Simplified attitude distributed control method for leader-follower spacecraft formation with pointing constraints

Abstract

The application provides a leader-follower spacecraft formation simplified attitude distributed control method with pointing constraints, which comprises the following steps: first, a simplified attitude error model between the spacecraft is established; second, a pointing constraint model of each follower spacecraft is constructed; third, an artificial potential field of each follower spacecraft is designed according to the pointing constraint, the simplified attitude error and a communication topology; fourth, a Lyapunov function is constructed based on the artificial potential field function, and a distributed cooperative virtual control quantity of each follower spacecraft is designed; and fifth, the difference between the angular velocity vector of each follower spacecraft and the virtual control quantity is taken as a sliding mode variable, a sliding mode surface is constructed, and a distributed cooperative sliding mode control law of each follower spacecraft is designed. The application can realize that the pointing vector of the follower spacecraft converges to the pointing vector of the leader spacecraft fixed in the inertial space under the condition of the undirectional communication topology, and can meet the pointing constraint of the follower spacecraft in the attitude maneuvering process.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control technology, and more specifically to a distributed cooperative control method for simplifying the attitude of multi-spacecraft formations with pointing constraints. Background Technology

[0002] Spacecraft swarms can distribute the functions of a traditional large spacecraft across several smaller spacecraft; these smaller spacecraft can achieve the functions of a large spacecraft through mutual cooperation, and offer advantages such as low cost, high adaptability, and high reliability. Therefore, spacecraft swarms represent an important direction for future spacecraft development.

[0003] Attitude consistency of spacecraft formations is crucial for technologies such as distributed astronomical observations and distributed synthetic aperture radar. In some cases, it is only necessary to point the spacecraft's aiming vector in a specific direction in inertial space without three-axis control. Rotational motion around the aiming vector does not affect the spacecraft's functionality. This motion, which only considers the aiming vector's direction in inertial space, is called simplified attitude motion, and the direction of the aiming vector represents the spacecraft's simplified attitude. Simplified attitude control only stabilizes or tracks two degrees of freedom of the spacecraft's attitude, saving fuel and avoiding attitude description singularities and redundancy of attitude variables. On the other hand, during spacecraft attitude adjustments, certain sensors (such as infrared sensors and star sensors) cannot be pointed at areas with strong infrared radiation or visible light; otherwise, it will lead to sensor damage or performance degradation. Therefore, it is essential to ensure that relevant sensors avoid pointing into prohibited areas during the spacecraft's attitude control process.

[0004] Because the rotational motion around the aiming vector in simplified attitude control is not fully controlled, it is impossible to derive a distributed cooperative control protocol for the simplified attitude of a multi-spacecraft formation based on the spacecraft aiming vector error using consistency theory. Furthermore, the pointing constraint of the tracking spacecraft is a constraint on the angle between the aiming vector and the pointing prohibition vector, making it even more difficult to integrate with the vector error. Therefore, designs based on vector error and consistency theory are not suitable for distributed cooperative control of the simplified attitude of multi-spacecraft formations considering pointing constraints. Summary of the Invention

[0005] To overcome the limitations of consistency theory in the distributed cooperative control of simplified attitude of multi-spacecraft formations, as well as the difficulties brought about by spacecraft pointing constraints, this invention proposes a simplified attitude distribution control method for lead and follower spacecraft formations with pointing constraints. This method can ensure that the aiming vector of the follower spacecraft converges to the aiming vector of the lead spacecraft fixed in inertial space, while the follower spacecraft can avoid pointing prohibition areas during attitude maneuvers.

[0006] The technical solution of this invention is as follows:

[0007] Step 1: Based on the angle between the aiming vectors of each spacecraft in the spacecraft formation, establish a simplified mathematical model of attitude error between the spacecraft; the spacecraft formation includes one lead spacecraft and n follower spacecraft.

[0008] Step 2: Consider the minimum angle between the aiming vector and the pointing prohibition vector of the follower spacecraft, and construct a mathematical model of the pointing constraint for each follower spacecraft;

[0009] Step 3: Based on the simplified attitude error model described in Step 1, the pointing constraint mathematical model described in Step 2, and the communication topology between spacecraft, design the artificial potential field function for each following spacecraft;

[0010] Step 4: Sum the artificial potential field functions of all following spacecraft as Lyapunov functions, and design the virtual control quantities for each following spacecraft accordingly;

[0011] Step 5: Use the difference between the angular velocity vector of each follower spacecraft and the virtual control quantity as the sliding mode variable, construct the sliding mode surface, and design the distributed sliding mode control law for each follower spacecraft based on the constructed sliding mode surface.

[0012] Furthermore, the simplified attitude error mathematical model established in step 1 includes the error model between the aiming vector of the following spacecraft and the aiming vector of the lead spacecraft, as well as the error model between the aiming vectors of the following spacecraft.

[0013] The error model between the aiming vector of the follower spacecraft and the aiming vector of the lead spacecraft is as follows:

[0014] The error between the aiming vector of the i-th follower spacecraft and the aiming vector of the lead spacecraft is expressed as follows:

[0015]

[0016] After differentiation, it becomes

[0017]

[0018] in The aiming vector of the pilot spacecraft in the inertial coordinate system The following represents R i For the body coordinate system fixed to the i-th following spacecraft to inertial coordinate system The rotation matrix, η i Indicates the i-th spacecraft body coordinate system The unit vector fixed to the spacecraft, function (·). × Defined as

[0019]

[0020] Let be the angular velocity vector of the i-th following spacecraft in the volume coordinate system. The representation in;

[0021] The error model between the aiming vectors of the following spacecraft is:

[0022] The error between the aiming vector of the i-th follower spacecraft and the aiming vector of the j-th follower spacecraft is expressed as follows:

[0023]

[0024] After differentiation, it becomes

[0025]

[0026] Where R j For the body coordinate system fixed to the j-th following spacecraft to inertial coordinate system The rotation matrix, η j Indicates the j-th following spacecraft body coordinate system The unit vector fixed to the spacecraft below. Let be the angular velocity vector of the j-th following spacecraft in the volume coordinate system. The representation in the text.

[0027] Furthermore, in step 2, the mathematical model for the pointing constraint of the i-th following spacecraft is:

[0028]

[0029] in For inertial coordinate system The origin points to the h-th unit vector pointing to the center of the forbidden region; θ min This is the minimum angle between the target vector of the spacecraft being followed and the pointing prohibition vector.

[0030] Furthermore, the artificial potential field function designed in step 3 is:

[0031]

[0032] in `a` is a constant, `m` is the number of points to forbidden regions; ij For the communication topology adjacency matrix of n follower spacecraft, when the i-th follower spacecraft and the j-th follower spacecraft can communicate with each other, a ij =1, otherwise a ij =0; a i0Let a be an element of the communication topology matrix between the lead spacecraft and the follower spacecraft. If the i-th follower spacecraft can obtain the state of the lead spacecraft, then a i0 =1, otherwise a i0 =0.

[0033] Furthermore, in step 4, the virtual control variable designed for the i-th following spacecraft is:

[0034]

[0035] in ψ is a constant; i for

[0036]

[0037] Furthermore, in step 5, the constructed sliding surface is...

[0038]

[0039] J i Let be the inertia matrix of the i-th spacecraft; the final distributed sliding mode control law is:

[0040]

[0041] Where τ i Let the torque be the force acting on the i-th following spacecraft. The constant is k3 ≥ d max d max For the disturbance d i The upper boundary.

[0042] Beneficial effects

[0043] This invention provides a distributed cooperative control method for simplifying the attitude of a navigator-follower spacecraft formation, taking into account pointing constraints. Under perturbed conditions, when the communication topology of the spacecraft formation is a connected undirected graph, it can not only achieve the convergence of the aiming vector of the follower spacecraft to the aiming vector of the navigator spacecraft, which is fixed in inertial space, but also satisfy the pointing constraints of the follower spacecraft during attitude maneuvers.

[0044] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0045] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0046] Figure 1Design steps for a simplified attitude distribution control method for guiding and following spacecraft formations with directional constraints;

[0047] Figure 2 Spacecraft communication topology in an example of this invention;

[0048] Figure 3 The initial state of the spacecraft and the aiming vector in the examples of this invention;

[0049] Figure 4 Comparison of the motion trajectories of the aiming vectors of all spacecraft on a unit sphere in the examples of this invention;

[0050] Figure 5 A comparison of the movement trajectories of the aiming vectors of all spacecraft in the longitude and latitude planes in the examples of this invention;

[0051] Figure 6 The aiming vector variation curves of all following spacecraft in the examples of this invention;

[0052] Figure 7 Error variation curves between the aiming vectors of all following spacecraft in the examples of this invention;

[0053] Figure 8 Examples of this invention include a pointing constraint change curve that follows the spacecraft. Detailed Implementation

[0054] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0055] This embodiment proposes a simplified attitude distribution control method for a directionally constrained lead and follow spacecraft formation. The aim is to ensure that the aiming vector of the follow spacecraft converges to the aiming vector of the lead spacecraft fixed in inertial space, while the follow spacecraft can avoid the pointing prohibition area during attitude maneuvers.

[0056] First, let's explain the relevant explanations regarding leading and following spacecraft formations:

[0057] The formation consists of n+1 spacecraft, with the lead spacecraft numbered 0 and the follower spacecraft numbered 1, 2, ..., n. The communication topology between the follower spacecraft is shown in the communication topology diagram. The description is that its adjacency matrix is ​​A = [a ij When the i-th follower spacecraft and the j-th follower spacecraft are able to communicate with each other, a ij =1; otherwise a ij =0, and the diagonal element a ii =0. The communication topology between the lead spacecraft and the follower spacecraft is represented by matrix B = diag([a10 ,a 20 ,…,a n0 The description states that if the i-th following spacecraft can obtain the state of the lead spacecraft, a i0 =1; otherwise a i0 =0. Communication topology diagram They are connected, and at least one follower spacecraft can obtain information from the lead spacecraft.

[0058] Let the body coordinate system of the i-th spacecraft be ? Its origin O B Located at the center of mass of the i-th spacecraft, the x-axis coincides with the principal axis of maximum inertia of the i-th spacecraft, the z-axis coincides with the principal axis of minimum inertia of the i-th spacecraft, and the y-axis forms a right-handed coordinate system with the x-axis and z-axis. Let the inertial coordinate system be denoted as . Its origin and coordinate axes are fixed in inertial space, forming a right-handed coordinate system.

[0059] If we consider the spacecraft as a rigid body, then the attitude of the i-th spacecraft can be determined by the body coordinate system fixed to the spacecraft. to inertial coordinate system rotation matrix R i In other words, matrix R i Belongs to the real special orthogonal group The rotational kinematics of the i-th spacecraft can be expressed as follows:

[0060]

[0061] In the formula: Let ω be the angular velocity vector of the i-th spacecraft in volume coordinates. In the representation, the function (·) × Defined as

[0062]

[0063] The attitude dynamics equation of the i-th spacecraft is:

[0064]

[0065] In the formula: J i Let τ be the inertia matrix of the i-th spacecraft; i d represents the torque acting on the i-th spacecraft; i Let be the disturbance acting on the i-th spacecraft.

[0066] Based on the above explanation of how to lead and follow spacecraft formations, the simplified attitude distribution control method in this embodiment will be explained in detail below:

[0067] Step 1: Based on the angle between the aiming vectors of each spacecraft in the spacecraft formation, establish a simplified mathematical model of attitude error between spacecraft.

[0068] Using η i In the i-th spacecraft body coordinate system The unit vector fixed to the spacecraft needs to be η when performing simplified attitude control. i A specific direction pointing into inertial space is called η. i Let η be the aiming vector of the i-th spacecraft. i In the inertial coordinate system Below is

[0069]

[0070] Differentiating the above equation, we obtain the simplified kinematic equations for the attitude.

[0071]

[0072] The error between the aiming vector of the follower spacecraft and the aiming vector of the lead spacecraft is expressed as:

[0073]

[0074] In the formula: The aiming vector of the pilot spacecraft in the inertial coordinate system The following representation is a constant unit vector determined by the task. Since the aiming vector is a unit vector, therefore e i ≥0. Taking the derivative of the above equation, we obtain the error model for the simplified attitude motion of the i-th spacecraft:

[0075]

[0076] The aiming vector η of the i-th spacecraft i With the aiming vector η of the j-th spacecraft j The error between them can be expressed as

[0077]

[0078] Taking the derivative of the above equation yields the simplified attitude consistency error model for spacecraft formation:

[0079]

[0080] Since the aiming vector is a unit vector, therefore e ij ≥0.

[0081] Step 2: Consider the minimum angle between the aiming vector and the pointing prohibition vector of the follower spacecraft, and construct a pointing constraint mathematical model for each follower spacecraft.

[0082] From the inertial coordinate system The unit vector pointing from the origin to the h-th point pointing to the center of the forbidden region is called the forbidden vector, which represents the direction of the forbidden region in the inertial coordinate system. Below is Then in the body coordinate system of the i-th spacecraft The following is represented as

[0083]

[0084] During attitude maneuvers, the spacecraft must ensure that η i With n ih Maintain at least θ between min The included angle, to ensure the safety of the sensor, i.e.

[0085] n ih ·η i =cosθ≤cosθ min

[0086] In the formula: θ is η i With n ih The angle between them. (The last part, "n", appears to be a typo and can be omitted.) ih Substituting the expression into the above equation yields the mathematical model pointing to the prohibition constraint.

[0087]

[0088] f ih The derivative is

[0089]

[0090] Step 3: Based on the simplified attitude error model described in Step 1, the pointing constraint mathematical model described in Step 2, and the communication topology between spacecraft, design the artificial potential field function for each following spacecraft:

[0091]

[0092] In the formula: P is a constant, where m is the number of points to forbidden regions. i The derivative with respect to time is

[0093]

[0094] Step 4: Sum the artificial potential field functions of all following spacecraft as Lyapunov functions, and design the virtual control quantities for each following spacecraft accordingly;

[0095] Choose the Lyapunov function

[0096]

[0097] Then the derivative of V1 with respect to time is

[0098]

[0099] Therefore, the virtual control quantity is designed as follows:

[0100]

[0101] In the formula: ψ is a constant; i for

[0102]

[0103] Step 5: Use the difference between the angular velocity vector of each follower spacecraft and the virtual control quantity as the sliding mode variable, construct the sliding mode surface, and design the distributed sliding mode control law for each follower spacecraft based on the constructed sliding mode surface.

[0104] Define the sliding surface as

[0105]

[0106] For s i Differentiate, and we get

[0107]

[0108] Based on sliding mode control theory, the approach law is designed as follows:

[0109]

[0110] The distributed collaborative control law is:

[0111]

[0112] In the formula: The constant is k3 ≥ d max d max For the disturbance d i The upper boundary.

[0113] The effectiveness of the proposed method is then verified through numerical simulation. A simplified attitude distributed cooperative control problem involving five spacecraft is considered, with the communication topology between the spacecraft as follows: Figure 2 As shown, this communication topology is a connected graph. The spacecraft's inertia matrix is...

[0114]

[0115] The initial attitude conditions and aiming vectors of each follower spacecraft are shown in [link to documentation]. Figure 3 The initial direction of the aiming vector is outside all pointing prohibition areas.

[0116] Pointing in the prohibited direction Spacecraft aiming vector and The minimum allowable angle is θ. min =π / 12. The aiming vector of the navigator spacecraft in the inertial coordinate system is... The control parameters are set to k1 = 1.0, k2 = 3.0, k3 = 0.06, c1 = 0.3, and c2 = 0.0001. The external disturbance is set to...

[0117]

[0118] The simulation results of this example are as follows: Figures 4-8 As shown. From Figure 4 and Figure 5 As can be seen, all the aiming vectors of the following spacecraft eventually converge to the same direction as the aiming vector of the lead spacecraft; and, in the presence of multiple pointing prohibition regions, the pointing constraint processing method in this invention effectively prevents the aiming vectors of the following spacecraft from entering the pointing prohibition regions. Figure 6 The curves showing the variation of the sum of the absolute values ​​of the aiming vector errors of all follower spacecraft and the aiming vector error of the lead spacecraft are presented, and the final convergence error is less than 5 × 10⁻⁶. -6 ; Figure 7 The curves showing the relative error variation between the following spacecraft are presented, and it can be seen that the error between each pair of aiming vectors of the following spacecraft is ultimately less than 1×10. -6 ; Figure 6 and Figure 7 The high control accuracy of the present invention has been verified. Figure 8 The curves showing the changes in the pointing prohibition constraints of the following spacecraft are displayed. It can be seen that the constraint values ​​of all following spacecraft relative to all pointing prohibition regions are less than 0, which verifies the effectiveness of the constraint processing method of the present invention.

[0119] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A simplified attitude distribution control method for a directional-constrained lead-following spacecraft formation, characterized in that: Includes the following steps: Step 1: Based on the angle between the aiming vectors of each spacecraft in the spacecraft formation, establish a simplified mathematical model of attitude error between the spacecraft; the spacecraft formation includes one lead spacecraft and n follower spacecraft. Step 2: Consider the minimum angle between the aiming vector and the pointing prohibition vector of the following spacecraft, and construct a pointing constraint mathematical model for each following spacecraft; Step 3: Based on the simplified attitude error model described in Step 1, the pointing constraint mathematical model described in Step 2, and the communication topology between spacecraft, design the artificial potential field function for each following spacecraft; Step 4: Sum the artificial potential field functions of all following spacecraft as Lyapunov functions, and design the virtual control quantities for each following spacecraft accordingly; Step 5: Use the difference between the angular velocity vector of each follower spacecraft and the virtual control quantity as the sliding mode variable, construct the sliding mode surface, and design the distributed sliding mode control law for each follower spacecraft based on the constructed sliding mode surface.

2. The simplified attitude distribution control method for a directional-constrained lead-following spacecraft formation according to claim 1, characterized in that: The simplified attitude error mathematical model established in step 1 includes the error model between the aiming vector of the following spacecraft and the aiming vector of the lead spacecraft, as well as the error model between the aiming vectors of the following spacecraft. The error model between the aiming vector of the follower spacecraft and the aiming vector of the lead spacecraft is as follows: The error between the aiming vector of the i-th follower spacecraft and the aiming vector of the lead spacecraft is expressed as follows: After differentiation, it becomes in The aiming vector of the pilot spacecraft in the inertial coordinate system The following represents R i For the body coordinate system fixed to the i-th following spacecraft to inertial coordinate system The rotation matrix, η i Indicates the i-th following spacecraft body coordinate system The unit vector fixed to the spacecraft, function (·). × Defined as Let be the angular velocity vector of the i-th following spacecraft in the volume coordinate system. The representation in; The error model between the aiming vectors of the following spacecraft is: The error between the aiming vector of the i-th follower spacecraft and the aiming vector of the j-th follower spacecraft is expressed as follows: After differentiation, it becomes Where R j For the body coordinate system fixed to the j-th following spacecraft to inertial coordinate system The rotation matrix, η j Indicates the j-th following spacecraft body coordinate system The unit vector fixed to the spacecraft below. Let be the angular velocity vector of the j-th following spacecraft in the volume coordinate system. The representation in the text.

3. The simplified attitude distribution control method for a directional-constrained lead-following spacecraft formation according to claim 2, characterized in that: In step 2, the mathematical model for the pointing constraint of the i-th following spacecraft is: in For inertial coordinate system The origin points to the h-th unit vector that points to the center of the forbidden region; θ min This is the minimum angle between the target vector for the following spacecraft and the pointing prohibition vector.

4. The simplified attitude distribution control method for a directional-constrained lead-following spacecraft formation according to claim 3, characterized in that: The artificial potential field function designed in step 3 is: in `a` is a constant, `m` is the number of points to forbidden regions; ij For the communication topology adjacency matrix of n follower spacecraft, when the i-th follower spacecraft and the j-th follower spacecraft can communicate with each other, a ij =1, otherwise a ij =0; a i0 Let a be an element of the communication topology matrix between the lead spacecraft and the follower spacecraft. If the i-th follower spacecraft can obtain the state of the lead spacecraft, then a i0 =1, otherwise a i0 =0.

5. The simplified attitude distribution control method for a directional-constrained lead-following spacecraft formation according to claim 4, characterized in that: In step 4, the virtual control variable designed for the i-th following spacecraft is: in ψ is a constant; i for 6. The simplified attitude distribution control method for a directional-constrained lead-following spacecraft formation according to claim 5, characterized in that: In step 5, the constructed sliding surface is J i Let be the inertia matrix of the i-th spacecraft; the final distributed sliding mode control law is: Where τ i The torque acting on the i-th following spacecraft The constant is k3 ≥ d max d max For the disturbance d i The upper boundary.

7. The simplified attitude distribution control method for a directional-constrained lead-following spacecraft formation according to claim 2, characterized in that: The body coordinate system of the i-th spacecraft is Its origin O B Located at the center of mass of the i-th spacecraft, the x-axis coincides with the principal axis of the maximum inertia of the i-th spacecraft, the z-axis coincides with the principal axis of the minimum inertia of the i-th spacecraft, and the y-axis forms a right-handed coordinate system with the x-axis and z-axis.

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