CN112591153B - Based on anti-interference multiple target H2/H∞Filtering space manipulator tail end positioning method - Google Patents

Based on anti-interference multiple target H2/H∞Filtering space manipulator tail end positioning method Download PDF

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CN112591153B
CN112591153B CN202011425466.8A CN202011425466A CN112591153B CN 112591153 B CN112591153 B CN 112591153B CN 202011425466 A CN202011425466 A CN 202011425466A CN 112591153 B CN112591153 B CN 112591153B
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乔建忠
丁玮隆
郭雷
崔洋洋
朱玉凯
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Beihang University
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Abstract

The invention relates to a method based on anti-interference multiple-target H2/H∞The filtering space manipulator tail end positioning method aims at a space manipulator system which is simultaneously subjected to vibration interference of a flexible accessory and measurement noise of a complex multi-sensor;firstly, determining vibration interference and multi-sensor measurement noise of a space manipulator, and establishing a terminal position filtering model; secondly, designing an interference observer to estimate and feed-forward compensate the interference, and combining Kalman filtering to form an anti-interference filter; finally, designing a distributed multi-sensor information fusion framework, carrying out weighted fusion on the estimated values of the interference resisting filter, and adopting multi-target H2/H∞And the fusion algorithm restrains the fusion error under the preset performance index and solves the estimation gain to obtain the global estimation of the tail end position. According to the method, the interference estimation and the multi-sensor fusion algorithm are combined, so that the precision and robustness of the positioning of the tail end of the space manipulator under the influence of complex interference and noise can be improved, and support is provided for the space manipulator to complete on-orbit high-precision operation.

Description

Based on anti-interference multiple target H2/H∞Filtering space manipulator tail end positioning method
Technical Field
The invention relates to a method based on anti-interference multiple-target H2/H∞The method fully considers the vibration interference of a flexible accessory, the noise of an actuating mechanism and the measurement noise with unknown sensor statistical characteristics of a space mechanical arm system, establishes a terminal position filter model on the basis, improves the anti-interference capability and the estimation precision of the terminal position estimation of the space mechanical arm by estimating the vibration interference torque in the filter model and comprehensively utilizing the measurement information of various sensors of an IMU and a camera, and provides support for the motion control of the space mechanical arm system in an on-orbit high-precision operation task.
Background
The space mechanical arm system is a space electromechanical system with high integration degree integrating the functions of machinery, electricity, heat and control, can complete the work of on-orbit assembly, fault device replacement, on-orbit filling, orbit cleaning and the like of the spacecraft in a ground teleoperation or autonomous operation mode, and is a core technology for realizing on-orbit assembly and maintenance of the spacecraft. The accurate positioning of the end tool is a precondition for alignment, connection and grabbing control of a task target, and is a key link for determining whether space on-orbit service is successful or not. However, the space manipulator system working on the rail faces the severe space working environment, on one hand, the end sensor is inevitably influenced by complex sensor noise, and on the other hand, the dynamic error of the serial joint caused by the vibration of the flexible attachment is transmitted to the dynamic error of the end through positive kinematics, and the measurement error of the position of the end is amplified. The above problems may cause the measurement precision of the tail end position of the space manipulator to be reduced, and the tail end position and speed information cannot be accurately fed back to the control system, so that the end effector is difficult to align with the working point, and even the on-orbit task fails. Therefore, in order to comprehensively utilize information of multiple sensors mounted on joints and tail ends and realize high-precision tail end positioning of a space manipulator under the conditions of interference and complex noise, a tail end positioning method with the capabilities of resisting interference and processing non-gaussian noise needs to be designed.
At present, various scholars propose different state estimation methods aiming at the problem of positioning the tail end of a space manipulator system. The filtering methods widely researched at the present stage include kalman filtering, robust filtering, particle filtering, and the like. The Kalman filtering and its expanding method respectively give the optimal solutions of the filtering problem under linear and nonlinear conditions, but the Kalman filtering is not suitable under the condition that the statistical characteristics of the noise do not satisfy the Gaussian distribution. The robust filtering can relax the condition limit, and is mainly used for solving the state estimation problem when the noise characteristics are unknown or the model parameters are uncertain, the influence of noise on estimation is minimized through parameter optimization, but the optimal gain solving under the constraint of the preset performance index requires a certain amount of calculation. In addition, particle filtering is a popular research direction in recent years, and has the advantage of being applicable to nonlinear and non-gaussian estimation problems, but the particle filtering has certain difficulty in engineering practice.
In summary, the measurement accuracy of the end position of the actual space manipulator joint system is affected by the vibration interference of the flexible attachment and the complex noise, and the existing filtering method rarely considers the direct and effective processing of the end position, so that the end positioning accuracy is limited. For example, the particle filtering method based on the space manipulator dynamics model in patent application No. 201810883670.0 ignores the influence of the unknown characteristic interference facing the system on track. Therefore, to design an ideal terminal position filter, a filtering model considering the interference moment and the non-gaussian measurement noise at the same time needs to be established, and measurement of multiple sensors is fused on the basis of interference estimation to estimate the position and the speed, so that the anti-interference capability and the state estimation accuracy of a terminal tool are improved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problem that the tail end positioning precision cannot meet the requirement of on-orbit operation due to the fact that the existing space manipulator system is simultaneously influenced by vibration interference of a flexible accessory and measurement noise with unknown statistical characteristics, the defects that the interference cannot be estimated and non-Gaussian noise cannot be processed by the traditional Kalman filtering and expansion method thereof are overcome, and the anti-interference multi-target H-based method is provided2/H∞The filtering space manipulator tail end positioning method improves the anti-interference capability and the estimation precision of the tail end state estimation of the space manipulator by estimating the interference torque in the filtering model and comprehensively utilizing the IMU and the camera multi-sensor measurement information.
The technical solution of the invention is as follows: based on anti-interference multiple target H2/H∞The filtering space manipulator tail end positioning method comprises the following steps: firstly, determining flexible accessory vibration interference, actuating mechanism noise and sensor measurement noise suffered by a space manipulator system, and establishing a terminal position filtering model according to positive kinematics and joint dynamics of the space manipulator system; secondly, designing an interference observer for the vibration interference of which part of prior information is known in a filtering model according to measurement data of a terminal IMU and a camera respectively to estimate the vibration interference, and adding an interference feedforward compensation link on the basis of Kalman filtering to form an anti-interference filter; finally, a distributed multi-sensor information fusion framework is designed, wherein an anti-interference filter is used as a sub-filter, and a main filter is designed to carry out estimation on the sub-filter in a weighting methodFusion, using multiple targets H2/H∞The fusion algorithm restrains the fusion error under the preset performance index, namely simultaneously restrains the Gaussian noise to the H of the fusion error2Norm and non-Gaussian noise to fusion error H∞Norm to reduce the influence of various noises on the fusion estimation precision as much as possible. And solving interference estimation gain, filtering gain and weighting weight through a linear matrix inequality group to finally obtain the global estimation of the tail end position of the space manipulator. The concrete design steps of the links are as follows:
the method comprises the following steps of firstly, determining flexible accessory vibration interference, actuating mechanism noise and sensor measurement noise of a space manipulator system, and establishing a terminal position filtering model by combining positive kinematics and joint dynamics of the space manipulator system:
the three-axis stable satellite is used as the spacecraft base, only the attitude of the base is controlled in a free flight mode, and the attitude angular rate omega of the base can be considered00, while the system linear momentum is conserved. Under this condition, the system positive kinematics and joint dynamics:
Figure BDA0002824614910000031
wherein p iseAs the end position of the arm, xbIs the posture of the base, q is the rotation angle of the connecting rod of the mechanical arm, tau is the control moment output by the joint motor, TdThe moment is a vibration disturbance moment; j. the design is a squarebAnd JmAre Jacobian matrixes related to a spacecraft base and a mechanical arm connecting rod respectively,
Figure BDA0002824614910000032
i is an identity matrix and is a matrix of the identity,
Figure BDA0002824614910000041
r0as a base position, Jm＝[k1×(pe-p1)…kn×(pe-pn)]，kiRepresenting unit vectors, p, of the axis of rotation of the connecting rod ii(i1, …, n) is the connecting point position of the connecting rod i-1 and the connecting rod i, H (q) is a system positive definite inertia parameter matrix,
Figure BDA0002824614910000042
a non-linear array containing coriolis forces and centrifugal forces, M is the pedestal mass,
Figure BDA0002824614910000043
JTi＝[k1×(ri-p1)k2×(ri-p2)…ki×(ri-pi)0…0]，mi、rirespectively connecting rod i mass and centroid position.
Finishing to obtain:
Figure BDA0002824614910000044
wherein
Figure BDA0002824614910000045
Let state quantity x ═ pe T ve T]TWherein p ise、veRespectively representing the position and velocity of the end tool in an inertial coordinate system, the control input u and the joint state q,
Figure BDA0002824614910000046
Regarding, assume q,
Figure BDA0002824614910000047
Measurable, the state equation of the end position filtering model can be expressed as:
Figure BDA0002824614910000048
wherein
Figure BDA0002824614910000049
w is zeroWhite gaussian noise of the mean value of the average,
Figure BDA00028246149100000410
Figure BDA00028246149100000411
d is disturbance torque TdThe mathematical model can be described as follows:
Figure BDA00028246149100000412
w, B therein2And V is a known parameter matrix.
Through discretization, the state equation of the filtering model is as follows:
xk＝Ak-1xk-1+Bk-1uk-1+Gk-1dk-1+Gk-1wk-1
wherein A isk＝I+FΔT，
Figure BDA0002824614910000051
tkThe Δ T is the time interval measured by the sensor.
The end position of the space manipulator can be directly measured by means of multiple sensors such as an IMU, a camera and the like. For a camera, the measurement noise of the camera is obviously influenced by the external complex space environment, including (1) electromagnetic interference, (2) illumination change and (3) temperature change. If the statistical properties of the camera measurement noise are considered to satisfy the assumptions of the kalman filter, the estimation performance is greatly degraded. Thus, the present patent treats the camera's measurement noise as a combination of white gaussian noise and norm-bounded non-gaussian noise.
Assuming that the IMU and camera sensors used are calibrated, the measurement equation for the filtering model for the end position is given directly as follows:
y1k＝H1kxk+D11kwk+D12kvk
y2k＝H2kxk+D21kwk+D22kvk
wherein y is1k、y2kMeasurement outputs of IMU and camera, H1k、H2kTo measure the coefficient, H1k＝H2k＝I，D11k、D12k、D21kAnd D22kIs a matrix of known parameters, wkWhite Gaussian noise of zero mean value, vkIs a norm-bounded non-gaussian noise. Initial state x0And wk、vkAre irrelevant.
And secondly, designing an interference observer to estimate the vibration interference according to measurement data of a terminal IMU and a camera aiming at part of vibration interference of which prior information is known in a filtering model, and adding an interference feedforward compensation link on the basis of Kalman filtering to form an anti-interference filter:
designing an interference observer for a single sub-filter
Figure BDA0002824614910000052
Namely:
Figure BDA0002824614910000053
wherein
Figure BDA0002824614910000054
Figure BDA0002824614910000055
K is the interference estimation gain to be designed for the state estimation value at the previous moment.
Based on this, the state update is represented as:
Figure BDA0002824614910000056
where L is the filter gain to be designed.
Will omegakExpansion into system equation of state, setting expansion state
Figure BDA0002824614910000061
The filter model is rewritten as follows:
Figure BDA0002824614910000062
wherein
Figure BDA0002824614910000063
Setting an estimate of an augmented state
Figure BDA0002824614910000064
The filter based on the disturbance observer is then sorted as:
Figure BDA0002824614910000065
wherein
Figure BDA0002824614910000066
The filter form is similar to the kalman filter of an augmented system for the gain matrix to be designed.
Thirdly, designing a distributed multi-sensor information fusion framework, wherein an anti-interference filter is used as a sub-filter, a main filter is designed, an estimation value of the sub-filter is fused in a weighting method, and multiple targets H are adopted2/H∞The fusion algorithm restrains the fusion error under the preset performance index, solves the interference estimation gain, the filtering gain and the weighting weight by means of the linear matrix inequality set, and obtains the global estimation of the tail end position of the space manipulator:
calculating main filter estimated value by adopting weighting method
Figure BDA0002824614910000067
The following were used:
Figure BDA0002824614910000068
wherein
Figure BDA0002824614910000069
Are all sub-filter estimates, Wi＝diag{wi1,wi2,…,winAnd (i ═ 1,2) are the sub-filter weighting weights. According to the unbiased requirement, W1+W2I. Defining an estimation error ekComprises the following steps:
Figure BDA00028246149100000610
is provided with
Figure BDA00028246149100000611
The following can be obtained:
Figure BDA0002824614910000071
wherein the content of the first and second substances,
Figure BDA0002824614910000072
Cm＝[I -W1 -W2]，
Figure BDA0002824614910000073
Figure BDA0002824614910000074
W1＝0，
Figure BDA0002824614910000075
for simultaneously processing Gaussian white noise wkAnd non-Gaussian noise v with uncertain statistical propertieskUsing robust H2/H∞The performance index is restricted, and the design target of the filter is (1) the system is asymptotically stable; (2) from vkTo the filtering error ekH of transfer function of∞Norm does not exceed a given upper bound γ; (3) fromWhite noise wkTo error ekH of transfer function of2Norm as small as possible to ensure ekSteady state variance of (G)m TP2Gm) As small as possible, wherein P2Lyapunov matrix equation A if more than 0m TP2Am+Cm TCm-P2A solution of 0.
If for a known coefficient r1＞0、r2> 0, sub-filter weight W to be designed1、W2And gamma > 0, presence matrix G1、G2、G3、Π＞0、Pi＞0(i＝1～3)、R1、R2Satisfies the following conditions:
minr1Trace(Π)+r2γ
s.t.
(1)
Figure BDA0002824614910000081
(2)
Figure BDA0002824614910000082
(3)
Figure BDA0002824614910000083
wherein xi1＝P1-G1-G1 T，Ξ2＝P2-G2-G2 T，Ξ3＝P3-G3-G3 T，Ξ25＝G2A-R1H1，Ξ36＝G3A-R2H2. Designing a filter gain K1＝G2 -1R1，K2＝G3 -1R2Under the gain, the filtering error system is stable and meets the robust performance index of the system. Thus far, multiple targets H are designed2/H∞The fusion estimation framework gives a sub-optimal estimation of vibration disturbances and tip position, velocity.
Compared with the prior art, the invention has the advantages that:
(1) the invention fully considers the vibration interference of a flexible accessory and the measurement noise of a sensor with uncertain statistical characteristics of a space manipulator system in on-orbit operation, and establishes a vibration interference and non-Gaussian measurement noise lower end position filtering model based on the positive kinematics and joint dynamics of the space manipulator;
(2) the invention establishes a distributed multi-sensor information fusion framework, respectively designs an interference observer to estimate interference, then carries out interference feedforward compensation on the basis of Kalman filtering, fuses the results of the anti-interference filtering in a weighting mode, and finally carries out interference feedforward compensation on preset multi-target H2/H∞And the fusion error is constrained under the performance index, and the global state estimation is completed, so that the anti-interference capability and the positioning precision of the system are improved.
Drawings
FIG. 1 shows a method for interference rejection based multiple targets H2/H∞A flow chart of the implementation of the filtering space manipulator end positioning method;
FIG. 2 is a diagram of multi-objective H based interference rejection2/H∞A structural diagram of a filtered space manipulator tail end position estimation loop;
FIG. 3 illustrates interference rejection multiple targets H2/H∞And (3) a disturbance and state estimation effect graph of the filtering method, wherein a is a flexible accessory vibration disturbance estimation effect, and b is a terminal position global estimation effect.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in FIG. 1, the invention provides a method based on anti-interference multiple targets H2/H∞Filtered nullThe specific design and implementation process of the positioning method for the tail end of the inter-mechanical arm is as follows:
the method comprises the following steps of firstly, determining flexible accessory vibration interference, actuating mechanism noise and sensor measurement noise of a space manipulator system, and establishing a terminal position filtering model by combining positive kinematics and joint dynamics of the space manipulator system:
the three-axis stable satellite is used as the spacecraft base, only the attitude of the base is controlled in a free flight mode, and the attitude angular rate omega of the base can be considered00, while the system linear momentum is conserved. Under this condition, positive kinematics and joint dynamics of the spatial arm system are obtained:
Figure BDA0002824614910000101
wherein p iseAs the end position of the arm, xbIs the posture of the base, q is the rotation angle of the mechanical arm connecting rod, tau is the control moment output by the joint motor, and TdThe moment is a vibration disturbance moment; j. the design is a squarebAnd JmAre Jacobian matrixes related to a spacecraft base and a mechanical arm connecting rod respectively,
Figure BDA0002824614910000102
i is an identity matrix and is a matrix of the identity,
Figure BDA0002824614910000103
r0as a base position, Jm＝[k1×(pe-p1)…kn×(pe-pn)]，kiUnit vector, p, representing the axis of rotation of the connecting rod ii(i is 1, …, n) is the connecting point position of the connecting rod i-1 and the connecting rod i, H (q) is a system positive definite inertia parameter matrix,
Figure BDA0002824614910000104
a non-linear array containing coriolis forces and centrifugal forces, M is the pedestal mass,
Figure BDA0002824614910000105
JTi＝[k1×(ri-p1) k2×(ri-p2)…ki×(ri-pi)0…0]，mi、rirespectively connecting rod i mass and centroid position.
Finishing to obtain:
Figure BDA0002824614910000106
wherein
Figure BDA0002824614910000107
Let state quantity x ═ pe T ve T]TWherein p ise、veRespectively representing the position and velocity of the end tool in an inertial coordinate system, the control input u and the joint state q,
Figure BDA0002824614910000108
Regarding, assume q,
Figure BDA0002824614910000109
Measurable, the state equation of the end position filtering model can be expressed as:
Figure BDA00028246149100001010
wherein
Figure BDA00028246149100001011
w is white gaussian noise with zero mean,
Figure BDA00028246149100001012
Figure BDA00028246149100001013
d is disturbance torque TdThe mathematical model can be described as follows:
Figure BDA0002824614910000111
w, B therein2And V is a known parameter matrix.
Through discretization, the state equation of the filtering model is as follows:
xk＝Ak-1xk-1+Bk-1uk-1+Gk-1dk-1+Gk-1wk-1
wherein A isk＝I+FΔT，
Figure BDA0002824614910000112
tkThe Δ T is the time interval measured by the sensor.
The end position of the space manipulator can be directly measured by means of multiple sensors such as an IMU, a camera and the like. For a camera, the measurement noise of the camera is obviously influenced by an external complex space environment, including (1) electromagnetic interference, (2) illumination change and (3) temperature change. If the statistical characteristics of the camera measurement noise are considered to satisfy the assumption of the kalman filter, the estimation performance is greatly degraded. Thus, the present invention treats the camera's measurement noise as a combination of white gaussian noise and norm-bounded non-gaussian noise.
Assuming that the IMU and camera used are calibrated, the measurement model is given directly as follows:
y1k＝H1kxk+D11kwk+D21kvk
y2k＝H2kxk+D21kwk+D22kvk
wherein y is1k、y2kMeasurement outputs of IMU and camera, H1k、H2kTo measure the coefficient, H1k＝H2k＝I，D11k、D12k、D21kAnd D22kIs a matrix of known parameters, wkWhite Gaussian noise of zero mean value, vkIs a norm-bounded non-gaussian noise. Initial state x0And wk、vkAre all irrelevant.
And secondly, designing an interference observer to estimate the vibration interference according to measurement data of a terminal IMU and a camera aiming at part of vibration interference of which prior information is known in a filtering model, and adding an interference feedforward compensation link on the basis of Kalman filtering to form an anti-interference filter:
for disturbance moment dkDesign of disturbance observer
Figure BDA0002824614910000113
Namely:
Figure BDA0002824614910000114
wherein
Figure BDA0002824614910000115
K is the interference estimation gain to be designed.
Based on this, the state update can be expressed as:
Figure BDA0002824614910000121
where L is the filter gain to be designed.
Will omegakExpansion into system equation of state, setting expansion state
Figure BDA0002824614910000122
The filter model can be rewritten as follows:
Figure BDA0002824614910000123
wherein
Figure BDA0002824614910000124
Setting an estimate of an augmented state
Figure BDA0002824614910000125
The disturbance observer based filter can be arranged as:
Figure BDA0002824614910000126
wherein
Figure BDA0002824614910000127
The filter form is similar to the kalman filter of an augmented system for the gain matrix to be designed.
Thirdly, designing a distributed multi-sensor information fusion framework, wherein an anti-interference filter is used as a sub-filter, a main filter is designed, an estimation value of the sub-filter is fused in a weighting method, and multiple targets H are adopted2/H∞The fusion algorithm restrains the fusion error under the preset performance index, solves the interference estimation gain, the filtering gain and the weighting weight by means of the linear matrix inequality set, and obtains the global estimation of the tail end position of the space manipulator:
calculating main filter estimated value by adopting weighting method
Figure BDA0002824614910000128
The following were used:
Figure BDA0002824614910000129
wherein
Figure BDA00028246149100001210
Are all sub-filter estimates, Wi＝diag{wi1,wi2,…,winAnd (i ═ 1,2) are the sub-filter weighting weights. According to the unbiased requirement, W1+W2I. Defining an estimation error ekComprises the following steps:
Figure BDA0002824614910000131
is provided with
Figure BDA0002824614910000132
The following can be obtained:
Figure BDA0002824614910000133
wherein the content of the first and second substances,
Figure BDA0002824614910000134
Cm＝[I-W1-W2]，
Figure BDA0002824614910000135
Figure BDA0002824614910000136
W1＝0，
Figure BDA0002824614910000137
for simultaneously processing Gaussian white noise wkAnd non-Gaussian noise v with uncertain statistical propertieskUsing robust H2/H∞The performance index is restricted, and the design target of the filter is (1) the system is asymptotically stable; (2) from vkTo the filtering error ekH of transfer function of∞Norm does not exceed a given upper bound γ; (3) from white noise wkTo error ekH of transfer function of2Norm as small as possible to ensure ekSteady state variance of (G)m TP2Gm) As small as possible, wherein P2Lyapunov matrix equation A if more than 0m TP2Am+Cm TCm-P2A solution of 0.
If for a known coefficient r1＞0、r2> 0, sub-filter weight W to be designed1、W2And gamma > 0, presence matrix G1、G2、G3、Π＞0、Pi＞0(i＝1～3)、R1、R2Satisfies the following conditions:
minr1Trace(Π)+r2γ
s.t.
(1)
Figure BDA0002824614910000141
(2)
Figure BDA0002824614910000142
(3)
Figure BDA0002824614910000143
wherein xi1＝P1-G1-G1 T，Ξ2＝P2-G2-G2 T，Ξ3＝P3-G3-G3 T，Ξ25＝G2A-R1H1，Ξ36＝G3A-R2H2. Designing a filter gain K1＝G2 -1R1，K2＝G3 -1R2Under the gain, the filtering error system is stable and meets the robust performance index of the system. Thus far, multiple targets H are designed2/H∞The fusion estimation framework gives a suboptimal estimation of multi-source interference and end position and speed.
As shown in fig. 2, in the space manipulator end position estimation loop, two anti-interference sub-filters are designed to perform filtering estimation on measurement data of the end IMU and the camera, respectively, and the estimation result is obtained
Figure BDA0002824614910000144
Transmitted to main filter, fused in a weighted manner, and combined in H2/H∞Calculating interference estimation gain, filtering gain and weighting weight under performance index, and obtaining global estimation value
Figure BDA0002824614910000145
Used for subsequent controller design, and forms a complete end position estimation loop.
As shown in fig. 3, (a) is a diagram of the estimation effect of the single anti-interference sub-filter on the vibration interference, it can be seen that the interference estimation error gradually decreases and stabilizes within the range of ± 0.02N after 12 seconds; (b) the method is a global estimation effect diagram of the X-axis position of the tail end, and can be seen that the tail end positioning error is stabilized within the range of +/-0.01 m, and the estimation effect is good.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (4)

1. Based on anti-interference multiple target H2/H∞The filtering space manipulator tail end positioning method is characterized by comprising the following steps:
firstly, determining flexible accessory vibration interference, actuating mechanism noise and sensor measurement noise suffered by a space manipulator system, and establishing a terminal position filtering model according to positive kinematics and joint dynamics of the space manipulator system;
secondly, aiming at the vibration interference of which part of prior information is known in the terminal position filtering model, designing an interference observer according to measurement data of a terminal IMU and a camera, estimating the vibration interference, and adding an interference feedforward compensation link on the basis of Kalman filtering to form an anti-interference filter;
thirdly, designing a distributed multi-sensor information fusion framework, wherein an anti-interference filter is used as a sub-filter, a main filter is designed, an estimation value of the sub-filter is fused in a weighting method, and multiple targets H are adopted2/H∞And the fusion algorithm restrains the fusion error under the preset performance index, and solves the interference estimation gain, the filtering gain and the weighting weight by means of the linear matrix inequality set to obtain the global estimation of the tail end position of the space manipulator.
2. Anti-interference multi-target based H according to claim 12/H∞The filtering space manipulator tail end positioning method is characterized in that: the first step is to determine the vibration interference of the flexible attachment, the noise of an actuating mechanism and the noise measured by a sensor on the space manipulator system, and establish a terminal position filtering model by combining the positive kinematics and the joint dynamics of the space manipulator system as follows:
let state quantity x ═ pe T ve T]TWherein p ise、veRespectively representing the position and the speed of the tail end of the space mechanical arm system under an inertial coordinate system, and establishing a state equation of a tail end position filtering model according to the positive kinematics and the joint dynamics of the system as follows:
Figure FDA0003596896060000011
wherein the control input
Figure FDA0003596896060000012
w is white gaussian noise with zero mean,
Figure FDA0003596896060000013
Figure FDA0003596896060000021
I3is an identity matrix; q is the rotation angle of the mechanical arm connecting rod, tau is the control moment output by the joint motor,
Figure FDA0003596896060000022
m is the base mass, JbAnd JmAre Jacobian matrixes related to a spacecraft base and a mechanical arm connecting rod respectively,
Figure FDA0003596896060000023
Figure FDA0003596896060000024
r0as a base position, Jm＝[k1×(pe-p1) … kn×(pe-pn)]，kiRepresenting unit vectors, p, of the axis of rotation of the connecting rod ii(i is 1, …, n) is the connecting point position of the connecting rod i-1 and the connecting rod i, H (q) is a system positive definite inertia parameter matrix,
Figure FDA0003596896060000025
a non-linear array containing coriolis forces and centrifugal forces,
Figure FDA0003596896060000026
JTi＝[k1×(ri-p1) k2×(ri-p2) … ki×(ri-pi) 0 … 0]，mi、rirespectively the mass and the mass center position of the connecting rod i, and n is the degree of freedom of the mechanical arm; d is disturbance torque TdThe mathematical model is described as follows:
Figure FDA0003596896060000027
w, B therein2And V is a known parameter matrix;
after discretization, the equation of state is written as:
xk＝Ak-1xk-1+Bk-1uk-1+Gk-1dk-1+Gk-1wk-1
wherein A isk＝I+FΔT，
Figure FDA0003596896060000028
tkThe delta T is a time interval measured by the sensor;
assuming that the IMU and the camera sensor are calibrated, the measurement equation for the filtering model of the end position is directly given as follows:
y1k＝H1kxk+D11kwk+D12kvk
y2k＝H2kxk+D21kwk+D22kvk
wherein y is1k、y2kMeasurement outputs of IMU and camera, H1k、H2kFor measuring the coefficient matrix, H can be considered1k＝H2k＝I，D11k、D12k、D21kAnd D22kIs a matrix of known parameters, wkWhite Gaussian noise with zero mean, vkIs norm-bounded non-Gaussian characteristic noise, initial state x0And wk、vkAre irrelevant.
3. Anti-interference multi-target based H according to claim 12/H∞The filtering space manipulator tail end positioning method is characterized in that: and in the second step, aiming at the vibration interference of which part of prior information is known in the terminal position filtering model, designing an interference observer to estimate the vibration interference according to measurement data of a terminal IMU and a camera respectively, and adding an interference feedforward compensation link on the basis of Kalman filtering to form an anti-interference filter, wherein the interference observer specifically comprises the following steps:
setting augmented system states
Figure FDA0003596896060000031
ykFor the measurement output of the terminal IMU or camera, the filter model is rewritten to the following form:
Figure FDA0003596896060000032
wherein
Figure FDA0003596896060000033
Setting an augmented state estimate
Figure FDA0003596896060000034
Design based on interferenceThe observed antijam filter is:
Figure FDA0003596896060000035
wherein
Figure FDA0003596896060000036
The gain matrix to be designed comprises an interference estimation gain K and a filtering estimation gain L.
4. Anti-interference multi-target based H according to claim 12/H∞The filtering space manipulator tail end positioning method is characterized by comprising the following steps: and the third step, designing a distributed multi-sensor information fusion framework, wherein an anti-interference filter is used as a sub-filter, a main filter is designed, the estimated values of the sub-filters are fused in a weighting method, and multiple targets H are adopted2/H∞The fusion algorithm restrains the fusion error under the preset performance index, and solves the interference estimation gain, the filtering gain and the weighting weight by means of the linear matrix inequality set to obtain the global estimation of the tail end position of the space manipulator;
and calculating the estimated value of the main filter by adopting a weighting method as follows:
Figure FDA0003596896060000041
wherein
Figure FDA0003596896060000042
Are all sub-filter estimates, weight Wi＝diag{wi1,wi2,…,winW is required according to unbiased requirement } (i ═ 1,2)1+W2Define the estimation error e as IkComprises the following steps:
Figure FDA0003596896060000043
is provided with
Figure FDA0003596896060000044
Obtaining:
Figure FDA0003596896060000045
wherein the content of the first and second substances,
Figure FDA0003596896060000046
Cm＝[I -W1 -W2]，
Figure FDA0003596896060000047
Figure FDA0003596896060000048
for simultaneously processing Gaussian white noise wkAnd non-Gaussian noise v with uncertain statistical propertieskUsing robust H2/H∞Performance index pair ekPerforming constraint, namely:
if for a known coefficient r1＞0、r2> 0, sub-filter weight W to be designed1、W2And gamma > 0, presence matrix G1、G2、G3、Π＞0、Pi＞0(i＝1～3)、R1、R2Satisfies the following conditions:
min r1Trace(Π)+r2γ
s.t.
(1)
Figure FDA0003596896060000051
(2)
Figure FDA0003596896060000052
(3)
Figure FDA0003596896060000053
wherein xi1＝P1-G1-G1 T，Ξ2＝P2-G2-G2 T，Ξ3＝P3-G3-G3 T，Ξ25＝G2A-R1H1，Ξ36＝G3A-R2H2(ii) a Let the filter gain K1＝G2 -1R1，K2＝G3 -1R2Ensuring that (1) the system is asymptotically stable; (2) from vkTo the filtering error ekH of transfer function of∞Norm does not exceed a given upper bound γ; (3) from white gaussian noise wkTo error ekH of transfer function of2The norm is as small as possible, and the robust performance index of a filtering error system is met.
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