Six-degree-of-freedom finite time space intersection control method under multiple constraints

Abstract

The invention discloses a six-degree-of-freedom finite time space intersection control method under multiple constraints, and belongs to the technical field of space. According to the implementation method, a six-degree-of-freedom kinetic model is established based on a Lie group SE (3) framework, so that the spacecraft rendezvous process can meet position end constraints and attitude end constraints, the attitude-orbit coupling problem caused by thruster installation errors in actual engineering is fully considered, the spacecraft rendezvous precision is improved, and the spacecraft rendezvous performance is improved. And the unwinding problem caused by a traditional six-degree-of-freedom dual quaternion representation method is avoided. A finite time sliding mode control strategy is designed, so that the rendezvous process can meet task time window constraints, and the error convergence speed is increased. In order to solve potential collision risks in the rendezvous process and meet safety constraints of rendezvous tasks, an artificial potential function is introduced, collision avoidance in the rendezvous process is achieved, and safety of the spacecraft rendezvous process is improved. The rendezvous time can be shortened, the space rendezvous precision of the spacecraft is improved, and the safety of the rendezvous process of the spacecraft is improved.

Description

Technical Field

[0001] The 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, with the successive networking of satellite constellations such as Starlink and OneWeb, the congestion in near-Earth space has intensified, increasing the risk of collisions between active spacecraft and non-cooperative objects. In order to dispose of failed spacecraft in orbit, deploying active spacecraft equipped with robotic arms is one of the widely studied solutions, which can capture and remove failed spacecraft through precise rendezvous. In addition, in some complex deep space exploration missions, the precise rendezvous operation between the ascender and the orbiter is crucial for sample return. Therefore, space rendezvous plays a vital role in space missions.

[0003] Combined with engineering practice, since the spacecraft space rendezvous needs to satisfy the terminal position and attitude errors of zero at the same time, the installation error of the thruster will cause the spacecraft attitude and orbit to be coupled, and the spacecraft needs to be modeled in six degrees of freedom. Since space debris removal missions usually have strict time constraints and deep space exploration mission sequences have strict time windows, the spacecraft space rendezvous process is time-sensitive and must be completed within a limited time. The control method should meet the finite time convergence condition. In addition, there is a risk of collision between the large physical attachments of the active spacecraft and the target spacecraft, so the rendezvous process must consider the collision avoidance control strategy to improve 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 achieving safe rendezvous.

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

[0006] The invention discloses a six-degree-of-freedom finite-time space rendezvous control method under multiple constraints. 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 terminal constraint while also satisfying the attitude terminal 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 task 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 task, an artificial potential function is introduced to achieve collision avoidance in the rendezvous process and improve the safety of the rendezvous process. The invention can shorten the rendezvous time, improve the spacecraft space rendezvous accuracy, and improve the safety of the spacecraft rendezvous process.

[0007] The 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 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 special orthogonal matrices 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 (2) × Represents the cross product matrix of a 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, 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 representation of the conjugate adjoint mapping is

[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 this 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 of the active spacecraft g cd and the angular velocity ξ cd Expressed as

[0036]

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

[0038]

[0039] The matrix representation of the adjoint mapping is

[0040]

[0041] in, express A 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 of attitude tracking error and position tracking error are respectively. The exponential coordinate vectors of active spacecraft position and attitude errors are It can be expressed as

[0046]

[0047] in represents a logarithmic mapping.

[0048]

[0049] trace The logarithmic mapping is expressed as

[0050]

[0051] in, Indicates (h d ) -1 The 3×3 block matrix of h, Indicates (h d ) -1 The 3×1 block matrix of h, 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 speed 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 this system.

[0059]

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

[0061]

[0062] in, Indicates h -1 A 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 the six-degree-of-freedom spatial rendezvous sliding mode control law.

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

[0078]

[0079] Where C = diag (c1, c2, c3, c4, c5, c6) is a positive definite matrix, q, 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 the external disturbances to the target spacecraft have

[0086]

[0087] in i=1,2,...,6 represent For a positive 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 of Lyapunov function

[0092]

[0093] Taking the first-order differential of equation (21)

[0094]

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

[0096]

[0097] Substituting equation (17) into equation (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, 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 achieved 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 space intersection artificial potential function.

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

[0105]

[0106] Among them, 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.

[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, the original control law (17) becomes

[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 collision avoidance strategy can still converge within a limited time, 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 differentiation is performed to obtain

[0120]

[0121] The parameter ε of the artificial potential function 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 under the conditions of 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 in 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 terminal constraint and the attitude terminal constraint, fully considers the attitude-orbit coupling problem caused by the thruster installation error 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 six-degree-of-freedom finite-time space rendezvous control method under multiple constraints disclosed in the present invention designs an artificial potential function collision avoidance control law on the basis of the designed six-degree-of-freedom space rendezvous finite-time sliding mode control law, and determines the parameter conditions of the artificial potential function 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 under the conditions of 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 active spacecraft attitude error varying with time.

[0133] Figure 5 is the variation of the attitude angular velocity error of the active spacecraft over 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: In the process of on-orbit disposal of a failed spacecraft in near-Earth space, in order to achieve the capture and removal of the failed spacecraft, the active spacecraft equipped with a robotic arm is deployed to control the six-degree-of-freedom space rendezvous with the failed 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 has the following specific implementation steps:

[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 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 special orthogonal matrices 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 a 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, 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 (33) and the dynamic equation of (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 representation of the conjugate adjoint mapping is

[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 this 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 of the active spacecraft g cd and the angular velocity ξ cd Expressed as

[0165]

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

[0167]

[0168] The matrix representation of the adjoint mapping is

[0169]

[0170] in, express A 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 of attitude tracking error and position tracking error are respectively. The exponential coordinate vectors of active spacecraft position and attitude errors are It can be expressed as

[0175]

[0176] in represents a logarithmic mapping.

[0177]

[0178] trace The logarithmic mapping is expressed as

[0179]

[0180] in, Indicates (h d ) -1 The 3×3 block matrix of h, Indicates (h d ) -1 The 3×1 block matrix of h, 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 speed 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 this system.

[0188]

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

[0190]

[0191] in, Indicates h -1 A 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 the six-degree-of-freedom spatial rendezvous sliding mode control law.

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

[0207]

[0208] Where C = diag (c1, c2, c3, c4, c5, c6) is a positive definite matrix, q, 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 the external disturbances to the target spacecraft have

[0215]

[0216] in i=1,2,...,6 represent For a positive 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 of Lyapunov function

[0221]

[0222] Taking the first-order differential of equation (53)

[0223]

[0224] Substituting equation (44) and equation (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, 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 achieved 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 space intersection artificial potential function.

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

[0234]

[0235] Among them, 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.

[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, the original control law (49) becomes

[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 collision avoidance strategy can still converge within a limited time, the new control law (61) and the six-degree-of-freedom relative dynamics model (62) are substituted into the Lyapunov function (53) and the first-order differentiation is performed to obtain

[0249]

[0250] The parameter ε of the artificial potential function 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 active spacecraft attitude error changes with time as Figure 4 As shown in the figure, the angular velocity error of the active spacecraft attitude changes with time as 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 realize the six-degree-of-freedom space rendezvous under the conditions of satisfying the terminal position attitude constraints, time constraints and safety constraints.

[0259] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above 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, and based on the two 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 dynamics 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 limited 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, 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 achieved while satisfying the terminal position attitude constraints, time constraints and safety constraints, thereby improving the safety of the spacecraft rendezvous process.

2. The six-degree-of-freedom finite-time space rendezvous control method under multiple constraints as claimed in 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 special orthogonal matrices 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 a 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 They represent the rotational angular velocity and translational velocity of the target spacecraft in the 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: According to 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; The desired position and attitude of the active spacecraft g cd and the angular velocity ξ cd Expressed as Among them, h d Represents the expected position and attitude relative to the target spacecraft. The matrix representation of the adjoint mapping is in, express A 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 trace The logarithmic mapping is expressed as in, Indicates (h d ) -1 The 3×3 block matrix of h, 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 speed 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 this system; h -1 The matrix representation of the adjoint mapping is in, Indicates h -1 A 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 six-degree-of-freedom finite-time space rendezvous control method under multiple constraints as claimed in claim 2, characterized in that: Step 2 is implemented as follows: Step 2.1: Design the six-degree-of-freedom spatial intersection sliding mode control law; Design of sliding surface in the SE(3) framework Where C = diag (c1, c2, c3, c4, c5, c6) is a positive definite matrix, q, p are positive odd numbers and satisfy q>p; the control law design is 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 the external disturbances to the target spacecraft have in Respectively six components; for a positive 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 Taking the first-order differential of equation (21) Substituting equation (12) and equation (15) into equation (22), we can obtain Substituting equation (17) into equation (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 six-degree-of-freedom finite-time space rendezvous control method under multiple constraints as claimed in claim 3, characterized in that: Step 3 is implemented as follows: Step 3.1: Design the collision avoidance control law of the artificial potential function for six-DOF spatial intersection; The distance between the active spacecraft and the target spacecraft is defined as Among them, 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; the positive definite artificial potential function is defined as 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, the original control law (17) becomes 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 collision avoidance strategy can still converge within a limited time, 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 differentiation is performed to obtain The parameter ε of the artificial potential function 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 under the conditions of satisfying the terminal position attitude constraints, time constraints and safety constraints.

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