A method for convex optimization of ascent trajectories under aircraft power failure conditions

Abstract

A convex optimization method for the ascent trajectory under dynamic failure conditions of an aircraft, belonging to the field of guidance and control technology, is proposed. This method designs a trajectory convex optimization solution process that adapts to different thrust failure magnitudes, using the aircraft's pitch and yaw angles as control variables and the aircraft's dynamic failure information, failure-time state variables, and target point trajectory information output by the onboard fault identification and navigation system as input variables. Based on an augmented objective function, a multi-stage sequential convex optimization switching condition is constructed, and replanning strategies, planning models, and corresponding convexification methods for different solution stages are given, achieving highly reliable solution of the aircraft trajectory under failure conditions. This method can adapt to the need for rapid replanning of the ascent trajectory under conditions of unknown terminal target reachability after a failure, improves the convergence of the sequential convex optimization solution process, and has a simple solution framework. It can provide a technical reference for convex optimization of high-speed aircraft trajectories with similar dynamic characteristics and flight profiles.

Description

Technical Field

[0001] This invention belongs to the field of guidance and control technology, and in particular relates to a convex optimization method for the ascent trajectory under the condition of aircraft power failure. Background Technology

[0002] During the ascent phase of a powered aircraft, thrust reduction or other propulsion system failures can occur, leading to partial or even complete loss of the aircraft's capabilities and mission failure, resulting in incalculable economic losses. Aircraft trajectory replanning technology is an effective means of mitigating the impact of malfunctions and achieving mission recovery by acquiring fault magnitude information online and adjusting flight commands. It has been researched and initially applied in some launch missions both domestically and internationally. This technology has enabled the onboard computer to promptly replan and generate a new flight trajectory after a malfunction, and by adjusting the operating time / commands of each engine stage, the launch mission was largely completed, effectively reducing the losses caused by the malfunction.

[0003] Highly real-time trajectory replanning algorithms are crucial for online mission recovery of aircraft under fault conditions. Current research on related algorithms mainly falls into two categories: offline trajectory design and online trajectory optimization. Offline design methods pre-consider the possible types and magnitudes of faults before launch and provide corresponding response strategies and emergency trajectories. However, these methods involve significant offline preparation work, lack adaptability to online random faults and combinations of different initial positions and terminal targets, and the trajectory results lack optimality, making it difficult to guarantee a reasonable trajectory online. Online trajectory optimization methods can quickly obtain trajectories with optimal performance indicators, fully utilizing the aircraft's capabilities and maximizing the achievement of the original orbital insertion mission, making it a current research hotspot. However, the reachability of the terminal target is unknown after an aircraft fault, making it difficult to guarantee a fast and reliable solution to the original problem. Furthermore, existing trajectory optimization methods generally require good initial value references; the combined effect of coarse initial trajectory values ​​and complex and stringent constraints during the ascent phase can also lead to difficulty in convergence or even solution failure.

[0004] In summary, traditional trajectory replanning methods for the ascent phase of powered aircraft have certain shortcomings in terms of real-time performance, reliability, and optimality under conditions such as unknown terminal target reachability, uncertain fault magnitude and initial conditions, and stringent and complex constraints. They are difficult to effectively adapt to increasingly complex aircraft fault conditions. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of trajectory replanning during the ascent phase of an aircraft under power system failure conditions such as thrust reduction, and to provide a convex optimization method for the ascent phase trajectory under such conditions. This method can be widely applied to trajectory planning for various types of aircraft during the active phase and orbit insertion phase, as well as trajectory planning for high-speed aircraft with similar flight profiles.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A convex optimization method for the ascent trajectory under aircraft power failure conditions, the method being:

[0008] Step 1: After the aircraft experiences a thrust reduction failure, the airborne fault identification and navigation measurement system starts working, outputting the magnitude of the thrust reduction κ, as well as the aircraft's position vector R0 and velocity vector V0 in the launch inertial frame, to the guidance system for trajectory replanning.

[0009] Step 2: Combine with the original target point position R f and velocity vector V f We directly construct a trajectory replanning problem model P0 under fault conditions in the launch inertial frame, and then use a two-stage sequential convex programming method to solve P0, then proceed to step three.

[0010] Step 3: In the first stage, a virtual control variable ν is introduced to relax the terminal constraints and dynamic constraints of problem P0 in order to improve the solvability of the problem;

[0011] Step 4: In the reference trajectory X * Linearize the problem model after relaxing the constraints in the vicinity to obtain the convex optimization subproblem model P1;

[0012] Step 5: Solve the convex optimization subproblem model P1 based on the interior point method, and determine the switching condition λ=|-(J k -J k-1 ) / (J k -1 -J k-2 Does -1|≤ε hold true? In the formula, J is the objective function value; the superscript k indicates the k-th iteration; ε is a constant; if not, then update the reference trajectory X. * Proceed to step four; if true, proceed to step six.

[0013] Step Six: Remove the virtual control quantity ν of the dynamic constraints from the problem model P1, introduce the trust region constraint adjustment coefficient η, and add it as a penalty function to the objective function J. Continue the sequential iterative solution. After the solution process converges, determine whether the terminal state quantity meets the accuracy requirements. If it does, the solution is successful and the optimal trajectory result is output. If it does not meet the requirements, proceed to Step Seven.

[0014] Step 7: Transform the solution model to the orbital coordinate system, relax the orbital element constraints, and prioritize ensuring the target orbital height h. * We construct the subproblem model P2 of the convex optimization problem;

[0015] Step 8: Solve the subproblem model P2 of the convex optimization problem through sequential iteration. If the solution process converges, output the trajectory result and the solution ends; if the solution fails, proceed to step 9.

[0016] Step 9: Reduce the target orbital altitude h * Solve for h * For the convex optimization subproblem of the terminal objective, if there is no solution, repeat step nine; if the convergence condition ||XX is satisfied... * If ||≤ε, proceed to step ten; X is the variable to be optimized.

[0017] Step 10: Trajectory replanning successful, output the replanned reference trajectory X. * and control sequence U * .

[0018] The advantages of this invention over the prior art are as follows:

[0019] This invention designs a trajectory convex optimization solution process that adapts to different thrust fault magnitudes, using aircraft pitch and yaw angles as control variables and aircraft power fault information, fault moment state variables, and target point trajectory information output by the airborne fault identification and navigation system as input variables. Based on the augmented objective function, a multi-stage sequential convex optimization switching condition is constructed, and replanning strategies, planning models, and corresponding convexification methods for different solution stages are presented, achieving highly reliable solution of aircraft trajectory under fault conditions.

[0020] The method proposed in this invention can adapt to the need for rapid replanning of the ascent trajectory under the condition that the reachability of the terminal target is unknown after a failure. It can improve the convergence of the sequential convex optimization solution process, has a simple solution framework, and has engineering application potential. At the same time, it can provide technical reference for convex optimization of the trajectory of high-speed aircraft with similar dynamic characteristics and flight profiles. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the trajectory replanning strategy of the present invention;

[0022] Figure 2 This is a flowchart of the two-stage trajectory sequence convex optimization method of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Example 1

[0025] A convex optimization method for the ascent trajectory under aircraft power failure conditions, the method being:

[0026] Step 1: After the aircraft experiences a thrust reduction failure, the airborne fault identification and navigation measurement system starts working, outputting the magnitude of the thrust reduction κ, as well as the aircraft's position vector R0 and velocity vector V0 in the launch inertial frame, to the guidance system for trajectory replanning.

[0027] Step 2: Combine with the original target point position R f and velocity vector V f We directly construct a trajectory replanning problem model P0 under fault conditions in the launch inertial frame, and then use a two-stage sequential convex programming method to solve P0, then proceed to step three.

[0028] Step 3: In the first stage, a virtual control variable ν is introduced to relax the terminal constraints and dynamic constraints of problem P0 in order to improve the solvability of the problem;

[0029] Step 4: In the reference trajectory X * Linearize the problem model after relaxing the constraints in the vicinity to obtain the convex optimization subproblem model P1;

[0030] Step 5: Solve the convex optimization subproblem model P1 based on the interior point method, and determine the switching condition λ=|-(J k -J k-1 ) / (J k -1 -J k-2 Does -1|≤ε hold true? In the formula, J is the objective function value; the superscript k indicates the k-th iteration; ε is a constant; if not, then update the reference trajectory X. * Proceed to step four; if true, proceed to step six.

[0031] Step Six: Remove the virtual control quantity ν of the dynamic constraints from the problem model P1, introduce the trust region constraint adjustment coefficient η, and add it as a penalty function to the objective function J. Continue the sequential iterative solution. After the solution process converges, determine whether the terminal state quantity meets the accuracy requirements. If it does, the solution is successful and the optimal trajectory result is output. If it does not meet the requirements, proceed to Step Seven.

[0032] Step 7: Transform the solution model to the orbital coordinate system, relax the orbital element constraints, and prioritize ensuring the target orbital height h. * We construct the subproblem model P2 of the convex optimization problem;

[0033] Step 8: Solve the subproblem model P2 of the convex optimization problem through sequential iteration. If the solution process converges, output the trajectory result and the solution ends; if the solution fails, proceed to step 9.

[0034] Step 9: Reduce the target orbital altitude h * Solve for h * For the convex optimization subproblem of the terminal objective, if there is no solution, repeat step nine; if the convergence condition ||XX is satisfied... * If ||≤ε, then proceed to step ten;

[0035] Step 10: Trajectory replanning successful, output the replanned reference trajectory X. * and control sequence U * .

[0036] Furthermore, the specific steps of step two are as follows:

[0037] Step 1: Construct the mathematical model P0 after the aircraft malfunction:

[0038]

[0039] In the formula: x is the x-axis position component of the inertial frame; y is the y-axis position component of the inertial frame; z is the z-axis position component of the inertial frame; V x V represents the x-axis velocity component of the inertial frame; y V represents the y-axis velocity component of the inertial frame; z φ is the velocity component along the z-axis of the inertial frame; φ is the pitch angle; ψ is the yaw angle; T is the available thrust amplitude after thrust reduction; I sp R0 is the engine specific impulse; R0 is the Earth's average radius; r is the distance from the Earth's center; μ is the gravitational constant; g0 is the acceleration due to gravity; m is the mass of the spacecraft. Additionally,

[0040]

[0041] Step 2: Add boundary constraints to P0, where the initial state constraint x(t0) is:

[0042] x(t0)=[xyz V x V y V z m] T

[0043] The terminal constraints are:

[0044] x(t f )=[x f ,y f ,z f V xf V yf V zf ] T

[0045] Step 3: Add control constraints to P0. The control constraints must satisfy the following:

[0046]

[0047] In the formula, u x For the new control variable in the x-direction; u y For the new control variable in the y direction; u z For the new control variable in the z direction;

[0048] Step 4: Add terminal mass and minimum flight altitude constraints to P0:

[0049] m(t f )≥m f h safe ≤r(t f )-R0

[0050] Where: m f For the dry weight of the aircraft; h safe This is the minimum flight altitude, i.e., the safe rescue orbit altitude; r(t) f ) represents the distance between the terminal's center and the Earth's core; m(t) f () represents the terminal mass of the aircraft.

[0051] Furthermore, the specific steps of step three are as follows:

[0052] Step 1: Introduce virtual control variable v = [ρ, Δx] f ,Δy f ,Δz f ,ΔV xf ,ΔV yf ,ΔV zf ] T Where ρ is the dynamic relaxation term, and Δx f The terminal x-direction position relaxation term; Δy f The terminal position relaxation term in the y-direction; Δz f The terminal position relaxation term in the z-direction; ΔV xf For the terminal x-direction velocity relaxation term; ΔV yf The terminal velocity relaxation term in the y-direction; ΔV zf This is the relaxation term for the terminal velocity in the z-direction;

[0053] Step 2: Add the virtual control variable to the constraints:

[0054]

[0055] In the formula, f is the set of dynamic constraints;

[0056] Step 3: Add the constraint relaxation term to the objective function. The new objective function J1 is then:

[0057] J1=γ ρ ρ+γ x ||Δxf ||+γ y ||Δy f ||+γ z ||Δz f ||+γ vx |Δv xf ||+γ vy |Δv yf ||+γ vz ||Δv zf ||

[0058] In the formula, γ is the weighting coefficient; γ ρ γ represents the weighting coefficients of the dynamic relaxation term; x γ represents the weighting coefficient of the terminal x-direction position relaxation term; y γ represents the weight coefficient of the relaxation term for the terminal's y-direction position; z γ represents the weighting coefficient of the relaxation term in the z-direction of the terminal; vx γ represents the weighting coefficient of the terminal x-direction velocity relaxation term; vy γ represents the weighting coefficient of the terminal y-direction velocity relaxation term; vz The weight coefficients are the terminal z-direction velocity relaxation terms.

[0059] Furthermore, the specific steps of step four are as follows:

[0060] Step 1: In the reference trajectory X * Linearize the objective function and constraints in the vicinity:

[0061]

[0062] In the formula: X is the variable to be optimized; g(X) is the general form of the objective function and constraints; g(X) * () represents the objective function and constraint values ​​at the reference trajectory;

[0063] Step 2: Achieve lossless convexity transformation of the control quantity equality constraints through the following relaxation transformation:

[0064]

[0065] Step 3: Construct a convex optimization subproblem P1 with the minimum trajectory change as the performance metric:

[0066] min x,u J2 = J1 + ||XX * || 2

[0067] subject to

[0068] x(t0)=[x0,y0,z0,V x0V y0 V z0 [m0] T

[0069] ||x(t f )-[x f ,y f ,z f V xf V yf V zf ] T ||≤[Δx f ,Δy f ,Δz f ,ΔV xf ,ΔV yf ,ΔV zf ] T

[0070] ||u||≤Γ,Γ=1

[0071] In the formula: A(X) * B, where B is the Jacobian matrix of the right-hand side function of the dynamic constraint relative to the state and control variables, respectively; Ω (x * ) represents the linearization remainder; u = [u x ,u y ,u z ] T J2 is the objective function of problem P1.

[0072] Furthermore, the specific steps of step five are as follows:

[0073] The specific expression for the switching condition λ is:

[0074] λ=|-(J k -J k-1 ) / (J k-1 -J k-2 )-1|≤ε

[0075] In the formula: ε is a human-defined constant; J k The augmented performance index is calculated from the result of the k-th solution, and the calculation method is shown in the following formula:

[0076]

[0077] Where: h i (X) represents the degree of violation of the equality constraint; g i (X) represents the degree of violation of the inequality constraint; μ1 represents h i (X) corresponds to the weighting coefficient; μ2 is the weighting coefficient of g. i (X) corresponds to the weighting coefficient; N eN represents the number of equality constraints. ie denoted as the number of inequality constraints.

[0078] Furthermore, the specific steps of step six are as follows:

[0079] Removing the constraint relaxation term from P1 and introducing trust region constraints into the objective function, the updated second-stage solution model is as follows:

[0080] min x,u J2=η

[0081] subject to

[0082] x(t0)=[x0,y0,z0,V x0 V y0 V z0 [m0] T

[0083] x(t f )=[x f ,y f ,z f V xf V yf V zf ] T

[0084] ||u||≤Γ,Γ=1

[0085] ||XX * ||≤ηδ

[0086] In the formula: δ is the radius of the trust region.

[0087] Furthermore, the specific steps of step seven are as follows:

[0088] Step 1: Construct a simplified form of the terminal constraints in the orbital coordinate system, specifically including:

[0089] (1) Track plane constraints

[0090] z f =0,V zf =0

[0091] (2) Terminal speed constraint

[0092]

[0093] In the formula: The orbital velocity of the spacecraft as it moves in a circular path around the target orbit.

[0094] (3) Target circular orbit eccentricity constraint

[0095] x f V xf +y f V yf =0

[0096] Step 2: Construct a convex optimization solution model P2 in the orbital coordinate system of the entry point:

[0097] min x,u

[0098] subject to

[0099] X0 = [x0, y0, z0, V] x0 V y0 V z0 [m0] T

[0100] ||z f +V zf ||≤error1

[0101]

[0102]

[0103] |u|≤Γ,Γ=1

[0104] ||XX * ||≤ηδ

[0105] In the formula: error i (i = 1, 2, 3) represent the relaxation errors of the track surface constraint, terminal velocity constraint, and eccentricity constraint, respectively; C1 is the weight coefficient of the relaxation error term; C2 is the weight coefficient of the trust region constraint term; J3 is the objective function of problem P2.

[0106] Furthermore, the specific steps of step nine are as follows:

[0107] When the solution fails, update h as follows: * :

[0108] h * =h safe +α(h * -h safe )

[0109] Where: h * h is the target orbital altitude; α is the adaptive coefficient, and α∈(0,1); safe The minimum safest rescue track must be designed in advance.

[0110] The above provides a detailed description of the convex trajectory optimization method for the ascent phase under the condition of aircraft power failure. Specific examples have been used to illustrate the principle and implementation of the invention. The above description of the embodiments is only for the purpose of helping to understand the method and core idea of ​​the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

Claims

1. A method for convex optimization of an ascent trajectory under aircraft power failure conditions, characterized by: The method is as follows: Step one: after the aircraft thrust failure, the airborne fault identification and navigation measurement system starts to work, outputting the aircraft thrust reduction level , and the position vector and velocity vector of the aircraft in the launch inertial system to the guidance system for trajectory re-planning; Step two: combine the original target point position and velocity vector , directly build the trajectory re-planning problem model P0 under the failure condition in the launch inertial system, solve P0 by using two-stage sequential convex programming method, and go to step three; Step three: First stage, introduce virtual control variables Relax the terminal constraints, dynamics constraints of problem P0; Step four: Linearization of the problem model after constraint relaxation in the vicinity of the reference trajectory Step 4: Linearization of the problem model after constraint relaxation in the vicinity of the reference trajectory Step five: solve the convex optimization sub-problem model P1 based on the interior point method, judge whether the switching condition is established , in which, is the objective function value; the superscript represents the th iteration; is a constant; if not, update the reference trajectory , go to step four; if yes, go to step six; Step six: remove the virtual control variable of dynamics constraint from the problem model P1 , introduce the trust region constraint adjustment coefficient , and add it as a penalty function to the objective function , continue the sequential iteration solution, after the solution process converges, judge whether the terminal state variable meets the accuracy requirement, if it meets, the solution is successful, and the optimal trajectory result is output; if it does not meet, go to step seven; Step seven: convert the model to the orbital coordinate system, release the orbital element constraint, and give priority to ensuring the target orbital height , and a convex optimization problem sub-problem model P2 is constructed. Step 8: Solve the subproblem model P2 of the convex optimization problem through sequential iteration. If the solution process converges, output the trajectory result and the solution ends; if the solution fails, proceed to step 9. Step nine: reduce the target orbit altitude , solve the convex optimization subproblem with as the terminal target, if there is no solution, then loop step nine; if the convergence condition is met, then go to step ten; Step ten: trajectory re-planning success, output the re-planned reference trajectory and control quantity sequence .

2. The method of claim 1, wherein: The specific steps of step two are as follows: Step 1: Construct the mathematical model P0 after the aircraft malfunction: In the formula: Inertial frame Axis position components; Inertial frame Axis position components; Inertial frame Axis position components; Inertial frame Axis velocity components; Inertial frame Axis velocity components; Inertial frame Axis velocity components; The pitch angle; Yaw angle; This represents the available thrust amplitude after the thrust decreases. For engine specific impulse; The average radius of the Earth; It is the distance from the Earth's center; It is the gravitational constant; It is the acceleration due to gravity; In addition to the mass of the aircraft, ； Step 2: Add the boundary value constraints in P0, where the initial state constraints are x0= 0, y0= 0. Terminal constraints are: Step 3: Add control constraints to P0. The control constraints must satisfy the following: In the formula, is a new control amount of direction; is a new control amount of direction; is a new control amount of direction; Step 4: Add terminal mass and minimum flight altitude constraints to P0: wherein: is the dry mass of the vehicle; is the minimum flight altitude, i.e. the safe rescue orbit altitude; is the terminal geodetic distance; is the terminal mass of the vehicle.

3. The method for convex trajectory optimization during the ascent phase under aircraft power failure conditions according to claim 1, characterized in that: The specific steps of step three are as follows: Step 1: Introduce virtual control variables ,in, This is a dynamic relaxation term. For the terminal Orientation and position relaxation terms; For the terminal Orientation and position relaxation terms; For the terminal Orientation and position relaxation terms; For the terminal Directional velocity relaxation term; For the terminal Directional velocity relaxation term; For the terminal Directional velocity relaxation term; Step 2: Add the virtual control variable to the constraints: In the formula, A set of dynamic constraints; Step 3: Add the constraint relaxation term to the objective function, then the new objective function... for: In the formula, These are weighting coefficients; These are the weighting coefficients for the dynamic relaxation term; For the terminal Weight coefficients of the directional and positional relaxation term; For the terminal Weight coefficients of the directional and positional relaxation term; For the terminal Weight coefficients of the directional and positional relaxation term; For the terminal Weight coefficients of the directional velocity relaxation term; For the terminal Weight coefficients of the directional velocity relaxation term; For the terminal The weighting coefficients of the directional velocity relaxation term.

4. The method for convex trajectory optimization during the ascent phase of an aircraft under power failure conditions according to claim 1, characterized in that: The specific steps of step four are as follows: Step 1: In the reference trajectory Linearize the objective function and constraints in the vicinity: In the formula: The variable to be optimized; This is the general form of the objective function and constraints; The objective function and constraint values ​​at the reference trajectory; Step 2: Achieve lossless convexity transformation of the control quantity equality constraints through the following relaxation transformation: Step 3: Construct a convex optimization subproblem P1 with the minimum trajectory change as the performance metric: In the formula: A , These are the Jacobian matrices of the right-hand side functions of the dynamic constraints relative to the state variables and control variables, respectively. For linearizing the remainder term; ; Let be the objective function of problem P1.

5. The method for convex optimization of the ascent trajectory under dynamic failure conditions of an aircraft according to claim 1, characterized in that: The specific steps of step five are as follows: Switching conditions The specific expression is: In the formula: A constant set by humans; For the first The augmented performance index obtained from the solution is calculated using the following formula: In the formula: The degree of violation of equality constraints; The degree to which the inequality constraints are violated; for The corresponding weighting coefficients; for The corresponding weighting coefficients; The number of equality constraints; denoted as the number of inequality constraints.

6. The method for convex optimization of the ascent trajectory under dynamic failure conditions of an aircraft according to claim 1, characterized in that: The specific steps of step six are as follows: Removing the constraint relaxation term from P1 and introducing trust region constraints into the objective function, the updated second-stage solution model is as follows: In the formula: Let be the radius of the trust region.

7. The method for convex optimization of the ascent trajectory under dynamic failure conditions of an aircraft according to claim 1, characterized in that: The specific steps of step seven are as follows: Step 1: Construct a simplified form of the terminal constraints in the orbital coordinate system, specifically including: (1) Track surface constraints (2) Terminal speed constraint In the formula: The orbital velocity of the aircraft when it performs circular motion in the target orbit; (3) Target circular orbit eccentricity constraint Step 2: Construct a convex optimization solution model P2 in the orbital coordinate system of the entry point: In the formula: These are the relaxation errors of the track surface constraint, terminal velocity constraint, and eccentricity constraint, respectively. These are the weighting coefficients for the relaxation error term; These are the weight coefficients for the trust region constraint terms; Let P2 be the objective function.

8. The method for convex trajectory optimization during the ascent phase of an aircraft under power failure conditions according to claim 1, characterized in that: The specific steps of step nine are as follows: When the solution fails, update as follows: : In the formula: The target orbital altitude; These are adaptive coefficients, and ; The minimum safest rescue track must be designed in advance.

Images