Spacecraft fixed-time redirection control method based on quadratic programming
By designing control obstacle functions and Lyapunov functions based on quadratic programming, the problems of energy consumption and pointing constraints in spacecraft attitude reversal control are solved, and efficient attitude adjustment and energy optimization within a fixed time are achieved.
Patent Information
- Application Number
- CN202411575980.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-06
- Publication Date
- 2025-11-21
- Estimated Expiration
- 2044-11-06
AI Technical Summary
Existing spacecraft attitude reorientation control methods, while satisfying pointing constraints, neglect energy consumption, leading to increased energy consumption and potentially excessive control inputs.
By employing a quadratic programming approach, a suitable control strategy is constructed by designing control obstacle functions and Lyapunov functions, combined with sliding mode dynamics, to optimize energy consumption and control performance, ensuring that attitude adjustment is completed within a fixed time.
Under the condition of satisfying the pointing constraints, the attitude adjustment of the spacecraft within a fixed time period was realized, while the energy consumption and control input were optimized, reducing unnecessary energy consumption.
Smart Images
Figure CN119536339B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of spacecraft control, in particular to a spacecraft fixed-time reorientation control method based on quadratic programming. BACKGROUND
[0002] Spacecraft attitude reorientation is a crucial technical link in the field of space engineering, involving 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 and hyperspectral imagers) carried by the spacecraft cannot point to areas with strong infrared radiation or visible light, otherwise these loads will be damaged or performance will decrease, so the pointing constraint needs to be considered during reorientation, that is, the light-sensitive sensing element needs to be kept at a certain angle away from the sun.
[0003] The existing reorientation attitude control method under the pointing constraint is mainly divided into two categories: the first category is path planning method, which designs a feasible trajectory in the state space that satisfies the state constraint, and then constructs a suitable control strategy to make the spacecraft attitude track the designed trajectory. This algorithm occupies a large amount of computing resources, and due to model uncertainty and external disturbance, the actual spacecraft 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 at the desired attitude, and becomes infinite when the constraint is violated; then combine backstepping method, sliding mode control technology or optimal control to design a suitable control law to solve the spacecraft reorientation control problem with pointing constraint. However, this method pays too much attention to the processing ability of the constraint, often resulting in excessive control input and unnecessary energy consumption.
[0004] The common spacecraft attitude reorientation control only considers how to satisfy the pointing constraint condition, ignoring the energy consumption problem during attitude adjustment. The energy carried by the actual spacecraft is limited and valuable, and the above attitude reorientation algorithm will inevitably increase energy consumption while meeting the specified constraints. SUMMARY
[0005] The purpose of the present application is to provide a spacecraft fixed-time reorientation control method based on quadratic programming, which takes into account the control performance and energy consumption problem while meeting the pointing constraint.
[0006] Technical scheme: The spacecraft fixed-time reorientation control method based on quadratic programming provided by the present application comprises the following steps:
[0007] (1) Obtain the current attitude and angular velocity of the spacecraft;
[0008] (2) Establish the description of the spacecraft attitude reorientation control problem with pointing constraints: the attitude dynamics equation of the spacecraft is established by using the Rodrigues parameter description method; the forbidden pointing constraints are mathematically described according to the geometric relationship between the luminous celestial body and the spacecraft;
[0009] (3) Design the control barrier function: construct the safe set by using the mathematical description of the forbidden constraints, and construct a suitable control barrier function;
[0010] (4) Design the 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 the sliding mode dynamics, and obtain the conditions required for the system to be fixed-time stable;
[0011] (5) Select a suitable quadratic cost function, combine the control Lyapunov function and the control barrier function, and form a quadratic programming problem, and obtain the optimal control input that satisfies the constraints by solving the problem.
[0012] Further, step (2) is as follows:
[0013] The spacecraft attitude dynamics model is expressed as
[0014]
[0015] wherein, is the modified Rodrigues parameter representation of the current attitude of the rigid spacecraft, is the angular velocity of the spacecraft in the body coordinate system, is the moment of inertia of the spacecraft, is the control torque.
[0016] Suppose that the field of view of the optical sensitive instrument carried by the spacecraft is conical, and the projection of the direction of the center axis of the i-th instrument in the body coordinate system fixed with the spacecraft is denoted as b i , and the projection of the attitude forbidden pointing of the j-th luminous celestial body in the inertial system is denoted as n j ; then the forbidden pointing constraint can be described as
[0017]
[0018] wherein, the matrix is the current attitude of the spacecraft, and its expression is
[0019]
[0020] Further, step (3) is as follows:
[0021] The safe set is defined as It is verified that the set is second order with respect to the attitude dynamics, thus, introduce the following function:
[0022]
[0023]
[0024] and the corresponding set and where α 1ij (·),α 2ij (·) are like functions; according to the definition of high order barrier function, the control strategy guarantees the existence of like functions α 1ij (·),α 2ij (·) such that for all states in the set ψ 2ij (σ,ω)30 holds, i.e.
[0025]
[0026] where L f ,L g are the Lie derivatives along the vector fields f,g, whose expressions are:
[0027]
[0028] then the function b ij (σ) is a high order barrier function with relative order 2, and the set is forward invariant for the spacecraft attitude dynamics. Combining the fact that the set is a subset of the safe set , this control barrier function can guarantee the system to satisfy the pointing forbidden constraint.
[0029] Further, the sliding surface in step (4) is designed as
[0030] s = ω + α1σ||σ|| g-1 + α2β(σ)
[0031] where
[0032]
[0033] where 0 < p < 1, 1 < g < 2, η ε is a small positive number, and
[0034]
[0035] The constructed control Lyapunov function is
[0036]
[0037] By constraining the control Lyapunov function to satisfy the following conditions, the fixed-time convergence of the system is ensured
[0038]
[0039] Wherein, δ1 is a real number satisfying the inequality , is a preset convergence time.
[0040] Further, the quadratic cost function in step (5) is selected as
[0041]
[0042] Wherein, u=[τ δ1 δ 2,j ] T ,
[0043]
[0044] Wherein, κ1>0, κ 2,j >0 is the proportion of the relaxation factor δ1 and δ 2,j , q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0;The control barrier function and the control Lyapunov function constructed in steps 3 and 4 are used as constraint conditions, and the attitude redirection control under the constraint is converted into the following quadratic programming problem:
[0045]
[0046] -λ≤τ≤λ
[0047]
[0048] Wherein, the introduction of the relaxation factor δ1, δ 2,j is to alleviate 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 satisfying the pointing constraint and the convergence time can be obtained.
[0049] The spacecraft fixed-time redirection control system based on quadratic programming provided by the application comprises:
[0050] The acquisition module is used for acquiring the current attitude and angular velocity of the spacecraft.
[0051] Constraint module: for establishing the description of the pointing constraint spacecraft attitude reorientation control problem: the attitude dynamics equation of the spacecraft is established by using the Rodrigues parameter description method; the mathematical description of the forbidden pointing constraint is made according to the geometric relationship between the luminous celestial body and the spacecraft;
[0052] Control barrier module: for designing the control barrier function: the safe set is constructed by using the mathematical description of the forbidden constraint, and the appropriate control barrier function is constructed;
[0053] Lyapunov function module: for designing the control Lyapunov function: the appropriate sliding surface is constructed according to the current attitude and angular velocity of the spacecraft, the appropriate control Lyapunov function is constructed based on the sliding mode dynamics, and the conditions required to be met for the system to be fixed time stable are obtained;
[0054] Quadratic cost function module: for selecting the appropriate quadratic cost function, combining the control Lyapunov function and the control barrier function to form a quadratic programming problem, and obtaining the optimal control input satisfying the constraint by solving the problem.
[0055] Further, in the constraint module, the formula is as follows:
[0056] The attitude dynamics model of the spacecraft is expressed as
[0057]
[0058] Wherein, is the modified Rodrigues parameter representation of the current attitude of the rigid spacecraft, is the representation of the angular velocity of the spacecraft in the body coordinate system, is the moment of inertia of the spacecraft, is the control torque.
[0059] Suppose the field of view of the optical sensitive instrument carried by the spacecraft is conical, and the projection of the direction of the center axis of the i th instrument in the body coordinate system fixed with the spacecraft is denoted as b i , and the projection of the attitude forbidden pointing of the j th luminous celestial body in the inertial system is denoted as n j ; then the forbidden pointing constraint can be described as
[0060]
[0061] Wherein, the matrix is the current attitude of the spacecraft, and its expression is
[0062]
[0063] Further, in the control barrier module, the formula is as follows:
[0064] The safe set is defined as It is verified that the set is second order with respect to the attitude dynamics, thus, the following function is introduced:
[0065]
[0066] and the corresponding set and where α 1ij (·),α 2ij (·) are like functions; according to the definition of high order barrier functions, the control strategy guarantees the existence of like functions α 1ij (·),α 2ij (·) such that ψ 2ij (σ,ω)≥0 holds for all states in the set , that is,
[0067]
[0068] where L f ,L g are the Lie derivatives along the vector fields f,g, respectively, and the expressions of the vector fields f,g are:
[0069]
[0070] then the function b ij (σ) is a high order barrier function with relative order 2, and the set is forward invariant with respect to the spacecraft attitude dynamics. Combining the fact that the set is a subset of the safe set , the control barrier function can guarantee that the system satisfies the pointing forbidden constraints.
[0071] Further, the sliding surface in the Lie algebra function module is designed as
[0072] s = ω + α1σ||σ|| g-1 + α2β(σ)
[0073] where
[0074]
[0075] where 0 < p < 1, 1 < g < 2, η ε is a small positive number, and
[0076]
[0077] The control Lie algebra function constructed is
[0078]
[0079] By constraining the control Lyapunov function to satisfy the following condition, the fixed-time convergence of the system is guaranteed
[0080]
[0081] wherein, δ1 is a real number satisfying the inequality , is a preset convergence time.
[0082] Further, the quadratic cost function in the quadratic cost function module is selected as
[0083]
[0084] wherein, u = [τ δ1 δ 2,j ] T ,
[0085]
[0086] wherein, κ1>0, κ 2,j >0 is the proportion of the relaxation factors δ1 and δ 2,j , q>0, the purpose of introducing the linear term qδ1 is to ensure δ1<0; the control barrier function and the control Lyapunov function constructed in steps 3 and 4 are taken as constraint conditions, and the pointing constraint attitude redirection control is converted into the following quadratic programming problem:
[0087]
[0088] -λ≤τ≤λ
[0089]
[0090] wherein, the introduction of the relaxation factors δ1, δ 2,j is to alleviate 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 satisfying the pointing constraint and the convergence time can be obtained.
[0091] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) The attitude reorientation control algorithm designed in the present invention can ensure that the spacecraft adjusts to the desired attitude within a predetermined fixed time under the premise of considering energy consumption; (2) The present invention introduces a control obstacle function to ensure that the spacecraft does not violate the attitude pointing constraint during the attitude adjustment process, and uses it together with the control Lyapunov function as the constraint condition of the quadratic programming problem, thus balancing the contradiction between control performance, energy and computational 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. Attached Figure Description
[0092] Figure 1 This is a flowchart of the present invention;
[0093] Figure 2 This invention relates to the geometric relationship between the luminous celestial body and the spacecraft.
[0094] Figure 3 This is the pointing constraint of the spacecraft attitude in this invention;
[0095] Figure 4 This is the convergence curve of the sliding mode variable s in this invention;
[0096] Figure 5 This is the response curve of the spacecraft's attitude changing over time according to the present invention;
[0097] Figure 6 This is the response curve of the spacecraft's angular velocity as a function of time according to the present invention;
[0098] Figure 7 This is the curve of the control torque required by the present invention changing over time; Detailed Implementation
[0099] The technical solution of the present invention will be further described below with reference to the accompanying drawings.
[0100] like Figure 1 As shown, this embodiment of the invention provides a spacecraft fixed-time redirection control method based on quadratic programming, including the following steps:
[0101] (1) Obtain the spacecraft's current attitude and angular velocity;
[0102] (2) Establishing a description of the orientation reversal control problem for a spacecraft with orientation constraints: Using the Rodrigues parameter description method, the attitude dynamics equations of the spacecraft are established; the prohibition of orientation constraints is mathematically described based on the geometric relationship between the luminous celestial body and the spacecraft; the formulas are as follows:
[0103] The spacecraft attitude dynamics model is expressed as
[0104]
[0105] where, is the modified Rodrigues parameter representation of the current attitude of the rigid spacecraft, is the representation of the angular velocity of the spacecraft in the body coordinate system, is the moment of inertia of the spacecraft, is the control torque.
[0106] Let the field of view of the optical sensitive instrument carried by the spacecraft be conical, and let the projection of the direction of the central axis of the i-th instrument field of view in the body coordinate system fixed with the spacecraft be b i , and the projection of the attitude forbidden pointing of the j-th luminous celestial body in the inertial system be n j ; then the forbidden pointing constraint can be described as
[0107]
[0108] where, the matrix is the current attitude of the spacecraft, and its expression is
[0109]
[0110] (3) Design the control barrier function: construct the safety set using the mathematical description of the forbidden constraint, and construct a suitable control barrier function; the formula is as follows:
[0111] The safety set is defined as It is verified by calculation that this set is second-order relative to the attitude dynamics, therefore, the following function is introduced:
[0112]
[0113] and the corresponding set and where, α 1ij (·), α 2ij (·) are class functions; according to the definition of the high-order barrier function, the control strategy guarantees the existence of class functions α 1ij (·), α 2ij (·) such that ψ 2ij (σ, ω) 30 is true for all states in the set , that is,
[0114]
[0115] where, L f , Lg are the Lie derivatives along the vector fields f, g, respectively, and the expressions of the vector fields f, g are
[0116]
[0117] then the function b ij (σ) is a high-order barrier function with relative order 2, and the set is forward invariant for the spacecraft attitude dynamics. Combining the fact that is a subset of the safe set , the control barrier function can guarantee that the system satisfies the pointing forbidden constraints.
[0118] (4) Design the 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 the sliding mode dynamics, and obtain the conditions required for the system to achieve fixed-time stability; the sliding surface is designed as
[0119] s = ω + α1σ||σ|| + α2β(σ) g-1
[0120] where
[0121]
[0122] where 0 < p < 1, 1 < g < 2, η ε is a small positive number, and
[0123]
[0124] The control Lyapunov function constructed is
[0125]
[0126] By restricting the control Lyapunov function to satisfy the following conditions, the fixed-time convergence of the system is guaranteed
[0127]
[0128] where δ1 is a real number that satisfies the inequality , and is a pre-set convergence time.
[0129] (5) Select a suitable quadratic cost function, combine the control Lyapunov function and the control barrier 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] where κ1>0, κ 2,j >0 is the weight of the slack variables δ1and δ 2,j , q>0 is introduced to ensure δ1<0; the constructed control barrier function and control Lyapunov function in steps 3 and 4 are taken as constraints, and the attitude redirection control under the pointing constraint is converted into the following quadratic programming problem:
[0134]
[0135] -λ≤τ≤λ
[0136]
[0137] where the introduction of the slack variables δ1, δ 2,j is to alleviate 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 the convergence time can be obtained.
[0138] 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 pointing constraint, corresponding simulation verification is performed. Consider the attitude redirection control problem of a spacecraft with an inertia matrix 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 , respectively. The spacecraft carries a photosensitive sensor, the boresight of which is aligned with the axis of the spacecraft body coordinate system, i.e., b1= [0 0 1] T , the half viewing angle θ is set to θ = 15°, and the directions of the light-emitting celestial bodies to be avoided relative to the spacecraft are n1= [-0.2310 0.4077 0.8834] T , n2= [-0.2750 0.0050 0.3250] T , and n3= [-0.0864 0.7564 0.6484] T .
[0139] The controller parameters are selected as:
[0140]
[0141] Figure 3 The pointing constraint b for the spacecraft attitude shown in this embodiment of the invention. ij As can be seen from the figure, the spacecraft's attitude never violated the pointing constraints during the retargeting process. Figure 4 The convergence curve of the defined sliding mode variable s shows that the sliding mode variable converges to the equilibrium point within a preset fixed time T. Figure 5 and 6 The figures show the response curves of the spacecraft's attitude and angular velocity as a function of time. As can be seen from the figures, the attitude and angular velocity converge rapidly to the origin along the sliding surface. Figure 7 The curve shows the change of the required control torque over time. As can be seen from the figure, its magnitude is within the range of the maximum allowable control torque.
[0142] This invention also provides a spacecraft fixed-time redirection control system based on quadratic programming, comprising:
[0143] Acquisition module: Used to acquire the spacecraft's current attitude and angular velocity;
[0144] Constraint Module: Used to establish the description of the attitude reversal control problem for a spacecraft with pointing constraints. It uses the Rodrigues parametric description method to establish the spacecraft's attitude dynamics equations; and mathematically describes the prohibition of pointing constraints based on the geometric relationship between the luminous celestial body and the spacecraft. The formulas are as follows:
[0145] The spacecraft attitude dynamics model is expressed as
[0146]
[0147] in, The corrected Rodrigues parameters represent the current attitude of the rigid spacecraft. This represents the angular velocity of the spacecraft in volume coordinates. For the spacecraft's rotational inertia, To control the torque.
[0148] Let the field of view of the optical sensing instruments carried by the spacecraft be conical, and let the direction of the central axis of the field of view of the i-th instrument lie in the body coordinate system fixed to the spacecraft. The projection below is b i The attitude of the j-th luminous celestial body is forbidden to be pointed in the inertial frame. The projection below is n j The prohibition of pointing constraints can then be described as follows:
[0149]
[0150] where matrix is the current attitude of the spacecraft, whose expression is
[0151]
[0152] Control Barrier Module: used to design control barrier function: construct safety set by using mathematical description of forbidden constraint, construct appropriate control barrier function; formula as follows:
[0153] The safety set is defined as It is verified by calculation that the set is second-order relative to attitude dynamics, therefore, the following function is introduced:
[0154]
[0155] and the corresponding set and where α 1ij (·),α 2ij (·) are class functions; according to the definition of high-order barrier function, the control strategy guarantees the existence of class functions α 1ij (·),α 2ij (·) such that ψ 2ij (σ,ω)≥0 holds for all states in the set , that is
[0156]
[0157] where L f ,L g are the Lie derivatives along the vector fields f,g, and the expressions of the vector fields f,g are:
[0158]
[0159] then the function b ij (σ) is a high-order barrier function with relative order 2, and the set is forward invariant for spacecraft attitude dynamics. Combined with the fact that the set is a subset of the safety set , this control barrier function can guarantee that the system meets the pointing forbidden 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 required for system fixed-time stability; the sliding surface is designed as
[0161] s = ω + α1σ||σ| g-1 + α2β(σ)
[0162] where
[0163]
[0164] where, 0 < p < 1, 1 < g < 2, η ε is a small positive number, and
[0165]
[0166] The constructed control Lyapunov function is
[0167]
[0168] By constraining the control Lyapunov function to satisfy the following conditions, the fixed-time convergence of the system is guaranteed
[0169]
[0170] where, δ1 is a real number satisfying the inequality , is a preset convergence time.
[0171] The quadratic cost function module is used to select a suitable quadratic cost function, combine the control Lyapunov function and the control barrier function, and form a quadratic programming problem, and the optimal control input satisfying the constraint is obtained by solving the problem. The quadratic cost function selected is
[0172]
[0173] where, u = [τ δ1 δ 2,j ] T ,
[0174]
[0175] where, κ1 > 0, κ 2,j > 0 is the proportion of the relaxation factors δ1 and δ 2,j , q > 0, the purpose of introducing the linear term qδ1 is to ensure δ1 < 0; The control barrier function and the control Lyapunov function constructed in steps 3 and 4 are used as constraint conditions, and the attitude redirection control under the constraint is converted into the following quadratic programming problem:
[0176]
[0177] -λ ≤ τ ≤ λ
[0178]
[0179] where 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, so as to guarantee the feasibility of the quadratic programming problem. By solving this quadratic programming problem, the optimal control input that satisfies the pointing constraint and the convergence time can be obtained.
Claims
1. A method for spacecraft fixed-time reorientation control based on quadratic programming, characterized in that, The method comprises the following steps: (1) obtaining the current attitude and angular velocity of the spacecraft; (2) establishing a description of the spacecraft attitude reorientation control problem with pointing constraints: using the Rodrigues parameter description method, the attitude dynamics equation of the spacecraft is established; the mathematical description of the forbidden pointing constraint is described according to the geometric relationship between the luminous celestial body and the spacecraft; the formula is as follows: The spacecraft attitude dynamics model is expressed as wherein, is a modified Rodrigues parameter representation of the current attitude of the rigid spacecraft, is a representation of the angular velocity of the spacecraft in the body coordinate system, is the moment of inertia of the spacecraft, is a control torque; Let the direction of the center axis of the field of view of the i-th instrument in the body coordinate system fixed to the spacecraft be b , and the direction of the projection of the i-th instrument in the inertial coordinate system be b i ; let the direction of the center axis of the field of view of the j-th light-emitting celestial body in the body coordinate system fixed to the spacecraft be n , and the direction of the projection of the j-th light-emitting celestial body in the inertial coordinate system be n j ; then the constraint of the forbidden pointing is described as where the matrix is the current attitude of the spacecraft, whose expression is (3) designing a control barrier function: constructing a safety set by using the mathematical description of the forbidden constraint, and constructing a control barrier function; the formula is as follows: The set of safe sets is defined as It is computationally verified that this set is quadratic with respect to the dynamics of the pose, so the following function is introduced: and the corresponding set and Where, α 1ij (·),α 2ij (·) represents a κ-type function; according to the definition of higher-order barrier functions, the control strategy guarantees their existence. Class function α 1ij (·),α 2ij (·) makes for the set All states on have ψ 2ij (σ,ω)≥0 holds true, that is where L f , L g are the Lie derivatives along the vector fields f, g, respectively, and f, g are given by Then the function b ij (σ) is a high-order barrier function with relative order 2 and the set is forward invariant for the spacecraft attitude dynamics; combined with the fact that is a subset of the safe set this control barrier function is able to guarantee that the system satisfies the pointing prohibition constraint; (4) designing a control Lyapunov function: constructing a sliding mode surface according to the current attitude and angular velocity of the spacecraft, constructing a control Lyapunov function based on sliding mode dynamics, and obtaining the conditions required to be met for the fixed-time stability of the system; (5) selecting a quadratic cost function, combining the control Lyapunov function and the control barrier function to form a quadratic programming problem, and obtaining the optimal control input satisfying the constraint by solving the problem.
2. The quadratically-programmed-based spacecraft fixed-time reorientation control method of claim 1, wherein, The sliding mode surface in step (4) is designed as s = ω + α1σ||σ| g-1 + α2β(σ) wherein where 0 < p < 1, 1 < g < 2, η ε is a small positive number, 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 ensured wherein δ1 is a real number satisfying the inequality is a preset convergence time. 3. The quadratically-programmed-based spacecraft fixed-time reorientation control method of claim 1, wherein, The quadratic cost function in step (5) is selected as where u = [τ δ1 δ 2,j ] T , where k1 > 0, k2 > 0 are positive constants, and 2,j > 0 is a relaxation factor, and q > 0 is a positive constant. 2,j The purpose of introducing the linear term qd1 is to ensure that d1 < 0. The constructed control barrier function and control Lyapunov function in steps 3 and 4 are taken as constraints, and the attitude redirection control under constraints is converted into the following quadratic programming problem: -j≤τ≤j where 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 this quadratic programming problem, the optimal control input that satisfies the pointing constraint and the convergence time can be obtained.
4. A quadratically-programmed based spacecraft fixed-time reorientation control system, characterized by, Comprise: The acquisition module is used for obtaining the current attitude and angular velocity of the spacecraft; The constraint module is used for establishing a description of the spacecraft attitude reorientation control problem with pointing constraints: using the Rodrigues parameter description method, the attitude dynamics equation of the spacecraft is established; the mathematical description of the forbidden pointing constraint is described according to the geometric relationship between the luminous celestial body and the spacecraft; the formula is as follows: The spacecraft attitude dynamics model is expressed as wherein is a modified Rodrigues parameter representation of the current attitude of the rigid spacecraft, is a representation of the angular velocity of the spacecraft in the body coordinate system, is the moment of inertia of the spacecraft, is a control torque; Let the direction of the center axis of the field of view of the i-th instrument in the body coordinate system fixed to the spacecraft be b ; the direction of the center axis of the field of view of the j-th instrument in the body coordinate system fixed to the spacecraft be n i ; the attitude of the j-th light-emitting celestial body in the inertial coordinate system be q ; the projection of the direction of the center axis of the field of view of the i-th instrument in the inertial coordinate system be b j ; the projection of the direction of the center axis of the field of view of the j-th instrument in the inertial coordinate system be n ; the projection of the attitude of the j-th light-emitting celestial body in the inertial coordinate system be q where the matrix is the current attitude of the spacecraft, expressed as The control barrier module is used for designing a control barrier function: constructing a safety set by using the mathematical description of the forbidden constraint, and constructing a control barrier function; the formula is as follows: The set of safe sets is defined as The set is verified to be second order with respect to the dynamics of the pose, thus, the following function is introduced: and the corresponding set and Where, α 1ij (·),α 2ij (·)for Class function; according to the definition of higher-order barrier functions, the control strategy guarantees the existence of a class function α of type κ. 1ij (·),α 2ij (·) makes for the set All states on have ψ 2ij (σ,ω)≥0 holds true, that is where L f L g are the Lie derivatives along the vector fields f, g, respectively, whose expressions are: Then the function b ij (σ) is a high-order barrier function with relative order 2 and the set is forward invariant for the spacecraft attitude dynamics; combined with the fact that is a subset of the safe set this control barrier function is able to guarantee that the system satisfies the pointing prohibition constraints; The Lyapunov function module is used for designing a control Lyapunov function: constructing a sliding mode surface according to the current attitude and angular velocity of the spacecraft, constructing a control Lyapunov function based on sliding mode dynamics, and obtaining the conditions required to be met for the fixed-time stability of the system; The quadratic cost function module is used for selecting a quadratic cost function, combining the control Lyapunov function and the control barrier function to form a quadratic programming problem, and obtaining the optimal control input satisfying the constraint by solving the problem.
5. The quadratically-programmed-based fixed-time spacecraft redirection control system of claim 4, wherein, The sliding mode surface in the Lyapunov function module is designed as s = ω + α1σ||σ| g-1 + α2β(σ) wherein where 0 < p < 1, 1 < g < 2, η ε is a small positive number, 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 ensured wherein δ1 is a real number satisfying the inequality δ1 < 1, is a preset convergence time.
6. The quadratically-programmed-based spacecraft fixed-time reorientation control system according to claim 4, wherein, The quadratic cost function in the quadratic cost function module is selected as where u = [τ δ1 δ 2,j ] T , Where κ1>0, κ 2,j >0 represents the relaxation factors δ1 and δ. 2,j The proportion of q>0, the purpose of introducing the linear term qδ1 is to ensure that δ1<0; taking the constructed control obstacle function and control Lyapunov function as constraints, the attitude redirection control under the pointing constraints is transformed into the following quadratic programming problem: -j≤τ≤j where 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 this quadratic programming problem, the optimal control input that satisfies the pointing constraint and the convergence time can be obtained.
Citation Information
Patent Citations
Dynamic sliding mode attitude tracking control method and system for flexible spacecraft
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Constrained spacecraft attitude control method
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