Finite-time spatial rendezvous control method for six degrees of freedom under multiple constraints

Abstract

A six-degree-of-freedom finite-time space rendezvous control method under multiple constraints belongs to the field of space technology. The implementation method of the present invention is as follows: a six-degree-of-freedom dynamic model is established based on the Lie group SE (3) framework, so that the spacecraft rendezvous process can satisfy the position end constraint while also satisfying the attitude end constraint, fully considering the attitude-orbit coupling problem caused by the thruster installation error in actual engineering, improving the spacecraft rendezvous accuracy, and avoiding the unwinding problem caused by the traditional six-degree-of-freedom dual quaternion representation method. A finite-time sliding mode control strategy is designed so that the rendezvous process can satisfy the mission time window constraint and improve the error convergence speed. In order to solve the potential collision risk in the rendezvous process and meet the safety constraints of the rendezvous mission, an artificial potential function is introduced to achieve collision avoidance in the rendezvous process and improve the safety of the spacecraft rendezvous process. The present invention can shorten the rendezvous time, improve the spacecraft space rendezvous accuracy, and improve the safety of the spacecraft rendezvous process.

Description

Technical Field

[0001] The present invention relates to a spacecraft space rendezvous control method, in particular to a six-degree-of-freedom finite-time space rendezvous control method under multiple constraints, and belongs to the field of space technology. Background Art

[0002] In recent years, the successive deployment of satellite constellations such as Starlink and OneWeb has led to increased congestion in near-Earth space, increasing the risk of collisions between active spacecraft and non-cooperative objects. For the in-orbit disposal of disabled spacecraft, deploying active spacecraft equipped with robotic arms is one widely studied option. Through precise rendezvous, they can capture and remove disabled spacecraft. Furthermore, in some complex deep space exploration missions, precise rendezvous between the ascender and orbiter is crucial for sample return. Therefore, space rendezvous plays a vital role in space missions.

[0003] In light of engineering practice, since spacecraft rendezvous requires both terminal position and attitude errors to be zero, thruster installation errors will cause coupled motion between the spacecraft's attitude and orbit, necessitating six-degree-of-freedom dynamic modeling of the spacecraft. Space debris removal missions typically have strict time constraints, and deep space exploration mission sequences have strict time windows. This makes the spacecraft rendezvous process time-sensitive and must be completed within a limited timeframe, requiring the control method to meet finite-time convergence conditions. Furthermore, the large physical attachments of the active and target spacecraft present a collision risk, necessitating collision avoidance control strategies to enhance the safety of the rendezvous process. Summary of the Invention

[0004] In view of the time sensitivity and potential collision risk of the space rendezvous process, the purpose of the present invention is to provide a six-degree-of-freedom finite-time space rendezvous control method under multiple constraints, which can achieve the convergence of position and attitude tracking errors within a finite time while ensuring safe rendezvous.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The present invention discloses a six-degree-of-freedom finite-time space rendezvous control method under multiple constraints. Based on the Lie group SE (3) framework, a six-degree-of-freedom dynamic model is established, so that the spacecraft rendezvous process can satisfy the position end constraint while also satisfying the attitude end constraint. The attitude-orbit coupling problem caused by the thruster installation error in actual engineering is fully considered, the rendezvous accuracy is improved, and the unwinding problem caused by the traditional six-degree-of-freedom dual quaternion representation method is avoided. On this basis, a finite-time sliding mode control strategy is designed so that the rendezvous process can satisfy the mission time window constraint and improve the error convergence speed. In order to solve the potential collision risk in the rendezvous process and meet the safety constraints of the rendezvous mission, an artificial potential function is introduced to achieve collision avoidance in the rendezvous process and improve the safety of the rendezvous process. The present invention can shorten the rendezvous time, improve the spacecraft space rendezvous accuracy, and improve the safety of the spacecraft rendezvous process.

[0007] The present invention discloses a six-degree-of-freedom finite-time space rendezvous control method under multiple constraints, comprising the following steps:

[0008] Step 1: Based on the Lie group SE (3) framework, a six-degree-of-freedom dynamic model of the active spacecraft and a six-degree-of-freedom dynamic model of the target spacecraft are established respectively. Based on the two obtained six-degree-of-freedom dynamic models, a six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft is established, so that the spacecraft rendezvous process satisfies both the terminal position and terminal attitude constraints.

[0009] Step 1.1: Establish a six-degree-of-freedom dynamic model of the active spacecraft.

[0010] The kinematic equations of an active spacecraft are expressed as

[0011]

[0012] where R c ∈SO(3) represents the attitude rotation matrix of the active spacecraft from its own system to the inertial system along the principal axis of inertia. SO(3) is the Lie group of the special orthogonal matrix representing the attitude of the spacecraft. represents the position vector from the origin of the coordinate system to the center of mass of the active spacecraft in the inertial frame, and They represent the rotational angular velocity and translational velocity of the active spacecraft system, Represents a set of three-dimensional real vectors. Symbol (2) × Represents the cross product matrix of the vector, for a three-dimensional vector x=[x1,x2,x3] T , the cross product matrix of x(x) × Defined as

[0013]

[0014] Among them, x1, x2, and x3 are the three components of vector x.

[0015] The dynamic equation of an active spacecraft is expressed as

[0016]

[0017] Among them J c is the moment of inertia of the active spacecraft, m c is the mass of the active spacecraft, is the control torque of the active spacecraft, is the disturbance torque of the active spacecraft, is the gravitational field of the active spacecraft, is the control force of the active spacecraft, is the disturbance force of the active spacecraft. The position and attitude of the active spacecraft can be expressed by the variable g of the Lie group SE(3) c Expressed as

[0018]

[0019] 0 1×3 represents a 1×3 zero matrix, and SE(3) is the Lie group of all translational and rotational motions of the spacecraft. The augmented velocity vector of the active spacecraft is expressed as

[0020]

[0021] represents a six-dimensional real vector set. Therefore, under the SE(3) framework, the kinematic equation of formula (1) and the dynamic equation of formula (2) are expressed as

[0022]

[0023] in

[0024]

[0025] is the Lie algebra of the Lie group SE(3), I3 represents the three-dimensional identity matrix, represents a 6×6 real matrix set, ξ c The matrix of the conjugate adjoint mapping is expressed as

[0026]

[0027] 0 3×3 Represents a 3×3 zero matrix.

[0028] Step 1.2: Establish a six-degree-of-freedom dynamic model of the target spacecraft.

[0029] The kinematic and dynamic models of the target spacecraft in the SE(3) framework can be expressed as

[0030]

[0031] in

[0032]

[0033] R t ∈SO(3) represents the attitude rotation matrix of the target spacecraft from the local system to the inertial system along the inertial principal axis, represents the position vector from the origin of the coordinate system to the center of mass of the target spacecraft in the inertial system, and They represent the rotational angular velocity and translational velocity of the target spacecraft in the system. t is the moment of inertia of the target spacecraft, m t is the mass of the target spacecraft, is the gravitational field of the target spacecraft, is the disturbance torque of the target spacecraft, is the disturbance force of the target spacecraft.

[0034] Step 1.3: Based on equation (5) obtained in step 1.1 and equation (6) obtained in step 1.2, a six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft is established.

[0035] The desired position and attitude g of the active spacecraft cd and the angular velocity ξ cd Expressed as

[0036]

[0037] Among them, h d Represents the desired position and attitude relative to the target spacecraft.

[0038]

[0039] The matrix of the adjoint mapping is represented as

[0040]

[0041] in, express The 3×3 block matrix, express The position and attitude error h between the active spacecraft and the target spacecraft is expressed as

[0042] h=(g t ) -1 gc (8)

[0043] The exponential coordinate vector used to represent the active spacecraft position and attitude errors is

[0044]

[0045] in, and The exponential coordinate vectors representing the attitude tracking error and position tracking error, respectively. The exponential coordinate vectors representing the position and attitude errors of the active spacecraft It can be expressed as

[0046]

[0047] in represents a logarithmic mapping.

[0048]

[0049] traces The logarithmic mapping is expressed as

[0050]

[0051] in, Indicates (h d ) -1 h is a 3×3 block matrix, Indicates (h d ) -1 h is a 3×1 block matrix, is the Lie algebra of the Lie group SO(3). (h d ) -1 The logarithmic mapping of h is expressed as

[0052]

[0053] in

[0054]

[0055] Among them, ψ1, ψ2, ψ3 are vectors Ψ = [ψ1, ψ2, ψ3] T The three components.

[0056] The relative velocity of the active spacecraft relative to the target spacecraft in this system Expressed as

[0057]

[0058] in and They represent the rotational angular velocity and translational velocity of the active spacecraft relative to the target spacecraft in the system.

[0059]

[0060] h -1 The matrix of the adjoint mapping is represented as

[0061]

[0062] in, Indicates h -1 The 3×3 block matrix, Indicates h -1 A 3×1 block matrix.

[0063] The kinematic equation in the exponential coordinate system is expressed as

[0064]

[0065] Expressed as

[0066]

[0067] in

[0068]

[0069] and relative acceleration Expressed as

[0070]

[0071] The matrix of the adjoint mapping is expressed as

[0072]

[0073] Substituting Equation (5) into Equation (14), we can obtain the six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft:

[0074]

[0075] Step 2. Based on the six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft obtained in step 1, a six-degree-of-freedom spatial rendezvous sliding mode control law is designed, and the parameter conditions of the control law gain are determined so that the control law can converge within a finite time, meet the time window constraints of the rendezvous mission, and improve the error convergence speed.

[0076] Step 2.1: Design a six-degree-of-freedom spatial rendezvous sliding mode control law.

[0077] Design of sliding surface under the SE(3) framework

[0078]

[0079] Where C=diag(c1,c2,c3,c4,c5,c6) is a positive definite matrix, q and p are positive odd numbers and satisfy q>p. The control law is designed as

[0080]

[0081] in K=diag(k1,k2,...,k6) is a positive definite gain matrix, and the sign function sgn(s) is

[0082]

[0083] where s = [s1, s2, ..., s6] T , s i ,i=1,2,...,6 represents the six components of the sliding surface s.

[0084] Step 2.2: Determine the parameter conditions of the control law gain so that the control law can converge within a finite time.

[0085] Since the external perturbation is bounded, define the perturbation boundary Therefore, for the external disturbances on active spacecraft and external disturbances to the target spacecraft have

[0086]

[0087] in i=1,2,...,6 respectively represent For the positive definite Lyapunov function V(t), when it satisfies

[0088]

[0089] It is semi-negative timing, the controller is stable in a finite time, and the convergence time satisfies

[0090]

[0091] Where c>0, V0 is the value of the Lyapunov function at the initial moment. Design Lyapunov function

[0092]

[0093] Perform the first-order differentiation of Equation (21)

[0094]

[0095] Substituting equations (12) and (15) into equation (22), we can obtain

[0096]

[0097] Substituting formula (17) into formula (23) we can obtain

[0098]

[0099] make i=1,2,...,6, then

[0100]

[0101] 0<γ<1, for From formula (19), we can see that when the positive definite matrix gain K satisfies When , the control law (17) can make the error converge within a finite time.

[0102] Step 3. Based on the finite-time sliding mode control law for the six-degree-of-freedom space rendezvous designed in step 2, design an artificial potential function collision avoidance control law, determine the parameter conditions of the artificial potential function so that the control law with the collision avoidance strategy can converge within a finite time, and according to the finite-time sliding mode control law and the artificial potential function collision avoidance strategy, realize the six-degree-of-freedom space rendezvous while satisfying the terminal position attitude constraints, time constraints and safety constraints, thereby improving the safety of the spacecraft rendezvous process.

[0103] Step 3.1: Design the collision avoidance control law of the six-degree-of-freedom spatial intersection artificial potential function.

[0104] The distance between the active spacecraft and the target spacecraft is defined as

[0105]

[0106] Where W>0 is a positive definite matrix

[0107]

[0108] W1 has physical units given by the ratio of the square of the length unit to the square of the angle unit, and W2 is dimensionless. Define the positive definite artificial potential function

[0109]

[0110] Where ε is a positive parameter, r d represents the desired relative distance between the active spacecraft and the target spacecraft. The control force generated to prevent collision is

[0111]

[0112] in

[0113]

[0114] After adding the collision avoidance strategy to the original control law (17), the new control law is:

[0115]

[0116] Step 3.2: Determine the parameter conditions of the artificial potential function so that the control law with the collision avoidance strategy can converge within a finite time.

[0117] After the collision avoidance strategy is introduced, the six-degree-of-freedom relative dynamics model (15) is modified to

[0118]

[0119] In order to ensure that the system can still converge within a limited time after adding the collision avoidance strategy, the new control law (29) and the six-degree-of-freedom relative dynamics model (30) are substituted into the Lyapunov function (21) and the first-order differential is performed to obtain

[0120]

[0121] The artificial potential function parameter ε is selected so that Then there is

[0122]

[0123] in i=1,2,...,6 means The six components of From formula (19), we can see that the selected artificial potential function parameter ε can make When the collision avoidance strategy is added, the control law (29) can make the error converge within a finite time.

[0124] The six-degree-of-freedom finite-time space rendezvous control problem under multiple constraints includes the six-degree-of-freedom relative dynamics model of the active spacecraft relative to the target spacecraft determined by Equation (15) and the six-degree-of-freedom space rendezvous finite-time sliding mode control law with collision avoidance strategy determined by Equation (29). Based on the six-degree-of-freedom relative dynamics model, a finite-time sliding mode control law and an artificial potential function collision avoidance strategy are designed to achieve six-degree-of-freedom space rendezvous while satisfying the terminal position attitude constraints, time constraints and safety constraints.

[0125] Beneficial effects:

[0126] 1. The six-degree-of-freedom finite-time space rendezvous control method under multiple constraints disclosed by the present invention establishes a six-degree-of-freedom relative dynamics model under the SE(3) framework, so that the spacecraft rendezvous process can satisfy both the position end constraint and the attitude end constraint, fully considers the attitude-orbit coupling problem caused by thruster installation errors in actual engineering, improves the spacecraft rendezvous accuracy, and avoids the unwinding problem caused by the traditional six-degree-of-freedom dual quaternion representation method.

[0127] 2. The six-degree-of-freedom finite-time spatial rendezvous control method under multiple constraints disclosed by the present invention enables the rendezvous process to meet the task time window constraints and improve the error convergence speed by designing a finite-time sliding mode control law.

[0128] 3. The present invention discloses a six-degree-of-freedom finite-time space rendezvous control method under multiple constraints. Based on the designed six-degree-of-freedom space rendezvous finite-time sliding mode control law, an artificial potential function collision avoidance control law is designed, and the parameter conditions of the artificial potential function are determined so that the control law with the collision avoidance strategy can converge within a finite time. According to the finite-time sliding mode control law and the artificial potential function collision avoidance strategy, the six-degree-of-freedom space rendezvous is realized while satisfying the terminal position attitude constraints, time constraints and safety constraints, thereby improving the safety of the spacecraft rendezvous process. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 This is a flow chart of the six-degree-of-freedom finite-time spatial rendezvous control method under multiple constraints.

[0130] Figure 2 is the active spacecraft position error varying with time.

[0131] Figure 3 is the active spacecraft velocity error varying with time.

[0132] Figure 4 is the attitude error of the active spacecraft varying with time.

[0133] Figure 5 is the attitude angular velocity error of the active spacecraft varying with time. DETAILED DESCRIPTION

[0134] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below in conjunction with embodiments and corresponding drawings.

[0135] Example: During the on-orbit disposal of a disabled spacecraft in near-Earth space, in order to capture and remove the disabled spacecraft, an active spacecraft equipped with a robotic arm is deployed to control the six-degree-of-freedom spatial rendezvous with the disabled spacecraft under the terminal position attitude constraints, time constraints, and safety constraints.

[0136] like Figure 1As shown, the six-degree-of-freedom finite-time space rendezvous control method under multiple constraints disclosed in this embodiment is specifically implemented as follows:

[0137] Step 1: Based on the Lie group SE (3) framework, a six-degree-of-freedom dynamic model of the active spacecraft and a six-degree-of-freedom dynamic model of the target spacecraft are established respectively. Based on the two obtained six-degree-of-freedom dynamic models, a six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft is established, so that the spacecraft rendezvous process satisfies both the terminal position and terminal attitude constraints.

[0138] Step 1.1: Establish a six-degree-of-freedom dynamic model of the active spacecraft.

[0139] The kinematic equations of an active spacecraft are expressed as

[0140]

[0141] where R c ∈SO(3) represents the attitude rotation matrix of the active spacecraft from its own system to the inertial system along the principal axis of inertia. SO(3) is the Lie group of the special orthogonal matrix representing the attitude of the spacecraft. represents the position vector from the origin of the coordinate system to the center of mass of the active spacecraft in the inertial frame, and They represent the rotational angular velocity and translational velocity of the active spacecraft system, Represents a three-dimensional real vector set. Symbol (·) × Represents the cross product matrix of the vector, for a three-dimensional vector x=[x1,x2,x3] T , the cross product matrix of x(x) × Defined as

[0142]

[0143] Among them, x1, x2, and x3 are the three components of vector x.

[0144] The dynamic equation of an active spacecraft is expressed as

[0145]

[0146] Among them J c is the moment of inertia of the active spacecraft, m c is the mass of the active spacecraft, is the control torque of the active spacecraft, is the disturbance torque of the active spacecraft, is the gravitational field of the active spacecraft, is the control force of the active spacecraft, is the disturbance force of the active spacecraft. The position and attitude of the active spacecraft can be expressed by the variable g of the Lie group SE(3) c Expressed as

[0147]

[0148] 0 1×3 represents a 1×3 zero matrix, and SE(3) is the Lie group of all translational and rotational motions of the spacecraft. The augmented velocity vector of the active spacecraft is expressed as

[0149]

[0150] represents a six-dimensional real vector set. Therefore, under the SE(3) framework, the kinematic equation of Equation (33) and the dynamic equation of Equation (34) can be expressed as

[0151]

[0152] in

[0153]

[0154] is the Lie algebra of the Lie group SE(3), I3 represents the three-dimensional identity matrix, represents a 6×6 real matrix set, ξ c The matrix of the conjugate adjoint mapping is expressed as

[0155]

[0156] 0 3×3 Represents a 3×3 zero matrix.

[0157] Step 1.2: Establish a six-degree-of-freedom dynamic model of the target spacecraft.

[0158] The kinematic and dynamic models of the target spacecraft in the SE(3) framework can be expressed as

[0159]

[0160] in

[0161]

[0162] R t ∈SO(3) represents the attitude rotation matrix of the target spacecraft from the local system to the inertial system along the inertial principal axis, represents the position vector from the origin of the coordinate system to the center of mass of the target spacecraft in the inertial system, and They represent the rotational angular velocity and translational velocity of the target spacecraft in the system. tis the moment of inertia of the target spacecraft, m t is the mass of the target spacecraft, is the gravitational field of the target spacecraft, is the disturbance torque of the target spacecraft, is the disturbance force of the target spacecraft.

[0163] Step 1.3: Based on equation (37) obtained in step 1.1 and equation (38) obtained in step 1.2, a six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft is established.

[0164] The desired position and attitude g of the active spacecraft cd and the angular velocity ξ cd Expressed as

[0165]

[0166] Among them, h d Represents the desired position and attitude relative to the target spacecraft.

[0167]

[0168] The matrix of the adjoint mapping is represented as

[0169]

[0170] in, express The 3×3 block matrix, express The position and attitude error h between the active spacecraft and the target spacecraft is expressed as

[0171] h=(g t ) -1 g c (40)

[0172] The exponential coordinate vector used to represent the active spacecraft position and attitude errors is

[0173]

[0174] in, and The exponential coordinate vectors representing the attitude tracking error and position tracking error, respectively. The exponential coordinate vectors representing the position and attitude errors of the active spacecraft It can be expressed as

[0175]

[0176] in represents a logarithmic mapping.

[0177]

[0178] traces The logarithmic mapping is expressed as

[0179]

[0180] in, Indicates (h d ) -1 h is a 3×3 block matrix, Indicates (h d ) -1 h is a 3×1 block matrix, is the Lie algebra of the Lie group SO(3). (h d ) -1 The logarithmic mapping of h is expressed as

[0181]

[0182] in

[0183]

[0184] Among them, ψ1, ψ2, ψ3 are vectors Ψ = [ψ1, ψ2, ψ3] T The three components.

[0185] The relative velocity of the active spacecraft relative to the target spacecraft in this system Expressed as

[0186]

[0187] in and They represent the rotational angular velocity and translational velocity of the active spacecraft relative to the target spacecraft in the system.

[0188]

[0189] h -1 The matrix of the adjoint mapping is represented as

[0190]

[0191] in, Indicates h -1 The 3×3 block matrix, Indicates h -1 A 3×1 block matrix.

[0192] The kinematics in the exponential coordinate system can be expressed as

[0193]

[0194] Expressed as

[0195]

[0196] in

[0197]

[0198] and relative acceleration It can be expressed as

[0199]

[0200] The matrix of the adjoint mapping is expressed as

[0201]

[0202] Substituting Equation (37) into Equation (46), we can obtain the six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft:

[0203]

[0204] Step 2. Based on the six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft obtained in step 1, a six-degree-of-freedom spatial rendezvous sliding mode control law is designed, and the parameter conditions of the control law gain are determined so that the control law can converge within a finite time, meet the time window constraints of the rendezvous mission, and improve the error convergence speed.

[0205] Step 2.1: Design a six-degree-of-freedom spatial rendezvous sliding mode control law.

[0206] Design of sliding surface under the SE(3) framework

[0207]

[0208] Where C=diag(c1,c2,c3,c4,c5,c6) is a positive definite matrix, q and p are positive odd numbers and satisfy q>p. The control law is designed as

[0209]

[0210] in K=diag(k1,k2,...,k6) is a positive definite gain matrix, and the sign function sgn(s) is

[0211]

[0212] where s = [s1, s2, ..., s6] T , s i ,i=1,2,...,6 represents the six components of the sliding surface s.

[0213] Step 2.2: Determine the parameter conditions of the control law gain so that the control law can converge within a finite time.

[0214] Since the external perturbation is bounded, define the perturbation boundary Therefore, for the external disturbances on active spacecraft and external disturbances to the target spacecraft have

[0215]

[0216] in i=1,2,...,6 respectively represent For the positive definite Lyapunov function V(t), when it satisfies

[0217]

[0218] It is semi-negative timing, the controller can be stable in a finite time, and the convergence time satisfies

[0219]

[0220] Where c>0, V0 is the value of the Lyapunov function at the initial moment. Design Lyapunov function

[0221]

[0222] Perform the first-order differentiation of Equation (53)

[0223]

[0224] Substituting equations (44) and (47) into equation (54), we can obtain

[0225]

[0226] Substituting equation (49) into equation (55) we can obtain

[0227]

[0228] make i=1,2,...,6, then

[0229]

[0230] 0<γ<1, for From formula (51), we can see that when the positive definite matrix gain K satisfies When , the control law (49) can make the error converge within a finite time.

[0231] Step 3. Based on the finite-time sliding mode control law for the six-degree-of-freedom space rendezvous designed in step 2, design an artificial potential function collision avoidance control law, determine the parameter conditions of the artificial potential function so that the control law with the collision avoidance strategy can converge within a finite time, and according to the finite-time sliding mode control law and the artificial potential function collision avoidance strategy, realize the six-degree-of-freedom space rendezvous while satisfying the terminal position attitude constraints, time constraints and safety constraints, thereby improving the safety of the spacecraft rendezvous process.

[0232] Step 3.1: Design the collision avoidance control law of the six-degree-of-freedom spatial intersection artificial potential function.

[0233] The distance between the active spacecraft and the target spacecraft is defined as

[0234]

[0235] Where W>0 is a positive definite matrix

[0236]

[0237] W1 has physical units given by the ratio of the square of the length unit to the square of the angle unit, and W2 is dimensionless. Define the positive definite artificial potential function

[0238]

[0239] Where ε is a positive parameter, r d represents the desired relative distance between the active spacecraft and the target spacecraft. The control force generated to prevent collision is

[0240]

[0241] in

[0242]

[0243] After adding the collision avoidance strategy to the original control law (49), the new control law is:

[0244]

[0245] Step 3.2: Determine the parameter conditions of the artificial potential function so that the control law with the collision avoidance strategy can converge within a finite time.

[0246] After the collision avoidance strategy is introduced, the six-degree-of-freedom relative dynamics model (47) is modified to

[0247]

[0248] In order to ensure that the system can still converge within a limited time after adding the collision avoidance strategy, the new control law (61) and the six-degree-of-freedom relative dynamics model (62) are substituted into the Lyapunov function (53) and first-order differentiated to obtain

[0249]

[0250] The artificial potential function parameter ε is selected so that Then there is

[0251]

[0252] in i=1,2,...,6 means The six components of From formula (51), we can see that the selected artificial potential function parameter ε can make When the collision avoidance strategy is added, the control law (61) can make the error converge within a finite time.

[0253] In this embodiment, the control gain q=5, p=3, C=diag(0.02, 0.005, 0.005, 8×10 -5 ,1×10 -6 ,8×10 -5 ), K=diag(1×10 -5 ,8×10 -6 ,5×10 -6 ,0.1,0.01,0.1). The position and attitude parameters of the active spacecraft are shown in Table 1, and the position and attitude parameters of the target spacecraft are shown in Table 2. The position error of the active spacecraft changes with time as shown in Figure 2 As shown, the active spacecraft velocity error varies with time as Figure 3 As shown, the attitude error of the active spacecraft changes with time as Figure 4 As shown, the attitude angular velocity error of the active spacecraft changes with time as follows Figure 5 shown.

[0254] Table 1 Active spacecraft position and attitude parameters

[0255]

[0256] Table 2 Target spacecraft position and attitude parameters

[0257]

[0258] The six-degree-of-freedom finite-time space rendezvous control problem under multiple constraints includes the six-degree-of-freedom relative dynamics model of the active spacecraft relative to the target spacecraft determined by Equation (47) and the six-degree-of-freedom space rendezvous finite-time sliding mode control law with collision avoidance strategy determined by Equation (61). Based on the six-degree-of-freedom relative dynamics model, a finite-time sliding mode control law and an artificial potential function collision avoidance strategy are designed to achieve six-degree-of-freedom space rendezvous while satisfying the terminal position attitude constraints, time constraints and safety constraints.

[0259] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A six-degree-of-freedom finite-time spatial rendezvous control method under multiple constraints, characterized by: The following steps are included: Step 1: Based on the Lie group SE (3) framework, a six-degree-of-freedom dynamic model of the active spacecraft and a six-degree-of-freedom dynamic model of the target spacecraft are established respectively. Based on the two obtained six-degree-of-freedom dynamic models, a six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft is established, so that the spacecraft rendezvous process satisfies both the terminal position and terminal attitude constraints. Step 2: Based on the six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft obtained in step 1, a six-degree-of-freedom spatial rendezvous sliding mode control law is designed, and the parameter conditions of the control law gain are determined so that the control law can converge within a finite time, meet the time window constraint of the rendezvous mission, and improve the error convergence speed; Step 3. Based on the finite-time sliding mode control law for the six-degree-of-freedom space rendezvous designed in step 2, design an artificial potential function collision avoidance control law, determine the parameter conditions of the artificial potential function so that the control law with the collision avoidance strategy can converge within a finite time, and according to the finite-time sliding mode control law and the artificial potential function collision avoidance strategy, realize the six-degree-of-freedom space rendezvous while satisfying the terminal position attitude constraints, time constraints and safety constraints, thereby improving the safety of the spacecraft rendezvous process.

2. The multi-constrained six-degree-of-freedom finite-time spatial rendezvous control method according to claim 1, characterized in that: Step 1 is implemented as follows: Step 1.1: Establish a six-degree-of-freedom dynamic model of the active spacecraft; The kinematic equations of an active spacecraft are expressed as where R c ∈SO(3) represents the attitude rotation matrix of the active spacecraft from its own system to the inertial system along the principal axis of inertia. SO(3) is the Lie group of the special orthogonal matrix representing the attitude of the spacecraft. represents the position vector from the origin of the coordinate system to the center of mass of the active spacecraft in the inertial frame, and They represent the rotational angular velocity and translational velocity of the active spacecraft system, represents a three-dimensional real vector set; the symbol (·) × Represents the cross product matrix of the vector, for a three-dimensional vector x=[x1,x2,x3] T , the cross product matrix of x(x) × Defined as Among them, x1, x2, x3 are the three components of vector x; The dynamic equation of an active spacecraft is expressed as Among them J c is the moment of inertia of the active spacecraft, m c is the mass of the active spacecraft, is the control torque of the active spacecraft, is the disturbance torque of the active spacecraft, is the gravitational field of the active spacecraft, is the control force of the active spacecraft, is the disturbance force of the active spacecraft; the position and attitude of the active spacecraft can be expressed by the variable g of the Lie group SE(3) c Expressed as 0 1×3 represents a 1×3 zero matrix, SE(3) is the Lie group of all translational and rotational motions of the spacecraft; the augmented velocity vector of the active spacecraft is expressed as represents a six-dimensional real vector set; therefore, in the SE(3) framework, the kinematic equation of formula (1) and the dynamic equation of formula (2) are expressed as in is the Lie algebra of the Lie group SE(3), I3 represents the three-dimensional identity matrix, represents a 6×6 real matrix set, ξ c The matrix of the conjugate adjoint mapping is expressed as 0 3×3 represents a 3×3 zero matrix; Step 1.2: Establish a six-degree-of-freedom dynamic model of the target spacecraft; The kinematic and dynamic models of the target spacecraft in the SE(3) framework are expressed as in R t ∈SO(3) represents the attitude rotation matrix of the target spacecraft from the local system to the inertial system along the inertial principal axis, represents the position vector from the origin of the coordinate system to the center of mass of the target spacecraft in the inertial system, and are the rotational angular velocity and translational velocity of the target spacecraft in its own system; J t is the moment of inertia of the target spacecraft, m t is the mass of the target spacecraft, is the gravitational field of the target spacecraft, is the disturbance torque of the target spacecraft, is the disturbance force of the target spacecraft; Step 1.3: Based on equation (5) obtained in step 1.1 and equation (6) obtained in step 1.2, establish a six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft; The desired position and attitude g of the active spacecraft cd and the angular velocity ξ cd Expressed as Among them, h d Represents the desired position and attitude relative to the target spacecraft. The matrix of the adjoint mapping is represented as in, express The 3×3 block matrix, express The position and attitude error h between the active spacecraft and the target spacecraft is expressed as h=(g t ) -1 g c (8) The exponential coordinate vector used to represent the active spacecraft position and attitude errors is in, and The exponential coordinate vectors representing the attitude tracking error and position tracking error respectively; the exponential coordinate vectors representing the position and attitude errors of the active spacecraft It can be expressed as in represents a logarithmic mapping; for traces The logarithmic mapping is expressed as in, Indicates (h d ) -1 h is a 3×3 block matrix, Indicates (h d ) -1 h is a 3×1 block matrix, is the Lie algebra of the Lie group SO(3); (h d ) -1 The logarithmic mapping of h is expressed as in Among them, ψ1, ψ2, ψ3 are vectors Ψ = [ψ1, ψ2, ψ3] T The three components of The relative velocity of the active spacecraft relative to the target spacecraft in this system Expressed as in and They represent the rotational angular velocity and translational velocity of the active spacecraft relative to the target spacecraft in the system; h -1 The matrix of the adjoint mapping is represented as in, Indicates h -1 The 3×3 block matrix, Indicates h -1 3×1 block matrix; The kinematic equation in the exponential coordinate system is expressed as Expressed as in and relative acceleration Expressed as The matrix of the adjoint mapping is expressed as Substituting Equation (5) into Equation (14), we can obtain the six-degree-of-freedom relative dynamic model of the active spacecraft relative to the target spacecraft:

3. The multi-constrained six-degree-of-freedom finite-time spatial rendezvous control method according to claim 2, characterized in that: Step 2 is implemented as follows: Step 2.1: Design a six-degree-of-freedom spatial intersection sliding mode control law; Design of sliding surface under the SE(3) framework Where C = diag (c1, c2, c3, c4, c5, c6) is a positive definite matrix, q and p are positive odd numbers and satisfy q>p; the control law is designed as in K=diag(k1,k2,...,k6) is a positive definite gain matrix, and the sign function sgn(s) is where s = [s1, s2, ..., s6] T , s i ,i=1,2,...,6 represents the six components of the sliding surface s; Step 2.2: Determine the parameter conditions of the control law gain so that the control law can converge within a finite time; Since the external perturbation is bounded, define the perturbation boundary Therefore, for the external disturbances on active spacecraft and external disturbances to the target spacecraft have in Respectively Six components; for the positive definite Lyapunov function V(t), when it satisfies It is semi-negative timing, the controller is stable in a finite time, and the convergence time satisfies Where c>0, 0<θ<1, V0 is the value of the Lyapunov function at the initial moment; Design the Lyapunov function Perform the first-order differentiation of Equation (21) Substituting equations (12) and (15) into equation (22), we can obtain Substituting formula (17) into formula (23) we can obtain make Then there is 0<γ<1, for The minimum eigenvalue of ; From formula (19), we know that when the positive definite matrix gain K satisfies When , the control law (17) can make the error converge within a finite time.

4. The multi-constrained six-degree-of-freedom finite-time spatial rendezvous control method according to claim 3, characterized in that: Step 3 is implemented as follows: Step 3.1: Design the collision avoidance control law of the six-degree-of-freedom space intersection artificial potential function; The distance between the active spacecraft and the target spacecraft is defined as Where W>0 is a positive definite matrix W1 has physical units given by the ratio of the square of the length unit to the square of the angle unit, and W2 is dimensionless; define the positive definite artificial potential function Where ε is a positive parameter, r d represents the desired relative distance between the active spacecraft and the target spacecraft; the control force generated to prevent collision is in After adding the collision avoidance strategy to the original control law (17), the new control law is: Step 3.2: Determine the parameter conditions of the artificial potential function so that the control law with the collision avoidance strategy can converge within a finite time; After the collision avoidance strategy is introduced, the six-degree-of-freedom relative dynamics model (15) is modified to In order to ensure that the system can still converge within a limited time after adding the collision avoidance strategy, the new control law (29) and the six-degree-of-freedom relative dynamics model (30) are substituted into the Lyapunov function (21) and the first-order differential is performed to obtain The artificial potential function parameter ε is selected so that Then there is in express The six components of From formula (19), we can see that the selected artificial potential function parameter ε can make When , the control law (29) after adding the collision avoidance strategy can make the error converge within a finite time; The six-degree-of-freedom finite-time space rendezvous control problem under multiple constraints includes the six-degree-of-freedom relative dynamics model of the active spacecraft relative to the target spacecraft determined by Equation (15) and the six-degree-of-freedom space rendezvous finite-time sliding mode control law with collision avoidance strategy determined by Equation (29). Based on the six-degree-of-freedom relative dynamics model, a finite-time sliding mode control law and an artificial potential function collision avoidance strategy are designed to achieve six-degree-of-freedom space rendezvous while satisfying the terminal position attitude constraints, time constraints and safety constraints.

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