Spacecraft fixed time redirection control method based on quadratic programming

Abstract

The invention discloses a spacecraft fixed time redirection control method based on quadratic programming. The method comprises the following steps: (1) obtaining the current attitude and angular velocity of a spacecraft; (2) establishing a directional constraint spacecraft attitude redirection control problem; (3) designing a control obstacle function; (4) designing and controlling a Lyapunov function; (5) selecting a proper quadratic cost function, forming a quadratic programming problem in combination with the control Lyapunov function and the control barrier function, and solving the problem to obtain optimal control input meeting constraints; according to the method, on the premise of considering energy consumption, it can be guaranteed that the spacecraft is adjusted to the expected attitude within the preset fixed time.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft control technology, and in particular to a spacecraft fixed-time redirection control method based on quadratic programming. Background Art

[0002] Spacecraft attitude redirection is a crucial technical link in the field of aerospace engineering, which involves how to accurately adjust the spacecraft in a complex space environment to ensure that its payload or exploration equipment accurately points to the target or area of ​​interest. Since some optical sensors (such as infrared imagers, hyperspectral imagers, etc.) carried by spacecraft cannot point to areas with strong infrared radiation or visible light, otherwise these payloads will be damaged or their performance will be degraded. Therefore, the pointing prohibition constraint needs to be considered during the redirection process, that is, the photosensitive sensor element needs to be kept at a certain angle away from the sun.

[0003] The existing methods for handling redirection attitude control under pointing constraints can be divided into two categories: the first is the path planning method, which is to design a feasible trajectory that satisfies the state constraints in the state space, and then construct a suitable control strategy so that the attitude of the spacecraft can track the designed trajectory. This algorithm occupies a large amount of computing resources, and due to the existence of model uncertainty and external disturbances, the actual spacecraft often cannot accurately track the planned path. The other method is the potential function method, which first constructs a non-negative potential function containing attractive potential and repulsive potential, so that the value of the potential function is zero when the system state is in the desired attitude, and becomes infinite when the constraint is violated; then, the backstepping method, sliding mode control technology or optimal control are combined to design a suitable control law to solve the problem of spacecraft redirection control with pointing constraints. However, this method places too much emphasis on the processing capability of constraints, which often generates excessive control inputs, resulting in unnecessary energy consumption.

[0004] Common spacecraft attitude redirection control only considers how to meet the pointing constraints, ignoring the energy consumption during attitude adjustment. However, the energy carried by actual spacecraft is limited and precious. The above attitude redirection algorithm will inevitably increase energy consumption while meeting the specified constraints. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a spacecraft fixed-time redirection control method based on quadratic programming, which takes into account both control performance and energy consumption issues while satisfying pointing constraints.

[0006] Technical solution: The invention discloses a method for controlling a fixed-time redirection of a spacecraft based on quadratic programming, comprising the following steps:

[0007] (1) Obtain the current attitude and angular velocity of the spacecraft;

[0008] (2) Establish the description of the attitude redirection control problem of a spacecraft with pointing constraints: Use the Rodriguez parameter description method to establish the attitude dynamics equation of the spacecraft; mathematically describe the prohibited pointing constraint based on the geometric relationship between the luminous celestial body and the spacecraft;

[0009] (3) Design of control barrier function: Use the mathematical description of prohibition constraints to construct a safety set and a suitable control barrier function;

[0010] (4) Design of control Lyapunov function: construct a suitable sliding surface according to the current attitude and angular velocity of the spacecraft, and construct a suitable control Lyapunov function based on sliding mode dynamics to obtain the conditions that need to be met for the system to be stable in fixed time;

[0011] (5) Select a suitable quadratic cost function, combine it with the control Lyapunov function and the control barrier function, and form a quadratic programming problem. By solving this problem, the optimal control input that satisfies the constraints is obtained.

[0012] Furthermore, the formula of step (2) is as follows:

[0013] The spacecraft attitude dynamics model is expressed as

[0014]

[0015] in, is the modified Rodriguez parameter representation of the current attitude of the rigid spacecraft, is the angular velocity of the spacecraft expressed in the body coordinate system, is the spacecraft's moment of inertia, To control the torque.

[0016] Assume that the field of view of the optical sensitive instrument carried by the spacecraft is conical, and the direction of the central axis of the field of view of the i-th instrument is in the body coordinate system fixed to the spacecraft The projection under is b i , the attitude of the jth luminous object is prohibited from pointing to the inertial frame The projection under is n j ; then the prohibition pointing constraint can be described as

[0017]

[0018] Among them, the matrix is the current attitude of the spacecraft, which is expressed as

[0019]

[0020] Furthermore, the formula of step (3) is as follows:

[0021] Define a safe set as It is verified by calculation that this set is second order relative to the attitude dynamics, so the following function is introduced:

[0022]

[0023]

[0024] and the corresponding collection and Among them, α 1ij (·),α 2ij (·)for Class function; According to the definition of high-order barrier function, the control strategy ensures the existence of Class function α 1ij (·),α 2ij (·) makes it possible for the set All states on have ψ 2ij (σ,ω)30 holds, that is,

[0025]

[0026] Among them, L f ,L g are the Lie derivatives along the vector field f and g respectively. The expressions of the vector field f and g are:

[0027]

[0028] Then function b ij (σ) is a high-order barrier function with a relative order of 2, and the set It is forward invariant with respect to the spacecraft attitude dynamics. Is a safe set The fact that is a subset of , the control barrier function can ensure that the system satisfies the pointing prohibition constraint.

[0029] Furthermore, the sliding surface in step (4) is designed as

[0030] s=ω+α1σ||σ|| g-1 +α2β(σ)

[0031] in

[0032]

[0033] Among them, 0 <p<1,1<g<2,η ε is a small positive constant, and

[0034]

[0035] The constructed control Lyapunov function is

[0036]

[0037] By constraining the control Lyapunov function to meet the following conditions, the fixed time convergence of the system is guaranteed

[0038]

[0039] in, δ1 satisfies the inequality The real number, The preset convergence time.

[0040] Furthermore, the quadratic cost function in step (5) is selected as

[0041]

[0042] Where, u = [τ δ1 δ 2,j ] T ,

[0043]

[0044] Among them, κ1>0, κ 2,j >0 is the relaxation factor δ1 and δ 2,j The proportion of q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0; the control obstacle function and the control Lyapunov function constructed in step 3 and step 4 are used as constraints, and the attitude redirection control under the pointing constraint is transformed into the following quadratic programming problem:

[0045]

[0046] -λ≤τ≤λ

[0047]

[0048] Among them, the relaxation factors δ1,δ 2,j The introduction of is to ease the conflict between the control Lyapunov function constraint and the control barrier function, so as to ensure the feasibility of the quadratic programming problem. By solving the quadratic programming problem, the optimal control input that satisfies the pointing constraint and convergence time can be obtained.

[0049] The invention provides a spacecraft fixed-time redirection control system based on quadratic programming, comprising:

[0050] Acquisition module: used to obtain the current attitude and angular velocity of the spacecraft;

[0051] Constraint module: used to establish the attitude redirection control of spacecraft with pointing constraints. Problem description: Use Rodriguez parameter description method to establish the attitude dynamics equation of the spacecraft; mathematically describe the prohibited pointing constraints based on the geometric relationship between the luminous celestial body and the spacecraft;

[0052] Control barrier module: used to design control barrier function: construct safety set using mathematical description of prohibition constraints and construct appropriate control barrier function;

[0053] Lyapunov function module: used to design control Lyapunov function: construct a suitable sliding surface according to the current attitude and angular velocity of the spacecraft, construct a suitable control Lyapunov function based on sliding mode dynamics, and obtain the conditions that need to be met for the system to be stable in fixed time;

[0054] Quadratic cost function module: used to select a suitable quadratic cost function, combine the control Lyapunov function and the control obstacle function to form a quadratic programming problem, and obtain the optimal control input that meets the constraints by solving the problem.

[0055] Furthermore, in the constraint module, the formula is as follows:

[0056] The spacecraft attitude dynamics model is expressed as

[0057]

[0058] in, is the modified Rodriguez parameter representation of the current attitude of the rigid spacecraft, is the angular velocity of the spacecraft expressed in the body coordinate system, is the spacecraft's moment of inertia, To control the torque.

[0059] Assume that the field of view of the optical sensitive instrument carried by the spacecraft is conical, and the direction of the central axis of the field of view of the i-th instrument is in the body coordinate system fixed to the spacecraft The projection under is b i , the attitude of the jth luminous object is prohibited from pointing to the inertial frame The projection under is n j ; then the prohibition pointing constraint can be described as

[0060]

[0061] Among them, the matrix is the current attitude of the spacecraft, which is expressed as

[0062]

[0063] Furthermore, in the obstacle control module, the formula is as follows:

[0064] Define a safe set as It is verified by calculation that this set is second order relative to the attitude dynamics, so the following function is introduced:

[0065]

[0066] and the corresponding collection and Among them, α 1ij (·),α 2ij (·)for Class function; According to the definition of high-order barrier function, the control strategy ensures the existence of Class function α 1ij (·),α 2ij (·) makes it possible for the set All states on have ψ 2ij (σ,ω)≥0 holds, that is,

[0067]

[0068] Among them, L f ,L g are the Lie derivatives along the vector field f and g respectively. The expressions of the vector field f and g are:

[0069]

[0070] Then function b ij (σ) is a high-order barrier function with a relative order of 2, and the set It is forward invariant with respect to the spacecraft attitude dynamics. Is a safe set The fact that is a subset of , the control barrier function can ensure that the system satisfies the pointing prohibition constraint.

[0071] Furthermore, the sliding surface in the Lyapunov function module is designed as

[0072] s=ω+α1σ||σ|| g-1 +α2β(σ)

[0073] in

[0074]

[0075] Among them, 0 <p<1,1<g<2,η ε is a small positive constant, and

[0076]

[0077] The constructed control Lyapunov function is

[0078]

[0079] By constraining the control Lyapunov function to meet the following conditions, the fixed time convergence of the system is guaranteed

[0080]

[0081] in, δ1 satisfies the inequality The real number, The preset convergence time.

[0082] Furthermore, the quadratic cost function in the quadratic cost function module is selected as

[0083]

[0084] Where, u = [τ δ1 δ 2,j ] T ,

[0085]

[0086] Among them, κ1>0, κ 2,j >0 is the relaxation factor δ1 and δ 2,j The proportion of q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0; the control obstacle function and the control Lyapunov function constructed in step 3 and step 4 are used as constraints, and the attitude redirection control under the pointing constraint is transformed into the following quadratic programming problem:

[0087]

[0088] -λ≤τ≤λ

[0089]

[0090] Among them, the relaxation factors δ1,δ 2,j The introduction of is to ease the conflict between the control Lyapunov function constraint and the control barrier function, so as to ensure the feasibility of the quadratic programming problem. By solving the quadratic programming problem, the optimal control input that satisfies the pointing constraint and convergence time can be obtained.

[0091] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) The attitude redirection control algorithm designed by the present invention can ensure that the spacecraft is adjusted to the desired attitude within a preset fixed time under the premise of considering energy consumption; (2) The present invention introduces a control obstacle function to ensure that the spacecraft will not violate the attitude pointing constraint during the attitude adjustment process, and uses it together with the control Lyapunov function as a constraint condition for the quadratic programming problem, balancing the contradiction between control performance, energy and computing resource consumption. (3) The introduction of the relaxation factor alleviates the conflict between the control Lyapunov function constraint and the control obstacle function, ensuring the feasibility of the quadratic programming problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a flow chart of the present invention;

[0093] Figure 2 is the geometric relationship between the luminous celestial body and the spacecraft of the present invention;

[0094] Figure 3 is the pointing constraint of the spacecraft attitude of the present invention;

[0095] Figure 4 is the convergence curve of the sliding mode variable s of the present invention;

[0096] Figure 5 is a response curve of the attitude of the spacecraft of the present invention changing with time;

[0097] Figure 6 is a response curve of the spacecraft angular velocity changing with time according to the present invention;

[0098] Figure 7 is a curve showing the change of the required control torque over time of the present invention; DETAILED DESCRIPTION

[0099] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0100] like Figure 1 As shown, an embodiment of the present invention provides a spacecraft fixed-time redirection control method based on quadratic programming, comprising the following steps:

[0101] (1) Obtain the current attitude and angular velocity of the spacecraft;

[0102] (2) Establish the description of the attitude redirection control problem of a spacecraft with pointing constraints: Use the Rodriguez parameter description method to establish the attitude dynamics equation of the spacecraft; mathematically describe the prohibited pointing constraint based on the geometric relationship between the luminous celestial body and the spacecraft; the formula is as follows:

[0103] The spacecraft attitude dynamics model is expressed as

[0104]

[0105] in, is the modified Rodriguez parameter representation of the current attitude of the rigid spacecraft, is the angular velocity of the spacecraft expressed in the body coordinate system, is the spacecraft's moment of inertia, To control the torque.

[0106] Assume that the field of view of the optical sensitive instrument carried by the spacecraft is conical, and the direction of the central axis of the field of view of the i-th instrument is in the body coordinate system fixed to the spacecraft The projection under is b i , the attitude of the jth luminous object is prohibited from pointing to the inertial frame The projection under is n j ; then the prohibition pointing constraint can be described as

[0107]

[0108] Among them, the matrix is the current attitude of the spacecraft, which is expressed as

[0109]

[0110] (3) Design of control barrier function: Use the mathematical description of the prohibition constraint to construct a safety set and a suitable control barrier function; the formula is as follows:

[0111] Define a safe set as It is verified by calculation that this set is second order relative to the attitude dynamics, so the following function is introduced:

[0112]

[0113] and the corresponding collection and Among them, α 1ij (·),α 2ij (·)for Class function; According to the definition of high-order barrier function, the control strategy ensures the existence of Class function α 1ij (·),α 2ij (·) makes it possible for the set All states on have ψ 2ij (σ,ω)30 holds, that is,

[0114]

[0115] Among them, L f ,Lg are the Lie derivatives along the vector field f and g respectively. The expressions of the vector field f and g are:

[0116]

[0117] Then function b ij (σ) is a high-order barrier function with a relative order of 2, and the set It is forward invariant with respect to the spacecraft attitude dynamics. Is a safe set The fact that is a subset of , the control barrier function can ensure that the system satisfies the pointing prohibition constraint.

[0118] (4) Design of control Lyapunov function: According to the current attitude and angular velocity of the spacecraft, a suitable sliding surface is constructed. Based on the sliding mode dynamics, a suitable control Lyapunov function is constructed to obtain the conditions that the system needs to meet for fixed-time stability. The sliding surface is designed as

[0119] s=ω+α1σ||σ|| g-1 +α2β(σ)

[0120] in

[0121]

[0122] Among them, 0 <p<1,1<g<2,η ε is a small positive constant, and

[0123]

[0124] The constructed control Lyapunov function is

[0125]

[0126] By constraining the control Lyapunov function to meet the following conditions, the fixed time convergence of the system is guaranteed

[0127]

[0128] in, δ1 satisfies the inequality The real number, The preset convergence time.

[0129] (5) Select a suitable quadratic cost function, combine the control Lyapunov function and the control obstacle function to form a quadratic programming problem, and obtain the optimal control input that satisfies the constraints by solving the problem. The quadratic cost function is selected as

[0130]

[0131] Where, u = [τ δ1 δ 2,j ] T ,

[0132]

[0133] Among them, κ1>0, κ 2,j >0 is the relaxation factor δ1 and δ 2,j The proportion of q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0; the control obstacle function and the control Lyapunov function constructed in step 3 and step 4 are used as constraints, and the attitude redirection control under the pointing constraint is transformed into the following quadratic programming problem:

[0134]

[0135] -λ≤τ≤λ

[0136]

[0137] Among them, the relaxation factors δ1,δ 2,j The introduction of is to ease the conflict between the control Lyapunov function constraint and the control barrier function, so as to ensure the feasibility of the quadratic programming problem. By solving the quadratic programming problem, the optimal control input that satisfies the pointing constraint and convergence time can be obtained.

[0138] In order to verify that the spacecraft fixed-time attitude redirection control input based on quadratic programming proposed in this embodiment can ensure that the spacecraft can complete the redirection task within a fixed time under the condition of pointing constraints, a corresponding simulation verification is performed here. Consider the attitude redirection control problem of a spacecraft with an inertia matrix of J = [20, 1.2, 0.9; 1.2, 17, 1.4; 0.9, 1.4, 15]. The initial attitude and angular velocity of the spacecraft are σ(0) = [-0.2735 -0.2099 -0.0844] T and ω(0)=[0 0 0] T The spacecraft is equipped with a photosensitive sensor whose visual axis is aligned with the spacecraft body coordinate system. Alignment, that is, b1 = [0 0 1] T , the half-viewing angle θ is set to θ = 15°, and the direction of the luminous object to be avoided relative to the spacecraft is n1 = [-0.2310 0.4077 0.8834] T , n2=[-0.2750 0.0050 0.3250] T , n3=[-0.0864 0.75640.6484] T .

[0139] The controller parameters are selected as follows:

[0140]

[0141] Figure 3 b is the pointing constraint of the spacecraft attitude shown in the embodiment of the present invention ij ,It can be seen from the figure that during the redirection process, the ,spacecraft attitude never violates the pointing constraint. Figure 4 is the convergence curve of the defined sliding mode variable s. It can be seen that the sliding mode variable converges to the equilibrium point within the preset fixed time T. Figure 5 and 6 They are the response curves of the spacecraft's attitude and angular velocity changing with time. It can be seen from the figure that the attitude and angular velocity converge quickly to the origin along the sliding surface. Figure 7 This is the curve of the required control torque changing with time. It can be seen from the figure that its size is within the range of the maximum allowable control torque.

[0142] The embodiment of the present invention further provides a spacecraft fixed-time redirection control system based on quadratic programming, comprising:

[0143] Acquisition module: used to obtain the current attitude and angular velocity of the spacecraft;

[0144] Constraint module: used to establish the attitude redirection control of spacecraft with pointing constraints. Problem description: Use Rodriguez parameter description method to establish the attitude dynamics equation of the spacecraft; mathematically describe the prohibited pointing constraint based on the geometric relationship between the luminous celestial body and the spacecraft; the formula is as follows:

[0145] The spacecraft attitude dynamics model is expressed as

[0146]

[0147] in, is the modified Rodriguez parameter representation of the current attitude of the rigid spacecraft, is the angular velocity of the spacecraft expressed in the body coordinate system, is the spacecraft's moment of inertia, To control the torque.

[0148] Assume that the field of view of the optical sensitive instrument carried by the spacecraft is conical, and the direction of the central axis of the field of view of the i-th instrument is in the body coordinate system fixed to the spacecraft The projection under is b i , the attitude of the jth luminous object is prohibited from pointing to the inertial frame The projection under is n j ; then the prohibition pointing constraint can be described as

[0149]

[0150] Among them, the matrix is the current attitude of the spacecraft, which is expressed as

[0151]

[0152] Control barrier module: used to design control barrier function: construct safety set using mathematical description of prohibition constraints and construct appropriate control barrier function; the formula is as follows:

[0153] Define a safe set as It is verified by calculation that this set is second order relative to the attitude dynamics, so the following function is introduced:

[0154]

[0155] and the corresponding collection and Among them, α 1ij (·),α 2ij (·)for Class function; According to the definition of high-order barrier function, the control strategy ensures the existence of Class function α 1ij (·),α 2ij (·) makes it possible for the set All states on have ψ 2ij (σ,ω)≥0 holds, that is,

[0156]

[0157] Among them, L f ,L g are the Lie derivatives along the vector field f and g respectively. The expressions of the vector field f and g are:

[0158]

[0159] Then function b ij (σ) is a high-order barrier function with a relative order of 2, and the set It is forward invariant with respect to the spacecraft attitude dynamics. Is a safe set The fact that is a subset of , the control barrier function can ensure that the system satisfies the pointing prohibition constraint.

[0160] Lyapunov function module: used to design control Lyapunov function: construct a suitable sliding surface according to the current attitude and angular velocity of the spacecraft, construct a suitable control Lyapunov function based on sliding mode dynamics, and obtain the conditions that need to be met for the system to be stable in fixed time; the sliding surface is designed as

[0161] s=ω+α1σ||σ|| g-1 +α2β(σ)

[0162] in

[0163]

[0164] Among them, 0 <p<1,1<g<2,η ε is a small positive constant, and

[0165]

[0166] The constructed control Lyapunov function is

[0167]

[0168] By constraining the control Lyapunov function to meet the following conditions, the fixed time convergence of the system is guaranteed

[0169]

[0170] in, δ1 satisfies the inequality The real number, The preset convergence time.

[0171] Quadratic cost function module: used to select a suitable quadratic cost function, combined with the control Lyapunov function and the control obstacle function, to form a quadratic programming problem, and to obtain the optimal control input that satisfies the constraints by solving the problem. The quadratic cost function is selected as

[0172]

[0173] Where, u = [τ δ1 δ 2,j ] T ,

[0174]

[0175] Among them, κ1>0, κ 2,j >0 is the relaxation factor δ1 and δ 2,j The proportion of q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0; the control obstacle function and the control Lyapunov function constructed in step 3 and step 4 are used as constraints, and the attitude redirection control under the pointing constraint is transformed into the following quadratic programming problem:

[0176]

[0177] -λ≤τ≤λ

[0178]

[0179] Among them, the relaxation factors δ1,δ 2,j The introduction of is to ease the conflict between the control Lyapunov function constraint and the control barrier function, so as to ensure the feasibility of the quadratic programming problem. By solving the quadratic programming problem, the optimal control input that satisfies the pointing constraint and convergence time can be obtained.

Claims

1. A spacecraft fixed-time redirection control method based on quadratic programming, characterized in that: The following steps are involved: (1) Obtain the current attitude and angular velocity of the spacecraft; (2) Establish the description of the attitude redirection control problem of a spacecraft with pointing constraints: Use the Rodriguez parameter description method to establish the attitude dynamics equation of the spacecraft; mathematically describe the prohibited pointing constraint based on the geometric relationship between the luminous celestial body and the spacecraft; (3) Design of control barrier function: Use the mathematical description of prohibition constraints to construct a safety set and a suitable control barrier function; (4) Design of control Lyapunov function: construct a suitable sliding surface according to the current attitude and angular velocity of the spacecraft, and construct a suitable control Lyapunov function based on sliding mode dynamics to obtain the conditions that need to be met for the system to be stable in fixed time; (5) Select a suitable quadratic cost function, combine it with the control Lyapunov function and the control barrier function, and form a quadratic programming problem. By solving this problem, the optimal control input that satisfies the constraints is obtained.

2. The method for spacecraft fixed-time redirection control based on quadratic programming according to claim 1, characterized in that: The formula for step (2) is as follows: The spacecraft attitude dynamics model is expressed as in, is the modified Rodriguez parameter representation of the current attitude of the rigid spacecraft, is the angular velocity of the spacecraft expressed in the body coordinate system, is the spacecraft's moment of inertia, To control the torque. Assume that the direction of the central axis of the field of view of the i-th instrument is in the body coordinate system fixed to the spacecraft The projection under is b i , the attitude of the jth luminous object is prohibited from pointing to the inertial frame The projection under is n j ; then the prohibition pointing constraint can be described as Among them, the matrix is the current attitude of the spacecraft, which is expressed as 3. The method for fixed-time redirection control of a spacecraft based on quadratic programming according to claim 1, characterized in that: The formula for step (3) is as follows: Define a safe set as It is verified by calculation that this set is second order relative to the attitude dynamics, so the following function is introduced: and the corresponding collection and Among them, α 1ij (·),α 2ij (·)for Class function; According to the definition of high-order barrier function, the control strategy ensures the existence of Class function α 1ij (·),α 2ij (·) makes it possible for the set All states on have ψ 2ij (σ,ω)≥0 holds, that is, Among them, L f ,L g are the Lie derivatives along the vector field f and g respectively. The expressions of the vector field f and g are: Then function b ij (σ) is a high-order barrier function with a relative order of 2, and the set It is forward invariant for the spacecraft attitude dynamics; combined with the set Is a safe set The fact that is a subset of , the control barrier function can ensure that the system satisfies the pointing prohibition constraint.

4. The method for fixed-time redirection control of a spacecraft based on quadratic programming according to claim 1, characterized in that: The sliding surface in step (4) is designed as s=ω+α1σ||σ|| g-1 +α2β(σ) in Among them, 0 <p<1,1<g<2,η ε is a small positive constant, and The constructed control Lyapunov function is By constraining the control Lyapunov function to meet the following conditions, the fixed time convergence of the system is guaranteed in, δ1 satisfies the inequality The real number, The preset convergence time.

5. The method for spacecraft fixed-time redirection control based on quadratic programming according to claim 1, characterized in that: The quadratic cost function in step (5) is chosen as Where, u=[τ δ1 δ 2,j ] T , Among them, κ1>0, κ 2,j >0 is the relaxation factor δ1 and δ 2,j The proportion of q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0; the control obstacle function and control Lyapunov function constructed in step 3 and step 4 are used as constraints, and the attitude redirection control under the pointing constraint is transformed into the following quadratic programming problem: Among them, the relaxation factors δ1,δ 2,j The introduction of is to alleviate the conflict between the control Lyapunov function constraint and the control barrier function; by solving the quadratic programming problem, the optimal control input that satisfies the pointing constraint and convergence time can be obtained.

6. A spacecraft fixed-time redirection control system based on quadratic programming, characterized in that: include: Acquisition module: used to obtain the current attitude and angular velocity of the spacecraft; Constraint module: used to establish the attitude redirection control of spacecraft with pointing constraints. Problem description: Use Rodriguez parameter description method to establish the attitude dynamics equation of the spacecraft; mathematically describe the prohibited pointing constraints based on the geometric relationship between the luminous celestial body and the spacecraft; Control barrier module: used to design control barrier function: construct safety set using mathematical description of prohibition constraints and construct appropriate control barrier function; Lyapunov function module: used to design control Lyapunov function: construct a suitable sliding surface according to the current attitude and angular velocity of the spacecraft, construct a suitable control Lyapunov function based on sliding mode dynamics, and obtain the conditions that need to be met for the system to be stable in fixed time; Quadratic cost function module: used to select a suitable quadratic cost function, combine the control Lyapunov function and the control obstacle function to form a quadratic programming problem, and obtain the optimal control input that meets the constraints by solving the problem.

7. The spacecraft fixed-time redirection control system based on quadratic programming according to claim 6 is characterized in that: In the constraint module, the formula is as follows: The spacecraft attitude dynamics model is expressed as in, is the modified Rodriguez parameter representation of the current attitude of the rigid spacecraft, is the angular velocity of the spacecraft expressed in the body coordinate system, is the spacecraft's moment of inertia, To control the torque. Assume that the direction of the central axis of the field of view of the i-th instrument is in the body coordinate system fixed to the spacecraft The projection under is b i , the attitude of the jth luminous object is prohibited from pointing to the inertial frame The projection under is n j ; then the prohibition pointing constraint can be described as Among them, the matrix is the current attitude of the spacecraft, which is expressed as 8. The spacecraft fixed-time redirection control system based on quadratic programming according to claim 6, characterized in that: In the obstacle control module, the formula is as follows: Define a safe set as It is verified by calculation that this set is second order relative to the attitude dynamics, so the following function is introduced: and the corresponding collection and Among them, α 1ij (·),α 2ij (·)for Class function; According to the definition of high-order barrier function, the control strategy ensures the existence of Class function α 1ij (·),α 2ij (·) makes it possible for the set All states on Established, that is Among them, L f ,L g are the Lie derivatives along the vector field f and g respectively. The expressions of the vector field f and g are: Then function b ij (σ) is a high-order barrier function with a relative order of 2, and the set It is forward invariant for the spacecraft attitude dynamics; combined with the set Is a safe set The fact that is a subset of , the control barrier function can ensure that the system satisfies the pointing prohibition constraint.

9. The spacecraft fixed-time redirection control system based on quadratic programming according to claim 6, characterized in that: The sliding surface in the Lyapunov function module is designed as s=ω+α1σ||σ|| g-1 +α2β(σ) in Among them, 0 <p<1,1<g<2,η ε is a small positive constant, and The constructed control Lyapunov function is By constraining the control Lyapunov function to meet the following conditions, the fixed time convergence of the system is guaranteed in, δ1 satisfies the inequality The real number, The preset convergence time.

10. The spacecraft fixed-time redirection control system based on quadratic programming according to claim 6, characterized in that: The quadratic cost function in the quadratic cost function module is selected as Where, u=[τ δ1 δ 2,j ] T , Among them, κ1>0, κ 2,j >0 is the relaxation factor δ1 and δ 2,j The proportion of q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0; the control obstacle function and control Lyapunov function constructed in step 3 and step 4 are used as constraints, and the attitude redirection control under the pointing constraint is transformed into the following quadratic programming problem: Among them, the relaxation factors δ1,δ 2,j The introduction of is to alleviate the conflict between the control Lyapunov function constraint and the control barrier function; by solving the quadratic programming problem, the optimal control input that satisfies the pointing constraint and convergence time can be obtained.

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