration due to gravity.

[0023] In a specific embodiment of the present invention, the endpoint constraints of the aircraft trajectory planning are expressed as follows:

[0024]

[0025] where, (x0, y0) are the coordinates of the initial position of the aircraft trajectory planning, x0 and y0 respectively represent the abscissa and ordinate values of the initial position; (x f , y f ) are the coordinates of the target position, x f and y f respectively represent the abscissa and ordinate values of the target position, θ0 is the yaw angle of the aircraft at the initial position, θ f is the yaw angle of the aircraft when it reaches the target position, t0 is the starting time of the planning, and t f is the end time of the planning;

[0026] The obstacle avoidance constraint expression during the flight of the aircraft is as follows:

[0027]

[0028] where, C m =(x z,m , y z,m ) is the center position of the mth circular no-fly zone within the flight range of the aircraft, x z,m is the abscissa of the center of the mth no-fly zone, y z,m is the ordinate of the center of the mth no-fly zone, the radius of the mth no-fly zone is R m , m = 1,..., N z , N z is the total number of no-fly zones.

[0029] In a specific embodiment of the present invention, the expression of the aircraft obstacle avoidance trajectory optimization problem is as follows:

[0030]

[0031] In a specific embodiment of the present invention, the method further includes:

[0032] 1) Construct a flight trajectory equation represented by an nth-order polynomial;

[0033]

[0034] where a i is a parameter, i = 0...n;

[0035] Let n = 4, then Equation (9) is transformed into the following form:

[0036]

[0037] where y on the left side of the equation, and are the 0th, 1st, and 2nd derivatives of y with respect to x respectively, and x i represents the ith power of x;

[0038] Let the parameters x and y be flat outputs, r be the instantaneous curvature radius of the flight trajectory, K be the instantaneous curvature of the flight trajectory, then the lateral overload N is represented by the derivatives of y:

[0039]

[0040] 2) Transform the endpoint constraints of the aircraft trajectory planning;

[0041] Using the trajectory equation shown in Equation (10), transform the endpoint constraints of the aircraft trajectory planning in Equation (3) into the following form:

[0042]

[0043] where l is the distance between the initial position and the target position;

[0044] Taking the first four degrees of freedom a0 to a3 of the fixed trajectory equation (10) as the cost, eliminate the four equality constraints shown in Equation (3); substitute Equation (12) into Equation (9), determine the parameters a0 and a1, and obtain the expressions of a2 and a3:

[0045]

[0046] 3) Discretize the flight trajectory equation;

[0047] Discretize the trajectory at equal intervals in the x-axis direction. Uniformly take k discrete points on x ∈ [0, l]. The abscissa of the j-th discrete point is The ordinate corresponding to the abscissa of this discrete point on the trajectory is y j , then the j-th discrete point of the trajectory is (x j , y j ); The flight trajectory equation after discretization is expressed as follows:

[0048]

[0049] When n = 4, the expression of the flight trajectory equation after discretization is as follows:

[0050]

[0051] 4) Transform the obstacle avoidance constraint;

[0052] After discretizing the flight trajectory equation, the obstacle avoidance constraint formula (4) during the flight of the aircraft is transformed into the following form:

[0053]

[0054] where D j,m is the distance between the m-th no-fly zone and the j-th discrete point;

[0055] According to formula (4), establish an instantaneous obstacle avoidance piecewise penalty function for a single no-fly zone. Let ω Z be the obstacle avoidance weighting coefficient and p be the penalty parameter. Then for the m-th no-fly zone:

[0056]

[0057] Φ Z (x j , a4) is the obstacle avoidance performance penalty function of the j-th discrete point;

[0058] Then construct the obstacle avoidance performance index function as follows:

[0059]

[0060] Incorporate the obstacle avoidance performance index function composed of penalty functions into the comprehensive performance index function to obtain the updated expression of the comprehensive performance index as follows:

[0061] J total = ω Z J Z + ω T J T + ω N J N (19)

[0062] where ωZ The weight corresponding to the obstacle avoidance performance index function;

[0063] 5) Simplify the time performance index function and the overload integral performance index function. The specific steps are as follows:

[0064] 5-1) Simplify the time performance index function;

[0065] Substitute the discretized flight trajectory equation (15) into the time performance index function in Equation (5) to obtain:

[0066]

[0067] where Δx is the length of each discrete segment on the x-axis after discretization, and Δt is the time required to fly through this discrete segment;

[0068] The expression of the simplified time performance index function is as follows:

[0069]

[0070] 5-2) Simplify the overload integral performance index function;

[0071] Let the instantaneous curvature of the flight trajectory of the aircraft corresponding to the j-th discrete point be K j , then the instantaneous overload N j ,y j ) of the aircraft at this discrete trajectory point (x j is:

[0072]

[0073] Add the overload square term to the overload function Φ N , Φ N represents the square of the overload per unit time:

[0074]

[0075] After performing weighted summation on Φ N , the expression of the simplified overload integral performance index function is as follows:

[0076]

[0077] 6) Solve through the performance index gradient to obtain the optimization result of the obstacle avoidance trajectory;

[0078] Regard the parameters a2 and a3 as functions of a4 and take the derivative:

[0079]

[0080] According to Equation (18), J ZTaking the partial derivative with respect to each order parameter a4 gives:

[0081]

[0082] Where:

[0083]

[0084] According to Equation (21), J T Taking the partial derivative with respect to each order parameter a4 gives:

[0085]

[0086] Where,

[0087]

[0088] According to Equation (24), J N Taking the partial derivative with respect to each order parameter a4 gives:

[0089]

[0090] Where,

[0091]

[0092] Substitute the solved performance index functions of Equations (18), (21) and (24) and their analytical derivative expressions of (26), (29) and (31) into the gradient descent algorithm to solve for the parameter a4;

[0093] Substitute a4 into Equation (9) to obtain the optimal fly-around trajectory of the aircraft.

[0094] The second aspect embodiment of the present invention proposes a device for quickly generating an obstacle avoidance trajectory of an aircraft, including:

[0095] A kinematics and dynamics model construction module for constructing the kinematics model and dynamics model of the aircraft;

[0096] An obstacle avoidance trajectory optimization problem construction module for constructing an obstacle avoidance trajectory optimization problem of the aircraft according to the kinematics model and the dynamics model; the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft; the objective function of the optimization problem is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function;

[0097] An obstacle avoidance trajectory optimization module, configured to transform the obstacle avoidance constraint into an obstacle avoidance performance index function in the form of a penalty function and add it to the comprehensive performance index by constructing a flight trajectory equation represented by a polynomial; simplify the time performance index function, the overload integral performance index function, and the obstacle avoidance performance index function respectively, and solve the optimization problem by iteratively calculating the analytical gradient to obtain the optimization result of the obstacle avoidance trajectory;

[0098] Among them, the expressions of the time performance index function and the overload integral performance index function are as follows:

[0099]

[0100] Among them, J T and J N are the time performance index function and the overload integral performance index function respectively, representing the completion time of the entire planned trajectory and the total overload consumed by the aircraft during the process of completing the planned trajectory; N f is the overload of the aircraft when it reaches the target position; t f is the end time of the plan; v is the constant speed of the aircraft, θ is the yaw angle, the abscissa of the real-time position of the aircraft is x, and the acceleration is a c ; g is the acceleration due to gravity; N is the lateral overload of the aircraft

[0101] The expressions of time T and overload N are as follows respectively:

[0102]

[0103] Then the expression of the comprehensive performance index J total is as follows:

[0104] J total = ω T J T + ω N J N (7)

[0105] Among them, ω T is the weighting coefficient corresponding to J T , ω N is the weighting coefficient corresponding to J N , and both ω T and ω N are greater than 0.

[0106] An embodiment of the third aspect of the present invention provides an electronic device, including:

[0107] At least one processor; and a memory communicatively connected to the at least one processor;

[0108] Among them, the memory stores instructions executable by the at least one processor, and the instructions are configured to execute the above-mentioned method for quickly generating an obstacle avoidance trajectory of an aircraft.

[0109] An embodiment of the fourth aspect of the present invention provides a computer-readable storage medium, and the computer-readable storage medium stores computer instructions for causing the computer to execute the above-mentioned method for quickly generating an obstacle avoidance trajectory of an aircraft.

[0110] The advantages and beneficial effects of the present invention are as follows:

[0111] 1. The input control quantity and state quantity of the present invention can be uniquely determined by the flat output and its derivatives of each order. The trajectory shape is smooth, and the overload has no mutation, greatly reducing the performance requirements for the aircraft control module.

[0112] 2. The present invention greatly reduces the difficulty of solving the trajectory planning problem, and can also run stably on an airborne computer with low computing power, improving the efficiency and practicability of the aircraft trajectory planning.

[0113] 3. The trajectory planning result of the present invention has both feasibility and optimality, and can obtain better planning results in actual trajectory planning tasks.

[0114] 4. The present invention can greatly improve the calculation speed on the premise of ensuring the same calculation accuracy, reduce the time cost of the aircraft obstacle avoidance trajectory planning, and can achieve real-time trajectory planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Figure 1 is the overall flowchart of a method for quickly generating an obstacle avoidance trajectory of an aircraft according to an embodiment of the present invention.

[0116] Figure 2 is a schematic diagram of the obstacle avoidance performance index function before simplification in a specific embodiment of the present invention.

[0117] Figure 3 is a schematic diagram of the obstacle avoidance performance index function after simplification in a specific embodiment of the present invention.

[0118] Figure 4 is a schematic diagram of the time performance index function before simplification in a specific embodiment of the present invention.

[0119] Figure 5 is a schematic diagram of the time performance index function after simplification in a specific embodiment of the present invention.

[0120] Figure 6 is a schematic diagram comparing the numerical calculation result and the analytical calculation result of the gradient of the comprehensive performance index in a specific embodiment of the present invention.

[0121] Figure 7It is a schematic diagram of the error between the numerical calculation gradient and the analytical calculation gradient of the comprehensive performance index in a specific embodiment of the present invention.

[0122] Figure 8 It is a schematic diagram of the trajectory planning when only the angle constraint exists and there is no no-fly zone in a specific embodiment of the present invention by using the method of the present invention.

[0123] Figure 9 It is a schematic diagram of the trajectory planning when both the angle constraint and the no-fly zone exist in a specific embodiment of the present invention by using the method of the present invention. Detailed implementation manners

[0124] The present invention provides a method and device for quickly generating an obstacle avoidance trajectory of an aircraft. The following is a detailed description with reference to specific embodiments in the accompanying drawings:

[0125] An embodiment of the first aspect of the present invention provides a method for quickly generating an obstacle avoidance trajectory of an aircraft, including:

[0126] Constructing a kinematic model and a dynamic model of the aircraft;

[0127] According to the kinematic model and the dynamic model, constructing an obstacle avoidance trajectory optimization problem of the aircraft; the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft; the objective function of the optimization problem is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function;

[0128] By constructing a flight trajectory equation represented by a polynomial, transforming the obstacle avoidance constraint into an obstacle avoidance performance index function in the form of a penalty function and adding it to the comprehensive performance index; simplifying the time performance index function, the overload integral performance index function and the obstacle avoidance performance index function respectively, and solving the optimization problem by iteratively calculating the analytical gradient to obtain the optimization result of the obstacle avoidance trajectory.

[0129] In a specific embodiment of the present invention, the overall process of the method for quickly generating an obstacle avoidance trajectory of an aircraft is as Figure 1 shown and includes the following steps:

[0130] 1) Constructing a kinematic model and a dynamic model of the aircraft; the specific steps are as follows

[0131] 1-1) Establishing a reference coordinate system;

[0132] In this embodiment, let the reference coordinate system be a follow-up coordinate system. The X-axis of the follow-up coordinate system points from the initial position of the trajectory planning to the target position. The follow-up coordinate system changes with the change of the mission phase. Therefore, when replanning during flight, the follow-up coordinate system will also change accordingly to ensure that the current position of the aircraft is always on the Y-axis of the coordinate system, and the end point (i.e., the target position) is always on the X-axis of the coordinate system. That is, the Y-axis of the coordinate system will be pushed forward with the change of the aircraft position to ensure that the Y-axis passes through the current position of the aircraft.

[0133] The initial origin of this reference coordinate system (i.e., the intersection position of the Y-axis and the X-axis at the current moment) is the initial position of the trajectory planning (i.e., the initial position of the aircraft). The ray direction from the coordinate origin to the target position is the X-axis direction, and the direction perpendicular to the X-axis and following the right-hand rule is the Y-axis direction. After that, the origin position will change with the forward push of the Y-axis. The aircraft flies at a constant speed v, the yaw angle is θ, the abscissa of the real-time position of the aircraft is recorded as x, the ordinate is y, and the acceleration is a. c 。

[0134] In this reference coordinate system, the kinematic model of the aircraft is established as follows:

[0135]

[0136] Among them, and are respectively the derivative of the abscissa of the real-time position of the aircraft with respect to time, the derivative of the ordinate of the real-time position of the aircraft with respect to time, and the derivative of the yaw angle of the real-time position of the aircraft with respect to time.

[0137] 1-2) Establish the dynamic model of the aircraft;

[0138] In this embodiment, since the speed is constant, the external control force only appears in the form of lateral overload and is used to adjust the heading of the aircraft. According to the definition of overload, the expression of the dynamic model of the aircraft is established as follows:

[0139] a c = Ng (2)

[0140] Among them, N is the lateral overload of the aircraft, and g is the acceleration due to gravity.

[0141] 2) Establish the constraint conditions for the obstacle avoidance trajectory planning of the aircraft. The constraint conditions include: the end point constraint of the aircraft trajectory planning and the obstacle avoidance constraint during the flight of the aircraft, specifically as follows:

[0142] 2-1) Establish the end point constraint of the aircraft trajectory planning;

[0143] In this embodiment, let the coordinates of the initial position of the aircraft trajectory planning be (x0, y0), which coincides with the initial origin of the reference coordinate system. x0 and y0 respectively represent the horizontal and vertical coordinate values of the initial position. The coordinates of the target position are (x f , y f ), where x f and y f respectively represent the horizontal and vertical coordinate values of the target position. Since the yaw angle θ changes continuously during flight, the yaw angle of the aircraft at the initial position is set to θ0, and the yaw angle when reaching the target position is θ f . The starting time of the planning is t0, and the planning ends after the aircraft reaches the target position. Denote the end time of the planning as t f . Then the endpoint constraints of the aircraft trajectory planning can be expressed as follows:

[0144]

[0145] 2-2) Establish the obstacle avoidance constraints during the flight of the aircraft;

[0146] In this embodiment, let there be N z circular no-fly zones within the flight range of the aircraft (in this embodiment, N z takes the value of 1). The center position of the m-th no-fly zone is C m = (x z,m , y z,m ), and the radius of the m-th no-fly zone is R m , m = 1,..., N z . x z,m is the abscissa of the center of the m-th no-fly zone, and y z,m is the ordinate of the center of the m-th no-fly zone. Then the obstacle avoidance constraints during the flight of the aircraft are established as follows:

[0147]

[0148] where D m is the distance from any point on the planned trajectory to the center of the no-fly zone m.

[0149] 3) Establish the performance index function of the aircraft trajectory planning;

[0150] In this embodiment, in combination with the actual mission requirements, in order to enable the aircraft to consume as little time and energy as possible while meeting the mission objectives and constraints, it is also necessary to set relevant performance index functions.

[0151] Let the distance between the initial position and the target position of the trajectory planning be l, and the component of the velocity v on the x-axis be v x . Then there is:

[0152]

[0153] Among them, J T and J N are the time performance index function and the overload integral performance index function respectively, representing the completion time of the entire planned trajectory and the total overload consumed by the aircraft during the process of completing the planned trajectory. N f is the overload of the aircraft when it reaches the target position, that is, the terminal overload. Among them, the expressions of time T and overload N are as follows:

[0154]

[0155] Since J T and J N need to be optimized simultaneously, it is also necessary to perform weighted integration on the two, and finally the expression of the comprehensive performance index J total is as follows:

[0156] J total =ω T J T +ω N J N (7)

[0157] Among them, ω T is the weighting coefficient corresponding to J T , and ω N is the weighting coefficient corresponding to J N . The weighting coefficients ω T and ω N are both greater than 0, and the specific values need to be adjusted according to the experimental results. In the simulation experiment of a specific embodiment of the present invention, considering normalization, the settings of these two coefficients are ω T =5.71×10 -4 and ω N =0.04.

[0158] 4) According to the results of steps 1)-3), construct the original aircraft obstacle avoidance trajectory optimization problem.

[0159] In this embodiment, by combining formulas (1)-(7), the expression of the original aircraft obstacle avoidance trajectory optimization problem is constructed as follows:

[0160]

[0161] Among them, the objective function of this optimization problem is to minimize the performance index, and the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft are the constraint conditions of this optimization problem.

[0162] 5) Construct a flight trajectory equation represented by a polynomial.

[0163] In the embodiments of the present invention, an nth-order polynomial is used to construct a flight trajectory equation, and the order of this equation is determined by n + 1 parameters a i where \(i = 0,\cdots,n\). The trajectory equation in the continuous form of the nth-order polynomial is as follows:

[0164]

[0165] In a specific embodiment of the present invention, \(n = 4\) is selected. The trajectory equation constructed by this method has the property of differential flatness, and its expression is as follows:

[0166]

[0167] where \(x\) and \(y\) represent the horizontal and vertical coordinates of any point on the trajectory. The \(y\) on the left side of the equation, and are the 0th, 1st, and 2nd derivatives of \(y\) with respect to \(x\) respectively. \(x i represents the \(i\)th power of \(x\).

[0168] Let the parameters \(x\) and \(y\) be the flat outputs, \(r\) be the instantaneous curvature radius of the flight trajectory, and \(K\) be the instantaneous curvature of the flight trajectory. Then the lateral overload \(N\) can be expressed by the derivatives of \(y\):

[0169]

[0170] It can be seen that from the perspective of control, the input control quantity and state quantity of the system can be uniquely determined by the flat output and its derivatives, the trajectory shape is smooth, and there is no sudden change in overload.

[0171] 6) Transform the endpoint constraints.

[0172] In this embodiment, by combining the equality constraint shown in Equation (3) and the trajectory equation shown in Equation (10), the endpoint constraints of the aircraft trajectory planning in Equation (3) can be transformed into the following form:

[0173]

[0174] where \(l\) is the distance between the initial position and the target position. In a specific embodiment of the present invention, \(l = 100\ km\),

[0175] In a specific embodiment of the present invention, at the cost of the first four degrees of freedom \(a_0\sim a_3\) of the fixed trajectory equation (10), four equality constraints shown in Equation (3) are eliminated. Substituting Equation (12) into Equation (9), the first two parameters \(a_0\) and \(a_1\) of the flight trajectory equation can be determined, and the expressions of the third and fourth parameters \(a_2\) and \(a_3\) can be derived:

[0176]

[0177] 7) Discretization of the flight trajectory equation.

[0178] In this embodiment, the trajectory is discretized at equal intervals in the x-axis direction. k discrete points are evenly taken on x ∈ [0, l], and the abscissa of the j-th discrete point is The ordinate corresponding to this abscissa of the discrete point on the trajectory is y j , then the j-th trajectory discrete point is (x j , y j ); After discretization, the flight trajectory equation can be expressed as follows:

[0179]

[0180] After substituting the specific implementation parameter n = 4, the expression of the discretized flight trajectory equation is as follows:

[0181]

[0182] Among them, the value of k can be selected according to the trajectory planning distance. The more points are taken, the better the trajectory optimization effect. However, correspondingly, the calculation time will also increase. It is recommended that the value range of k is between 50 and 200. In a specific embodiment of the present invention, k = 100 is selected.

[0183] 8) Transformation of the obstacle avoidance constraint.

[0184] After discretizing the flight trajectory equation, the obstacle avoidance constraint formula (4) during the flight of the aircraft can be expressed in the following form:

[0185]

[0186] Among them, D j,m is the distance between the m-th no-fly zone and the j-th discrete point.

[0187] For the convenience of optimal solution, the obstacle avoidance constraint is transformed into the form of a penalty function (obstacle avoidance performance function) and added to the comprehensive performance index function. According to formula (4), an instantaneous obstacle avoidance piecewise penalty function for a single no-fly zone is designed. Let ω Z be the obstacle avoidance weighting coefficient, and p be the penalty parameter (the value of the penalty parameter is determined according to the scenario requirements). Then for the m-th no-fly zone:

[0188]

[0189] Φ Z (x j , a4) is the obstacle avoidance performance penalty function of the j-th discrete point.

[0190] Among them, in a specific embodiment of the present invention, the parameter ω z = 5.36×10 -4 .

[0191] It should be noted that the penalty function in this embodiment is not designed completely according to the physical meaning of the distance, but the square root term in the penalty function is eliminated by squaring. This operation is beneficial to the subsequent derivative calculation and does not affect the obtaining of the optimal solution. The final constructed obstacle avoidance performance index function can be expressed as:

[0192]

[0193] Incorporating the obstacle avoidance performance index function composed of the penalty function into the comprehensive performance index function, the updated expression of the comprehensive performance index is as follows:

[0194] J total = ω Z J Z + ω T J T + ω N J N (19)

[0195] Among them, ω Z is the weight corresponding to the obstacle avoidance performance index function.

[0196] In this embodiment, Figure 2 is a schematic diagram of the obstacle avoidance performance index function before simplification in a specific embodiment of the present invention, Figure 3 is a schematic diagram of the obstacle avoidance performance index function after simplification in a specific embodiment of the present invention. The abscissa of both figures is the value of parameter a4, Figure 2 the ordinate of Figure 3 is the function value of the obstacle avoidance performance index before simplification corresponding to different values of parameter a4;

[0197] From the comparison of the trend charts of the obstacle avoidance performance index before and after simplification ( Figure 2 , Figure 3 ), it can be seen that such simplification does not change the overall change trend of the obstacle avoidance performance index function, so the simplification is effective.

[0198] 9) Simplify the time performance index function and the overload integral performance index function. The specific steps are as follows:

[0199] 9-1) Simplify the time performance index function;

[0200] In this embodiment, substituting the discrete flight trajectory equation (15) into the time performance index function in Equation (5) gives:

[0201]

[0202] Among them, Δx is the length of each discrete segment on the x-axis after discretization, and Δt is the time required to fly through this discrete segment.

[0203] In this embodiment, the square root is removed by squaring, and the constant term is ignored, and only the most important terms that affect the changing trend of the time performance function are retained. The expression of the simplified time performance index function is as follows:

[0204]

[0205] Figure 4 It is a schematic diagram of the time performance index function before simplification in a specific embodiment of the present invention. Figure 5 It is a schematic diagram of the time performance index function after simplification in a specific embodiment of the present invention. The abscissa of both figures is the value of parameter a4, Figure 4 and the ordinate is the function value of the time performance index before simplification corresponding to different values of parameter a4; Figure 5 and the ordinate is the function value of the time performance index after simplification corresponding to different values of parameter a4.

[0206] From the comparison of the trend graphs of the time performance index functions before and after simplification ( Figure 4 , Figure 5 ), it can be seen that such simplification will not change the overall changing trend of the time performance index function. Therefore, the simplification is effective.

[0207] 9-2) Simplification of the overload integral performance index function;

[0208] In this embodiment, for the overload integral performance index, since the speed of the aircraft is constant, the acceleration only has the tangential acceleration in the direction perpendicular to the speed direction, which only changes the speed direction and does not change the speed magnitude. After discretizing the polynomial trajectory equation (9), let the instantaneous curvature of the aircraft's flight trajectory corresponding to the jth trajectory discrete point be K j , that is, the curvature of the trajectory curve at the trajectory discrete point (x j , y j ). Then the instantaneous overload N j of the aircraft at this discrete trajectory point (x j , y j is:

[0209]

[0210] The overload square term is added to the overload function Φ N , and the meaning of Φ N is the square of the overload per unit time:

[0211]

[0212] For Φ N After performing weighted summation, the expression of the simplified overload integral performance index function is as follows:

[0213]

[0214] 10) By solving the gradient of the performance index, the optimization result of the obstacle avoidance trajectory is obtained.

[0215] After discretizing the polynomial trajectory equation (9) at equal intervals in the x-axis direction, for the performance index function formula (7) that was originally non-differentiable, using the property that "the order of derivative and summation operations can be interchanged", the respective gradients with respect to the parameter a i can be obtained, and finally substituted into the calculation to achieve higher calculation efficiency.

[0216] After eliminating the equality constraints, since a2 and a3 are expressed as linear combinations of a4, when taking partial derivatives, the parameters a2 and a3 need to be regarded as functions of a4 and included in the derivative process:

[0217]

[0218] According to Equation (18), J Z Taking the partial derivative of J with respect to each order of the parameter a4 gives:

[0219]

[0220] Where:

[0221]

[0222] According to Equation (21), J T Taking the partial derivative of J with respect to each order of the parameter a4 gives:

[0223]

[0224] Among them,

[0225]

[0226] According to Equation (24), J N Taking the partial derivative of J with respect to each order of the parameter a4 gives:

[0227]

[0228] Among them,

[0229]

[0230] Substitute the performance index functions (18), (21), and (24) to be solved and their analytical derivative formulas (26), (29), and (31) into the gradient descent algorithm for solution, and the undetermined parameter a4 can be quickly solved. Since there is ultimately only one optimization variable a4 in this optimization problem, substituting it into the polynomial trajectory equation (9) can obtain the optimal fly-around trajectory (the corresponding relationship between the horizontal and vertical coordinates of the aircraft), and the method for quickly generating the aircraft obstacle avoidance trajectory ends here.

[0231] In actual flight missions, after each dynamic iteration of the aircraft, its state changes (position, velocity, yaw angle, etc.). The trajectory planning method proposed in the present invention can be used to re-plan the trajectory once and calculate the corresponding current control quantity. By iterating in this way, the complete aircraft guidance process can be completed. Since the single planning speed of this method is fast, it can re-plan after each dynamic iteration to obtain the current optimal control quantity and achieve real-time planning.

[0232] Figure 6 It is a schematic diagram comparing the numerical calculation results and analytical calculation results of the gradient of the comprehensive performance index J in a specific embodiment of the present invention. Figure 6 In it, the abscissa is the value of the parameter a4, and the ordinate is the value of the gradient of the comprehensive performance index; the dark "x" marked line represents the analytical calculation result, and the light-colored thick dashed line represents the numerical calculation result. Figure 7 It is a schematic diagram of the error between the numerical calculation gradient and the analytical calculation gradient of the comprehensive performance index J in a specific embodiment of the present invention. Figure 7 In it, the abscissa is the value of the parameter a4, and the ordinate is the error value between the analytical gradient and the numerical gradient of the comprehensive performance index. It can be seen that the analytical solution and the numerical solution provided by the present invention are very close, and the order of magnitude of the error is within an acceptable range.

[0233] Furthermore, adjust the combined weight of the objective function.

[0234] In this embodiment, when combining the obstacle avoidance performance index function, the time objective function, and the overload integral objective function, there is a problem of adjusting the combined weight. An embodiment of the present invention determines the combined weight of each index function in the comprehensive performance index expression by separately optimizing each index function and comparing the results.

[0235] Table 1 List of results of separately optimizing each objective function in an embodiment of the present invention

[0236] <![CDATA[a4]]> <![CDATA[J Z > <![CDATA[J T > <![CDATA[J N > <![CDATA[J total > <![CDATA[Only optimize J Z > <![CDATA[2.5564×10 -5 > 0 0.0087 0.0118 0.0205 <![CDATA[Only optimize J T > <![CDATA[-2.7590×10 -6 > 0.2978 <![CDATA[4.4163×10 -5 > <![CDATA[1.1488×10 -3 > 0.2990 <![CDATA[Only optimize J N > <![CDATA[-3.3107×10 -7 > 0.4128 <![CDATA[1.0768×10 -4 > <![CDATA[3.6052×10 -4 > 0.4131 <![CDATA[Optimized combination J total > <![CDATA[1.0645×10 -6 > <![CDATA[4.1227×10 -6 > <![CDATA[2.0169×10 -4 > <![CDATA[5.3691×10 -4 > <![CDATA[7.4272×10 -4 >

[0237] In a specific embodiment of the present invention, after comparison and adjustment, the final determined weight is:

[0238] ω Z = 5.36×10 -4

[0239] ω T = 5.71×10 -6

[0240] ω N = 0.04

[0241] p = 1

[0242] Determine the initial value and substitute it into the optimization calculation.

[0243] Set the distance between the starting point and the ending point to 100 km, the speed of the aircraft to 1 km / s, and take 100 equally spaced discrete points between the starting point and the ending point for calculation. Optimize the trajectory equation with one degree of freedom (the parameter with the largest subscript is a4, and there are a total of 5 parameters). Select the gradient descent learning rate L = 2×10 -7 , the attenuation coefficient γ = 0.99, the center position of the no-fly zone is x = 40, y = 20, and the radius is 15, with the unit of km; the yaw angle at the starting point is The yaw angle at the ending point is The initial optimization value is 0, and the comparison of the calculation speed with the traditional method is as follows:

[0244] Table 2 Comparison table of a specific embodiment of the present invention using the method of the present invention and the traditional method

[0245] Algorithm BFGS quasi-Newton method Simplex method Analytical gradient descent method Computation time (s) 0.5837 0.0557 0.0325 Objective function value <![CDATA[1.9262×10 -3 > <![CDATA[2.4950×10 -3 > <![CDATA[1.9806×10 -3 > <![CDATA[a4]]> <![CDATA[2.0654×10 -6 > <![CDATA[2.8687×10 -6 > <![CDATA[2.1418×10 -6 >

[0246] Figure 8 and Figure 9 show the performance of the trajectory planning using the method of the present invention in two different required scenarios. The abscissa of the two graphs is the lateral flight distance, with the unit of kilometer (km), and the ordinate is the longitudinal flight distance, with the unit of kilometer (km). Figure 8 The scenario only requires the initial and final positions and angle constraints, Figure 9 The scenario additionally adds a circular no-fly zone on the basis of Figure 8 . It can be seen that the method of the present invention can well complete the trajectory planning tasks in both scenarios, and the single calculation time is very fast, about 0.02 s.

[0247] At the same time, since the objective function and its derivative of the optimization problem of the present invention are both in analytical form, the overall speed is improved compared with the traditional algorithm. Among them, the analytical gradient descent method uses its analytical derivative in addition to the analytical objective function, and the calculation speed is further improved, and there is also a certain advantage in the optimization result. Experiments prove that the present invention is very suitable for quickly solving the problem of generating the obstacle avoidance trajectory of the aircraft.

[0248] To implement the above embodiment, the second aspect embodiment of the present invention proposes a device for quickly generating an obstacle avoidance trajectory of an aircraft, including:

[0249] A kinematics and dynamics model construction module for constructing a kinematic model and a dynamic model of an aircraft;

[0250] An obstacle avoidance trajectory optimization problem construction module for constructing an obstacle avoidance trajectory optimization problem of an aircraft according to the kinematic model and the dynamic model; the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft; the objective function of the optimization problem is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function;

[0251] An obstacle avoidance trajectory optimization module for converting the obstacle avoidance constraint into an obstacle avoidance performance index function in the form of a penalty function and adding it to the comprehensive performance index by constructing a flight trajectory equation represented by a polynomial; simplifying the time performance index function, the overload integral performance index function, and the obstacle avoidance performance index function respectively, and solving the optimization problem by iterative calculation of the analytical gradient to obtain the optimized result of the obstacle avoidance trajectory.

[0252] It should be noted that the foregoing explanation of the embodiments of a method for quickly generating an obstacle avoidance trajectory of an aircraft also applies to an apparatus for quickly generating an obstacle avoidance trajectory of an aircraft according to this embodiment, and will not be repeated here. An apparatus for quickly generating an obstacle avoidance trajectory of an aircraft according to an embodiment of the present invention constructs a kinematic model and a dynamic model of the aircraft; constructs an obstacle avoidance trajectory optimization problem of the aircraft according to the kinematic model and the dynamic model; the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft; the objective function of the optimization problem is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function; converts the obstacle avoidance constraint into an obstacle avoidance performance index function in the form of a penalty function and adds it to the comprehensive performance index by constructing a flight trajectory equation represented by a polynomial; simplifies the time performance index function, the overload integral performance index function, and the obstacle avoidance performance index function respectively, and solves the optimization problem by iterative calculation of the analytical gradient to obtain the optimized result of the obstacle avoidance trajectory. Thus, the complex obstacle avoidance trajectory planning problem can be transformed into an unconstrained and analytically solvable optimization problem, and the solution speed can be greatly improved under the condition of ensuring the obstacle avoidance effect and calculation accuracy, making real-time online trajectory planning possible.

[0253] To implement the above embodiments, a third aspect embodiment of the present invention proposes an electronic device, including:

[0254] At least one processor; and a memory communicatively connected to the at least one processor;

[0255] Among them, the memory stores instructions executable by the at least one processor, and the instructions are configured to execute the above-mentioned method for quickly generating an obstacle avoidance trajectory of an aircraft.

[0256] To implement the above embodiments, a fourth aspect embodiment of the present invention proposes a computer-readable storage medium storing computer instructions for causing a computer to execute the above-mentioned method for quickly generating an obstacle avoidance trajectory of an aircraft.

[0257] It should be noted that the computer-readable medium in the present disclosure may be a computer-readable signal medium, a computer-readable storage medium, or any combination of the two above. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, the computer-readable storage medium may be any tangible medium that contains or stores a program, which can be used by or in conjunction with an instruction execution system, apparatus, or device. In the present disclosure, the computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The computer-readable signal medium may also be any computer-readable medium other than the computer-readable storage medium, and the computer-readable signal medium may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted by any appropriate medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination of the above.

[0258] The above computer-readable medium may be included in the above electronic device; or it may exist separately without being assembled into the electronic device. The above computer-readable medium carries one or more programs, and when the one or more programs are executed by the electronic device, the electronic device executes the method for quickly generating an obstacle avoidance trajectory of the above embodiments.

[0259] Computer program code for performing the operations of the present disclosure may be written in one or more programming languages or combinations thereof. The programming languages include object-oriented programming languages such as Java, Smalltalk, C++, and also include conventional procedural programming languages such as the "C" language or similar programming languages. The program code may execute entirely on the user's computer, partially on the user's computer, execute as a stand-alone software package, execute partially on the user's computer and partially on a remote computer, or execute entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (for example, by connecting through the Internet using an Internet service provider).

[0260] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of this application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0261] In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be construed as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, "a plurality of" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0262] Any process or method description in the flowchart or described in other ways herein may be understood to represent a module, segment, or portion of code including one or more executable instructions for implementing a specific logical function or process. The scope of the preferred embodiments of this application includes additional implementations, where the functions may be executed in a manner that is not shown or discussed, including in a substantially simultaneous manner or in a reverse order according to the functions involved, which should be understood by those skilled in the art to which the embodiments of this application belong.

[0263] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a definite sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device), or used in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection portion with one or more wirings (electronic device), a portable computer diskette (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable media on which a program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or other appropriate processing as necessary, and then stored in a computer memory.

[0264] It should be understood that various parts of the present application can be implemented by hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0265] Those of ordinary skill in the art of this technology can understand that all or part of the steps carried by the methods of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiments.

[0266] In addition, each functional unit in various embodiments of the present application may be integrated into one processing module, may exist separately as individual physical units, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. When the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0267] The above-mentioned storage medium may be a read-only memory, a magnetic disk, an optical disc, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present application. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. A method for quickly generating an obstacle avoidance trajectory of an aircraft, characterized in that Including: Constructing the kinematic model and dynamic model of the aircraft; According to the kinematic model and the dynamic model, constructing an aircraft obstacle avoidance trajectory optimization problem; the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft; the objective function of the optimization problem is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function; By constructing a flight trajectory equation represented by a polynomial, transforming the obstacle avoidance constraint into an obstacle avoidance performance index function in the form of a penalty function and adding it to the comprehensive performance index; simplifying the time performance index function, the overload integral performance index function and the obstacle avoidance performance index function respectively, and solving the optimization problem by iterative calculation of the analytical gradient to obtain the optimization result of the obstacle avoidance trajectory; Among them, the expressions of the time performance index function and the overload integral performance index function are as follows: Among them, J T and J N are the time performance index function and the overload integral performance index function respectively, representing the completion time of the entire planned trajectory and the total overload consumed by the aircraft during the process of completing the planned trajectory; N f is the overload of the aircraft when it reaches the target position; t f is the planned end time; v is the constant speed of the aircraft, θ is the yaw angle, the abscissa of the real-time position of the aircraft is x, and the acceleration is a c ; g is the acceleration due to gravity; N is the lateral overload of the aircraft; The expressions of time T and overload N are respectively as follows: Then the comprehensive performance index J total The expression is as follows: J total = ω T J T + ω N J N (7) Among them, ω T is the weighting coefficient corresponding to J T , ω N is the weighting coefficient corresponding to J N , ω T and ω N are both greater than 0.

2. The method according to claim 1, characterized in that The expression of the kinematic model is as follows: Wherein, v is the constant speed of the aircraft, θ is the yaw angle, the abscissa of the real-time position of the aircraft is x, the ordinate is y, and the acceleration is a c ; and are respectively the derivative of the abscissa of the real-time position of the aircraft with respect to time, the derivative of the ordinate of the real-time position of the aircraft with respect to time, and the derivative of the yaw angle of the real-time position of the aircraft with respect to time; the reference coordinate system of the kinematic model is a follow-up coordinate system, the X-axis of the follow-up coordinate system points from the initial position of the trajectory planning to the target position, the Y-axis of the follow-up coordinate system changes with the position of the aircraft so that the current position of the aircraft is always on the Y-axis, and the initial origin of the follow-up coordinate system is the initial position of the trajectory planning; The expression of the dynamic model is as follows: a c = Ng (2) Among them, N is the lateral overload of the aircraft, and g is the acceleration due to gravity.

3. The method according to claim 2, characterized in that, The endpoint constraint of the aircraft trajectory planning is expressed as follows: Among them, (x0, y0) are the coordinates of the initial position of the aircraft trajectory planning, where x0 and y0 respectively represent the horizontal and vertical coordinate values of the initial position; (x f , y f ) are the coordinates of the target position, where x f and y f respectively represent the horizontal and vertical coordinate values of the target position, θ0 is the yaw angle of the aircraft at the initial position, θ f is the yaw angle of the aircraft when it reaches the target position, t0 is the starting time of the planning, and t f is the ending time of the planning; The obstacle avoidance constraint expression during the flight of the aircraft is as follows: Among them, C m =(x z,m , y z,m ) is the center position of the m-th circular no-fly zone within the flight range of the aircraft, x z,m is the abscissa of the center of the m-th no-fly zone, y z,m is the ordinate of the center of the m-th no-fly zone, and the radius of the m-th no-fly zone is R m , m = 1, ..., N z , N z is the total number of no-fly zones.

4. The method according to claim 3, characterized in that The expression of the aircraft obstacle avoidance trajectory optimization problem is as follows:

5. The method according to claim 4, characterized in that The method further includes: 1) Constructing a flight trajectory equation represented by an nth-order polynomial; where a i is a parameter, and i = 0...n; Let n = 4, then Equation (9) is transformed into the following form: where y on the left side of the equation, and are the 0th, 1st, and 2nd derivatives of y with respect to x respectively, and x i represents the i-th power of x; Let the parameters x and y be the flat outputs, r be the instantaneous curvature radius of the flight trajectory, K be the instantaneous curvature of the flight trajectory, then the lateral overload N is represented by the derivatives of each order of y: 2) Transforming the endpoint constraints of the aircraft trajectory planning; Using the trajectory equation shown in Equation (10), transforming the endpoint constraints of the aircraft trajectory planning in Equation (3) into the following form: Among them, l is the distance between the initial position and the target position; At the cost of the first four degrees of freedom a0~a3 of the fixed trajectory equation (10), eliminating the four equality constraints shown in Equation (3); substituting Equation (12) into Equation (9), determining the parameters a0 and a1, and obtaining the expressions of a2 and a3: 3) Discretizing the flight trajectory equation; Discretize the trajectory at equal intervals in the x-axis direction. Uniformly take k discrete points on x ∈ [0, l]. The abscissa of the j-th discrete point is The ordinate corresponding to the abscissa of this discrete point on the trajectory is y j , then the j-th discrete point of the trajectory is (x j , y j ); The equation of the flight trajectory after discretization is expressed as follows: When n = 4, the expression of the discretized flight trajectory equation is as follows: 4) Transforming the obstacle avoidance constraint; After discretizing the flight trajectory equation, the obstacle avoidance constraint equation (4) during the flight of the aircraft is transformed into the following form: Among them, D j,m is the distance between the m-th no-fly zone and the j-th discrete point; Establish an instantaneous obstacle avoidance piecewise penalty function for a single no-fly zone according to Equation (4). Let ω Z be the obstacle avoidance weighting coefficient and p be the penalty parameter. Then, for the m-th no-fly zone: Φ Z (x j , a4) is the obstacle avoidance performance penalty function for the j-th discrete point; Then construct the obstacle avoidance performance index function as follows: Incorporating the obstacle avoidance performance index function composed of the penalty function into the comprehensive performance index function, and obtaining the updated expression of the comprehensive performance index as follows: J total = ω Z J Z + ω T J T + ω N J N (19) Among them, ω Z is the weight corresponding to the obstacle avoidance performance index function; 5) Simplifying the time performance index function and the overload integral performance index function, the specific steps are as follows: 5-1) Simplifying the time performance index function; Substituting the discretized flight trajectory equation (15) into the time performance index function in Equation (5), we get: Among them, Δx is the length of each discrete segment on the x-axis after discretization, and Δt is the time required to fly through this discrete segment; The expression of the simplified time performance index function is obtained as follows: 5-2) Simplifying the overload integral performance index function; Let the instantaneous curvature of the flight trajectory of the aircraft corresponding to the j-th discrete point be K j , then the instantaneous overload N j ,y j ) of the aircraft at this discrete trajectory point (x j is: Add the overload square term to the overload function Φ N , Φ N represents the square of the overload per unit time: For Φ N After performing weighted summation, the expression of the simplified overload integral performance index function is as follows: 6) By solving the gradient of the performance index, the optimization result of the obstacle avoidance trajectory is obtained; regarding parameters a2 and a3 as functions of a4 for derivation: According to Equation (18), J Z Taking the partial derivative with respect to each order parameter a4 gives: Where: According to Equation (21), J T Taking the partial derivative of each order parameter a4 gives: Among them, According to Equation (24), J N Taking the partial derivative with respect to the parameters a4 of each order gives: Among them, Substitute the solved performance index function formulas (18), (21), and (24) and their analytical derivative formulas (26), (29), and (31) into the gradient descent algorithm to solve for parameter a4; Substitute a4 into formula (9) to obtain the optimal fly-around trajectory of the aircraft.

6. An apparatus for quickly generating an obstacle avoidance trajectory of an aircraft, characterized in that, Including: A kinematic and dynamic model construction module for constructing the kinematic model and dynamic model of the aircraft; An obstacle avoidance trajectory optimization problem construction module for constructing an aircraft obstacle avoidance trajectory optimization problem according to the kinematic model and the dynamic model; the constraint conditions of the optimization problem are the endpoint constraints of the aircraft trajectory planning and the obstacle avoidance constraints during the flight of the aircraft; the objective function of the optimization problem is the minimization of the comprehensive performance index of the aircraft considering the time performance index function and the overload integral performance index function; An obstacle avoidance trajectory optimization module for converting the obstacle avoidance constraint into an obstacle avoidance performance index function in the form of a penalty function and adding it to the comprehensive performance index by constructing a flight trajectory equation represented by a polynomial; simplify the time performance index function, the overload integral performance index function, and the obstacle avoidance performance index function respectively, and solve the optimization problem by iterative calculation of the analytical gradient to obtain the optimization result of the obstacle avoidance trajectory; Among them, the expressions of the time performance index function and the overload integral performance index function are as follows: Among them, J T and J N are the time performance index function and the overload integral performance index function respectively, representing the completion time of the entire planned trajectory and the total overload consumed by the aircraft during the process of completing the planned trajectory; N f is the overload of the aircraft when it reaches the target position; t f is the planned end time; v is the constant speed of the aircraft, θ is the yaw angle, the abscissa of the real-time position of the aircraft is x, and the acceleration is a c ; g is the acceleration due to gravity; N is the lateral overload of the aircraft; The expressions of time T and overload N are respectively as follows: Then the comprehensive performance index J total The expression is as follows: J total = ω T J T + ω N J N (7) where, ω T is the weighting coefficient corresponding to J T , ω N is the weighting coefficient corresponding to J N , ω T and ω N are both greater than 0.

7. An electronic device, characterized in that, Including: At least one processor; And a memory communicatively connected to the at least one processor; Wherein, the memory stores instructions executable by the at least one processor, and the instructions are configured to execute the method according to any one of claims 1-5 above.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the method according to any one of claims 1-5.

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