CN110789738B - A distributed model predictive control method for nanosatellites to take over the attitude motion of a failed spacecraft - Google Patents

Abstract

The invention relates to a distributed model prediction control method for attitude motion of a nanosatellite connected and failed spacecraft. The distributed model predictive control method can enable each nanostar to independently carry out control quantity calculation, realizes autonomous distributed take-over control on attitude motion of the failed spacecraft, does not need a central processing unit, and can conveniently consider control amplitude constraint of the nanostars. Compared with centralized control distribution, the distributed model predictive control method of the multiple nanostars has better fault tolerance, and the nanostars can adjust the weight matrix in the local objective function according to the self energy consumption condition so as to realize the balance of energy consumption among the nanostars, so that the distributed model predictive control method of the multiple nanostars has important application value in the control task of implementing the attitude motion takeover of the failed spacecraft through the multiple nanostars.

Description

A distributed model predictive control method for nanosatellites to take over the attitude motion of a failed spacecraft

technical field

The invention belongs to the technical field of aerospace dynamics and control, and in particular relates to a distributed model prediction control method for a nano-satellite taking over the attitude motion of a failed spacecraft.

Background technique

Implementing attitude takeover control for spacecraft that fail due to thruster failure or fuel exhaustion in space can realize the reuse of high-value payloads such as cameras and antennas (References: Chen Luojing, Hao Jinhua, et al. "Phoenix "The key technology of the plan and its enlightenment [J]. Spacecraft Engineering, 2013, 22(5): 119-128.). Currently, there are two main ways to implement the attitude motion takeover control of a failed spacecraft. One is to capture the failed spacecraft through the robotic arm of the space robot, and then control its attitude movement (Reference: Huang P, Wang M, Meng Z, et al. Attitude takeover control for post-capture of target spacecraft using space robot[J].Aerospace Science and Technology,2016,51:171-180.Wang Z,Yuan J,CheD.Adaptive attitude takeover control for space non-cooperative targets with stochastic actuator faults[J].Optik,2017,137 :279-290.); the other is to control the attitude of the failed spacecraft by attaching multiple nanostars to the surface of the failed spacecraft and providing it with control torque (Reference: Han N, Luo J, Ma W,et al.Integrated identification and control fornanosatellites reclaiming failed satellite[J].Acta Astronautica,2018,146:387-398.Chang H,Huang P,Zhang Y,et al.Distributed control allocation for spacecraft attitude takeover control via cellular space robot[J]. Journal of Guidance, Control, and Dynamics, 2018, 41(11): 2495-2502.). The space robot has strong control ability and can achieve the attitude control goal of the failed spacecraft in a short period of time, but its manufacturing cost is high and the development cycle is long. When the failed spacecraft needs long-term attitude orientation, the space robot is difficult to meet. Economical requirements for space missions. Nanostar has the advantages of low development cost and short development cycle. It can be attached to the surface of the failed spacecraft for a long time to provide it with the control torque required for attitude motion. Compared with space robots, it can better meet the attitude takeover of the failed spacecraft. The economic requirements of the control task.

At present, only a small amount of research has been done on the problem of multiple nanosatellites taking over to control the attitude motion of a failed spacecraft. These studies can be divided into two categories. The first category is similar to the attitude control method combined with the traditional spacecraft centralized control solution and distribution, that is, the control required for the attitude movement of the combined body formed by the nano-satellite and the failed spacecraft is calculated first. The control torque is then distributed to each nanosatellite in a centralized manner (Han N, Luo J, Ma W, et al. Integrated identification and control for nanosatellites reclaiming failed satellite [J]. Acta Astronautica, 2018, 146: 387-398.), so a central processing unit is required to calculate and distribute the control torque of the combination. When the number of nano-satellites participating in the takeover control is large, the central processing unit faces a large computational burden. The second type is different from the first type in the way of control distribution. It adopts the distributed optimization and control method, and each nano-satellite calculates and executes its own control instructions. Literature (Chang H, Huang P, Zhang Y, et al. Distributed control allocation for spacecraft attitude takeover control via cellularspace robot[J]. Journal of Guidance, Control, and Dynamics, 2018, 41(11): 2495-2502.) A distributed thrust distribution method is designed based on the distributed optimization method to avoid the centralized control distribution. When the number of cell stars is large, the control can be effectively decentralized. Allocated computational burden. However, the literature (Chang H, Huang P, Zhang Y, et al. Distributed control allocation for spacecraft attitude takeover control via cellularspace robot [J]. Journal of Guidance, Control, and Dynamics, 2018, 41(11): 2495-2502. ) does not take into account the control amplitude constraints of the cell star. At present, for the problem of attitude takeover control of a failed spacecraft, there is a lack of a Dona satellite control method that can effectively consider the amplitude constraint of nano-satellite control and supports distributed execution. The problem of distributed realization of nano-satellite control, the separation of nano-satellite control variables is realized by constructing the control model of each nano-satellite, and on this basis, a distributed method for controlling the attitude motion of failed spacecraft by dona-satellite is designed. Model predictive control methods.

SUMMARY OF THE INVENTION

technical problem to be solved

In order to avoid the shortcomings of the prior art, the present invention proposes a distributed model predictive control method in which nano-satellites take over the attitude motion of a failed spacecraft, so that through the autonomous decision-making of each nano-satellite, the nano-satellite control amplitude constraint is satisfied when the nano-satellite control amplitude constraint is satisfied. In this case, the control of the attitude motion of the failed spacecraft can be realized.

Technical solutions

A distributed model predictive control method for a nanostar to take over the attitude motion of a failed spacecraft, characterized in that the steps are as follows:

Step 1: Establish the attitude motion model of the nanosatellite-failed spacecraft combination

事先已知，且纳星沿着其本体坐标系的坐标轴产生控制力矩，

为N颗纳星的集合；假设组合体本体坐标系oxyz的坐标轴平行于纳星1本体坐标系o₁x₁y₁z₁的坐标轴，组合体在空间只受到纳星所提供的控制力矩的作用，则其姿态运动模型可表示为：Assuming that there are N nano-satellites attached and fixed on the surface of the failed spacecraft to form a combination, the relative position between the nano-satellites is fixed during the attitude takeover control process; the attitude control actuator of the nano-satellite is a reaction flywheel, which can take over the failure The attitude motion of the spacecraft provides the control torque; the body coordinate system of each nano-satellite

is known in advance, and the nanostar generates control torque along the coordinate axis of its body coordinate system,

is a collection of N nanostars; assuming that the coordinate axis of the composite body coordinate system oxyz is parallel to the coordinate axis of the nanostar 1 body coordinate system o ₁ x ₁ y ₁ z ₁ , the composite body is only controlled by the nanostar in space The action of the moment, its attitude motion model can be expressed as:

Among them, x=[σ ^T ,ω ^T ] ^T is the attitude state quantity of the composite body, σ is the modified Rodrigues parameter describing the posture motion of the composite body, ω is the attitude angular velocity of the composite body, and u _j is the position of the nanostar j. the applied control torque, and:

为纳星j本体坐标系到组合体本体坐标系的转换矩阵，G(σ)由下式给出：Among them, J is the moment of inertia matrix of the combined body, 0 _m×n is the all-zero matrix of m×n,

is the transformation matrix from the nanostar j ontology coordinate system to the composite ontology coordinate system, G(σ) is given by the following formula:

Among them, I _n is the identity matrix of n×n, σ ^× is the antisymmetric matrix of σ=[σ ₁ σ ₂ σ ₃ ] ^T , which is defined as:

σ ^× =[0,-σ ₃ ,σ ₂ ;σ ₃ ,0,-σ ₁ ;-σ ₂ ,σ ₁ ,0] (4)

Step 2: Establish a nanosatellite control model in the finite time domain

其中x_d为组合体期望姿态状态值，σ_d、ω_d分别为组合体期望姿态MRPs和角速度，则式(1)可在x_d附近线性化为：given a set of nominal trajectories

where x _d is the desired attitude state value of the combined body, σ _d and ω _d are the desired attitude MRPs and angular velocity of the combined body, respectively, then equation (1) can be linearized near x _d as:

in:

After discretizing equation (5), the combined body error attitude motion model can be obtained as:

为组合体的误差姿态状态，包含组合体误差MRPsσ_e和组合体误差角速度ω_e，x_d,k+1＝x_d(t_k+1)，且：Among them, x _k =x(t _k ), u _j,k =u _j (t _k ), t _k is the update time of nano-satellite control, x _e,k+1 =x _e (t _k+1 ),

is the error attitude state of the assembly, including the assembly error MRPsσ _e and the assembly error angular velocity ω _e , x _d,k+1 =x _d (t _k+1 ), and:

为t_k+1时刻期望轨迹上组合体本体坐标系到当前时刻组合体实际本体坐标系的转换矩阵；令Δt为相邻控制更新时刻之差，则：in,

is the transformation matrix from the body coordinate system of the composite body on the desired trajectory at time t _k+1 to the actual body coordinate system of the composite body at the current moment; let Δt be the difference between the adjacent control update times, then:

则根据式(7)，可得有限时域内各颗纳星的控制模型为：Considering the case where both the prediction and control time domains are _Nc , let

Then according to formula (7), the control model of each nano-satellite in the finite time domain can be obtained as:

包含t_p时刻除纳星i以外其余纳星的控制量，即

且：in,

Including the control quantities of other nanostars except nanostar i at time t _p , namely

and:

in,

Step 3: Design the Distributed Model Predictive Controller for Nanosatellite

In order to make the composite body track the desired attitude trajectory with as little control cost as possible, the following local objective function is designed for each nano-satellite:

将式(10)代入式(12)中，可得：Among them, _qi and _ri are positive definite matrices,

Substituting equation (10) into equation (12), we can get:

Since in equation (13), each nano-satellite can only adjust its own control sequence Vi _,k , the first term in equation (13) can be omitted in the optimization process. In this way, the distributed model of nano-satellite predicts The controller can be given by the following quadratic optimization problem:

u_m为纳星所能产生的最大控制力矩幅值；in,

u _m is the maximum control torque amplitude that the nano-satellite can generate;

Each nano-satellite obtains the control sequence Vi _,k by solving the optimization problem in Equation (14), and takes over the attitude control of the failed spacecraft through the first set of data ui _{,k in} Vi,k.

beneficial effect

The invention proposes a distributed model predictive control method in which nano-satellites take over to control the attitude movement of a failed spacecraft. The proposed distributed model predictive control method can enable each nano-satellite to independently calculate the control quantity, so as to realize the control of the attitude of the failed spacecraft. The autonomous distributed takeover control of the motion does not require a central processing unit, and can easily consider the control amplitude constraints of the nanosatellite. Compared with the centralized control distribution, Donastar's distributed model predictive control method has better fault tolerance, and Nanostar can adjust the weight matrix in its local objective function according to its own energy consumption, so as to realize Nanostar It has important application value in the control task of taking over the attitude motion of the failed spacecraft through multiple nano-satellites.

Description of drawings

Figure 1 is a schematic diagram of the attitude takeover control of the failed spacecraft;

In the example of Fig. 2, the variation curve of the combined body error attitude MRPs with time;

In the example of Fig. 3, the combined body error attitude angular velocity changes curve with time;

Figure 4. Curves of the control torques of the four nanosatellites that implement attitude takeover control over time.

Detailed ways

The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

Facing the task of controlling the attitude movement of the failed spacecraft with multiple nano-satellites, the present invention proposes a distributed model predictive control method for the multiple nano-satellites. The method enables each nano-satellite to independently calculate the control quantity to realize the takeover control of the attitude motion of the failed spacecraft, without the need for a central processing unit, and can easily consider the control constraints of the nano-satellite. The implementation of the present invention mainly includes the following three steps:

Step 1: Establish an attitude motion model of the nanosatellite-invalid spacecraft combination.

事先已知，且纳星沿着其本体坐标系的坐标轴产生控制力矩，

为N颗纳星的集合。假设组合体本体坐标系oxyz的坐标轴平行于纳星1本体坐标系o₁x₁y₁z₁的坐标轴，组合体在空间只受到纳星所提供的控制力矩的作用，则其姿态运动模型可表示为：Assuming that there are N nano-satellites attached and fixed on the surface of the failed spacecraft to form a combination, the relative positions between the nano-satellites are fixed during the attitude control process. Nanostar's attitude control actuator is a reaction flywheel, which can take over the attitude motion of the failed spacecraft to provide control torque. Ontological coordinate system of each nanostar

is known in advance, and the nanostar generates control torque along the coordinate axis of its body coordinate system,

is a collection of N nanostars. Assuming that the coordinate axis of the combined body coordinate system oxyz is parallel to the coordinate axis of the nanostar 1 body coordinate system o ₁ x ₁ y ₁ z ₁ , the combined body is only affected by the control torque provided by the nanostar in space, then its attitude movement The model can be expressed as:

where x=[σ ^T ,ω ^T ] ^T is the attitude state quantity of the combined body, σ is the modified Rodrigues parameters (MRPs) describing the attitude motion of the combined body, ω is the attitude angular velocity of the combined body, u _j is the control torque exerted by nanostar j, and:

为纳星j本体坐标系到组合体本体坐标系的转换矩阵，G(σ)由下式给出：J is the moment of inertia matrix of the combined body, 0 _m×n is the all-zero matrix of m×n,

is the transformation matrix from the nanostar j ontology coordinate system to the composite ontology coordinate system, G(σ) is given by the following formula:

where In is the identity matrix of n× _n , and σ ^× is the antisymmetric matrix of σ=[σ ₁ σ ₂ σ ₃ ] ^T , defined as:

σ ^× =[0,-σ ₃ ,σ ₂ ;σ ₃ ,0,-σ ₁ ;-σ ₂ ,σ ₁ ,0] (18)

Step 2: Establish a nano-satellite control model in a finite time domain.

其中x_d为组合体期望姿态状态值，σ_d、ω_d分别为组合体期望姿态MRPs和角速度，则式(1)可在x_d附近线性化为：given a set of nominal trajectories

where x _d is the desired attitude state value of the combined body, σ _d and ω _d are the desired attitude MRPs and angular velocity of the combined body, respectively, then equation (1) can be linearized near x _d as:

in:

After discretizing equation (5), the combined body error attitude motion model can be obtained as:

为组合体的误差姿态状态，包含组合体误差MRPsσ_e和组合体误差角速度ω_e，x_d,k+1＝x_d(t_k+1)，且：where x _k =x(t _k ), u _j,k =u _j (t _k ), t _k is the update time of nano-satellite control, x _e,k+1 =x _e (t _k+1 ),

is the error attitude state of the assembly, including the assembly error MRPsσ _e and the assembly error angular velocity ω _e , x _d,k+1 =x _d (t _k+1 ), and:

为t_k+1时刻期望轨迹上组合体本体坐标系到当前时刻组合体实际本体坐标系的转换矩阵。令Δt为相邻控制更新时刻之差，则：

is the transformation matrix from the body coordinate system of the composite body on the desired trajectory at time t _k+1 to the actual body coordinate system of the composite body at the current moment. Let Δt be the difference between adjacent control update times, then:

则根据式(7)，可得有限时域内各颗纳星的控制模型为：Considering the case where both the prediction and control time domains are _Nc , let

Then according to formula (7), the control model of each nano-satellite in the finite time domain can be obtained as:

包含t_p时刻除纳星i以外其余纳星的控制量，即

且：in

Including the control quantities of other nanostars except nanostar i at time t _p , namely

and:

in

Step 3: Design the distributed model predictive controller of nanosatellite.

In order to make the composite body track the desired attitude trajectory with as little control cost as possible, the following local objective function is designed for each nano-satellite:

将式(10)代入式(12)中，可得：where _qi and _ri are positive definite matrices,

Substituting equation (10) into equation (12), we can get:

Since in equation (13), each nano-satellite can only adjust its own control sequence Vi _,k , the first term in equation (13) can be omitted in the optimization process. In this way, the distributed model of nano-satellite predicts The controller can be given by the following quadratic optimization problem:

u_m为纳星所能产生的最大控制力矩幅值。in

_um is the maximum control torque amplitude that the nano-satellite can generate.

Each nano-satellite obtains the control sequence Vi _,k by solving the optimization problem in Equation (14), and takes over the attitude control of the failed spacecraft through the first set of data ui _{,k in} Vi,k.

Example 1:

Taking the task of taking over control of the attitude motion of four nanosatellites attached to the surface of the failed spacecraft as an example, the effectiveness of the distributed model predictive control method of the donastars in the present invention is illustrated. The moment of inertia matrix of the combined body is:

Consider the following composite body desired attitude angular velocity trajectory:

为可调系数矢量，

为可调系数，且k₂>0。式(29)能够保证随着时间t的增加，组合体的期望姿态角速度趋近于零。in

is the adjustable coefficient vector,

is an adjustable coefficient, and k ₂ >0. Equation (29) can ensure that with the increase of time t, the expected attitude angular velocity of the composite body tends to zero.

Given the initial pose MRPsσ ₀ of the combined body and the desired pose MRPsσ _f of the terminal moment, adjust k ₁ and k ₂ to satisfy the following constraints:

where σ _df is the attitude MRPs of the combined body at the terminal moment when the attitude angular velocity of the combined body changes according to equation (29). t ₀ and t _f are the start and end moments of the attitude takeover control task, respectively. When the selected k ₁ and k ₂ can satisfy the constraints in Eq. (30), the obtained desired attitude MRPs and angular velocity trajectory can guide the attitude of the failed spacecraft to the specified direction.

The initial attitude MRPs of the combined body is σ ₀ =[-0.2515 -0.3152 -0.2430] ^T , and the expected attitude MRPs of the terminal moment is σ _f =0 _3×1 , then when k ₁ =[0.6561 0.8223 0.6340] ^T ×10 ^-2 , k When ₂ = 0.007, the constraint in equation (30) can be satisfied. Assuming that the initial attitude angular velocity of the composite body is ω ₀ =0 _3×1 , there are four nano-satellites to take over the attitude control of the failed spacecraft, the nano-satellite control amplitude is u _m =0.003(N·m), q ₁ =q ₄ =I ₆ , q ₂ =q ₃ =2I ₆ , r ₁ =r ₂ =r ₃ =r ₄ =0.005I ₃ , t ₀ =0, t _f =1300s, N _c =5, the coordinates of the four nanosatellites The transformation matrices from the system to the composite body coordinate system are:

Under the Donastar distributed model predictive control method, the curves of the combined body error attitude MRPs and the error attitude angular velocity with time are shown in Figure 2 and Figure 3, respectively. It can be seen that when the attitude control task ends, the combined body The error attitude MRPs and the error attitude angular velocity of both tend to zero, which indicates that multiple nanosatellites can control the attitude of the failed spacecraft to the specified direction, thus realizing the attitude takeover control of the failed spacecraft. Figure 4 shows the curves of the control torque of the four nano-satellites with time, in which the horizontal dotted line shows the control amplitude constraints of the nano-satellites. It can be seen that in the whole attitude control stage, the control amplitude constraints of the nano-satellites are all can be satisfied.

Claims (1)

1. A distributed model prediction control method for spacecraft attitude motion with failure of a nano-satellite receiving tube is characterized by comprising the following steps:

step 1: establishing a Naxing-failure spacecraft combination attitude motion model

Supposing that N receiving stars are attached and fixed on the surface of the failure spacecraft to form a combined body with the failure spacecraft, and the relative positions of the receiving stars are fixed in the attitude connecting pipe control process; the attitude control actuating mechanism of the nano-satellite provides control torque for a reaction flywheel and can receive and manage attitude motion of the failed spacecraft; body coordinate system of each satellite

Known in advance, and the nanostars generate control moments along the coordinate axes of their body coordinate systems,

is a set of N nanostars; suppose that the coordinate axis of the complex body coordinate system oxyz is parallel to the nanostar 1 body coordinate system o₁x₁y₁z₁The complex is only acted by the control moment provided by the nanosatellite in the space, and then the attitude motion model can be expressed as:

wherein x ═ σ^T,ω^T]^TIs the attitude state quantity of the composition body, sigma is the modified Rodrigues parameter describing the attitude motion of the composition body, omega is the attitude angular velocity of the composition body, u_jA control torque applied for nanosatellite j, and:

wherein J is the moment of inertia matrix of the assembly, 0_m×nIs an all-zero matrix of m x n,

for the transformation matrix of the nanostar j body coordinate system to the assembly body coordinate system, G (σ) is given by:

wherein, I_nIs an identity matrix of n × n, σ^×Is sigma ═ sigma₁ σ₂ σ₃]^TIs defined as:

σ^×＝[0,-σ₃,σ₂；σ₃,0,-σ₁；-σ₂,σ₁,0] (4)

step 2: nanxing control model for establishing finite time domain

Given a set of nominal trajectories

Wherein x_dDesired attitude state value, σ, for the combination_d、ω_dFor the desired attitude MRPs and angular velocity of the combination, respectively, equation (1) may be at x_dThe neighborhood is linearized as:

wherein:

after discretizing the formula (5), the obtained combination error posture motion model is as follows:

wherein x is_k＝x(t_k)，u_j,k＝u_j(t_k)，t_kControlling the update time, x, for nanosategories_e,k+1＝x_e(t_k+1)，

For error attitude state of the composition, including composition error MRPs σ_eAnd the angular velocity omega of the combined body_e，x_d,k+1＝x_d(t_k+1) And, and:

wherein,

is t_k+1A transformation matrix from the assembly body coordinate system on the moment expected track to the assembly body coordinate system at the current moment; let Δ t be the difference between adjacent control update times, then:

considering that the prediction and control time domains are both N_cIn the case of (1), let

Then, according to equation (7), the control model for each satellite in the finite time domain is:

wherein,

containing t_pThe control quantity of the other nanostars except nanostars i at the moment, i.e.

And:

wherein,

and step 3: distributed model predictive controller for designing nanostars

In order to make the combined body track the expected attitude motion trail with the lowest control consumption as possible, the following local objective function is designed for each nano star:

wherein q is_i、r_iIn order to be a positive definite matrix,

by substituting formula (10) for formula (12), it is possible to obtain:

because in the formula (13), each satellite can only adjust its own control sequence V_i,kTherefore, the first term in equation (13) is omitted in the optimization process, so that the distributed model predictive controller for nanostars can be given by the quadratic optimization problem as follows:

wherein,

u_mthe amplitude of the maximum control moment which can be generated by the nanostars;

each nanostar obtains the control sequence V by solving the optimization problem in equation (14)_i,kAnd through V_i,kOf (3) a first set of data u_i,kAnd carrying out attitude takeover control on the failed spacecraft.

Images