Method for improving precision of rigid-flexible coupling space robot system

Abstract

The invention belongs to the technical field of robot control, and particularly discloses a precision improving method of a rigid-flexible coupling space robot system. According to the method, a rigid-flexible coupling dynamic model of the space robot is constructed, a sliding mode controller based on a non-singular sliding mode surface is designed, a radial basis function (RBF) neural network is used for estimating flexible structure vibration and space environment interference, total disturbance and estimation errors of the neural network are overcome through self-adaptive gains, and the space robot rigidity-flexible coupling dynamic model is obtained. Therefore, the robustness and the response speed of the system are improved. According to the method, the high precision and stability of the space robot can be effectively ensured when the space robot executes tasks such as capturing operation, on-orbit maintenance and space junk cleaning, and the method is suitable for various space task scenes with flexible structures.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot control, and in particular relates to a method for improving the accuracy of a rigid-flexible coupling space robot system. Background Art

[0002] Space robots play a vital role in performing tasks such as satellite maintenance, space debris cleaning, and on-orbit construction. When operating on-orbit, they usually need to perform high-precision operations on target objects in complex external environments (such as microgravity, space radiation, etc.). With the increasing frequency of space exploration activities and the continued growth in the demand for on-orbit operation tasks, space robot systems that traditionally rely only on rigid robotic arms and fixed bases have become unable to cope with complex operating environments. This challenge has led to the complexity of the structural design of space robots, and the introduction of flexible structural components such as solar panels has not only significantly enhanced the environmental adaptability and flexibility of space robots, but also effectively improved the autonomous operation capability and mission execution efficiency of the entire system.

[0003] In the space robot system, the coupling effect of the flexible sailboard and the rigid manipulator poses a challenge to the tracking control accuracy and stability of the system. Although the introduction of flexible structures brings many advantages, it is also easy to excite structural vibrations. This vibration effect will introduce additional dynamic uncertainties, which may lead to reduced accuracy of space robots when performing tasks and increase the complexity and difficulty of the control system. Traditional control methods are difficult to effectively cope with the effects of flexible structure vibration coupling and space environment interference while maintaining high-precision operation. Therefore, in space capture missions, there is an urgent need for an advanced control method that can adapt to the dynamic characteristics of flexible structures and compensate for them to ensure the stability and accuracy of the manipulator when performing capture, manipulation and other tasks. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a method for improving the accuracy of a rigid-flexible coupling space robot system to cope with the influence of flexible structure vibration and external environmental interference on the operating accuracy of the space robot, so as to improve stability and accuracy.

[0005] The method for improving the precision of the rigid-flexible coupling space robot system of the present invention comprises the following steps:

[0006] S1. Based on the recursive group set and velocity variation method, a dynamic model of a rigid-flexible coupling space robot system is established, wherein the rigid-flexible coupling space robot system includes a central rigid body base, a rigid link of a robotic arm, and a flexible sailboard; establishing the dynamic model specifically includes the following steps:

[0007] S1.1. Define the generalized coordinates of the system. For the central rigid body base, the generalized coordinates are defined as r1 and ψ1 are the position vector of the center of mass of the central rigid body base and the Euler angle vector expressed in the form of xyz respectively; for the rigid link of the robot arm, the generalized coordinate is defined as y i =q i (i=2,3...n+1); For the flexible sailboard, the generalized coordinates are defined as where a i is the modal coordinate of the flexible sailboard, q i is the rotation angle of the hinge;

[0008] S1.2. Define the moving body B i The generalized speed is as follows:

[0009]

[0010] Among them, v i and w i are the linear velocity and angular velocity of the moving body’s body coordinate system relative to the inertial coordinate system respectively;

[0011] S1.3, get the rigid body B i and B j The motion relationship between i and B j Through the hinge H j connect, and Movement body B i The hinge point and sports body B j The hinge point The coordinate system at and Represents the transformation matrix of each hinge point relative to the floating coordinate system of the body. Here, the coordinate system of the hinge point is set to be the same as the floating coordinate system of the object, that is, Will and The transformation relationship between them is defined as R j , sports body B j The posture can be expressed as:

[0012]

[0013] Among them, C j =C j0 R j , C j0 represents the initial installation matrix of the two hinge points;

[0014] Fixed coordinate system O of space robot system j x j y j z jThe position relative to the inertial frame is expressed as:

[0015]

[0016] By taking the derivative of formula (3), we can get:

[0017]

[0018] Sports body B j The angular velocity of the moving body B i The angular velocity is expressed as:

[0019] w j =w i +w rj (5)

[0020] By taking the derivative of formula (5), we can get:

[0021]

[0022] Among them, h j ′ represents the rotary hinge H j The rotation vector in the inertial coordinate system, h j =A 0i h j ′;h j ′ represents the moving body B j Relative to the moving body B i The rotation vector of

[0023] Substituting formula (5) into formula (4), we have:

[0024]

[0025] Derivative of formula (4):

[0026]

[0027] Substituting equations (5) and (6) into equation (8), we can obtain:

[0028]

[0029] Combining equation (6) and equation (7), we can get:

[0030]

[0031] in,

[0032] Combining equation (6) and equation (9), we can get:

[0033]

[0034] Equations (10) and (11) are the kinematic relationships between rigid bodies;

[0035] S1.4. Analyze the kinematic relationship between the central rigid base and the flexible sailboard, that is, the recursive relationship between the velocity and acceleration between the rigid body and the flexible structure:

[0036]

[0037] in,

[0038] S1.5. Obtain the kinematic recursive relationship between the various moving bodies of the space rigid-flexible coupling robot; for a multi-body system, the relationship can be expressed as:

[0039]

[0040] Among them, i=i + (j) represents the moving body B j the internal body of

[0041]

[0042] According to formula (13), the speed change of the system can be calculated as:

[0043]

[0044] The system dynamics equation is established based on Jourdain velocity variation principle:

[0045]

[0046] Among them, M i , f i ω , f i o , f i u They are called generalized mass matrix, generalized inertia force matrix, generalized external force matrix and generalized deformation force matrix respectively; ΔP is the virtual power of ideal constraint force and non-ideal constraint force;

[0047] Substituting equation (13) and equation (14) into equation (15), we can obtain:

[0048]

[0049] Using the joint coordinates of the robot and the modal coordinates of the flexible body as generalized variables, the dynamic model of the rigid-flexible coupling space robot is expressed as:

[0050]

[0051] The first equation of the spatial rigid-flexible coupling robot dynamics model (17) can be transformed into:

[0052]

[0053] Among them, q r is the generalized coordinate of the central rigid base and the rigid manipulator, q f is the generalized coordinate of the flexible sailboard, u is the control vector;

[0054] From the first line of formula (18), we get:

[0055]

[0056] Considering various uncertainties, formula (19) can be written as:

[0057]

[0058] Among them, d e is the external disturbance, d is the set of various disturbance forces that will affect the control accuracy of the manipulator; Formula (20) includes all disturbances to the central rigid base and the rigid manipulator. The effect of the control force on the system is also affected by the generalized inertia tensor, and the system has strong nonlinearity;

[0059] S2. Controller design adopts a control strategy combining sliding mode control and radial basis function neural network. The specific steps are as follows:

[0060] S2.1. Define the non-singular terminal sliding surface:

[0061]

[0062] Where e = q r -q d is the tracking error vector of the system state, q d For a given desired trajectory, is the error change rate of system state tracking. 1<q / p<2, p and q are positive odd numbers;

[0063] By taking the derivative of the sliding mode function (21) and substituting the first line of (20) into it, we can get the expression:

[0064]

[0065] Among them, diag(*) means constructing a diagonal matrix with the elements in the vector as the main diagonal;

[0066] S2.2. Design the following control law for the space robot system:

[0067] u=u1+u2 (23)

[0068] make The equivalent control law u1 can be obtained:

[0069]

[0070] in, is the estimation of uncertainty by RBF neural network;

[0071] Set the switching control law to:

[0072] u2=-Z 11 (k0s+diag(k1)sat(s)) (25)

[0073] Among them, k0 is a positive definite diagonal matrix; sat(*) is a saturation function, and the saturation boundary thickness is υ; k1 is the adaptive gain, and the designed adaptive law is:

[0074]

[0075] Among them, η>0 is the adaptive learning rate;

[0076] S2.3. Set the adaptive law of the neural network:

[0077]

[0078] in, is the estimated weight of the RBF neural network; ζ is a positive definite diagonal matrix, which represents the learning rate of the neural network; h is the radial basis vector of the RBF neural network, which is a column vector. The i-th formula can be expressed as:

[0079]

[0080] Among them, x is the input signal of the neural network; b i is the basis function width; c i It is the data center of the neural node.

[0081] The beneficial effects of the present invention are:

[0082] (1) High nonlinear approximation capability: Through rigid-flexible coupling dynamics modeling, the present invention comprehensively considers the coupling effects of the vibration of the flexible sailboard and the interference of the external space environment on the rigid base and rigid manipulator system at the center of the space. By using the online adaptive estimation capability of the radial basis function (RBF) neural network, the system can dynamically learn and update the estimated value of the uncertainty caused by the flexible structure and external interference in real time. The nonlinear approximation capability of the RBF neural network ensures the high adaptability and robustness of the system in complex dynamic environments, thereby improving the control accuracy.

[0083] (2) Efficient adaptive and robust control: The sliding mode controller of the present invention combines the adaptive control strategy of the neural network, effectively estimates the impact of the external environmental disturbance of the flexible structure vibration on the robot control, and combines the robustness characteristics of the sliding mode control to suppress these disturbances. This combination not only ensures the stability of the system under uncertain conditions, but also gives the system the ability to quickly respond to changes in the system state, achieving efficient control in a dynamic task environment. In addition, the system can adjust the control parameters in real time according to the actual operating status, ensuring the high-precision operation of the robot arm under various task conditions, demonstrating excellent adaptive capabilities.

[0084] (3) High applicability and wide application scenarios: The present invention is not only applicable to space missions with flexible structures, such as space capture, on-orbit maintenance, and space debris cleaning, but can also be extended to spacecraft operation, flexible robotic arms, industrial automation, and other fields involving flexible-rigid coupling systems. This wide range of application prospects makes the present invention have great technical promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0086] Figure 1 It is a schematic diagram of the rigid-flexible coupling space robot system.

[0087] Figure 2 It is a schematic diagram of the kinematic relationship between adjacent objects.

[0088] Figure 3 It is the fixed coordinate system of the space robot system.

[0089] Figure 4 This is a diagram of the control effect of the space robot, including (a) the position and posture of the base, (b) the trajectory of the joint angle of the robot arm, (c) the position tracking error of the base, (d) the position tracking error of the base, (e) the tracking error of the joint angle of the robot arm, (f) the control force of the base, (g) the control torque of the base, and (h) the control torque of the robot arm.

[0090] Figure 5 is the node displacement diagram at the edge of the sailboard. DETAILED DESCRIPTION

[0091] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0092] Example 1

[0093] like Figure 1 As shown, the space robot system includes a central rigid base B1, an n-degree-of-freedom mechanical arm rigid link, and two flexible sailboards B n+2 and B n+3 , virtual body B0 and virtual hinge H1 are used to describe the motion of the central rigid body B1. Virtual hinge H1 is fixed on virtual body B0 and has three translational degrees of freedom and three rotational degrees of freedom. The inertial coordinate system O0x0y0z0 is fixed on the virtual body. The floating coordinate system O1x1y1z1 is fixed on the central rigid body B1, and the origin is fixed on the center of mass of the central rigid body B1. The origin of the floating coordinates of the robot arm link is fixed on the center of mass of each link. The floating coordinate system of the flexible sailboard is fixed on the center of mass before deformation.

[0094] A method for improving the accuracy of a rigid-flexible coupling space robot system comprises the following steps:

[0095] S1. Establishment of rigid-flexible coupling dynamics model based on recursive grouping and velocity variation method

[0096] In order to obtain the dynamic model of the space robot system, it is necessary to analyze the recursive relationship between the moving bodies. First, define the generalized coordinates of the system. For the base, define the generalized coordinates as r1 and ψ1 are the position vector of the center of mass of the base and the Euler angle vector expressed in the form of xyz respectively; for the rigid link of the robot arm, the generalized coordinate is defined as y i =q i (i=2,3...n+1); For the flexible sailboard, the generalized coordinates are defined as where a i is the modal coordinate of the flexible sailboard, q i is the rotation angle of the hinge.

[0097] Define moving body B i The generalized speed is as follows:

[0098]

[0099] Among them, v i and w i are the linear velocity and angular velocity of the moving body's body coordinate system relative to the inertial coordinate system, respectively.

[0100] The two flexible sailboards of the space robot are fixed-end constraints, that is, one end is fixed, and there is no deformation at the hinge point between the central rigid body and the flexible sailboard, so it is only necessary to analyze the kinematic relationship between the rigid bodies. Figure 2 As shown, the moving body B i and B j , between them there is a hinge H j connect. and Movement body B i The hinge point and sports body B j The hinge point The coordinate system at . and Represents the transformation matrix of each hinge point relative to the floating coordinate system of the body. Here, the coordinate system of the hinge point is set to be the same as the floating coordinate system of the object, that is, Will and The transformation relationship between them is defined as R j . Sports body B j The posture can be expressed as:

[0101]

[0102] Among them, C j =C j0 R j , C j0 represents the initial installation matrix of the two hinge points;

[0103] like Figure 3 As shown, the coordinate system O j x j y j z j The position relative to the inertial frame can be expressed as:

[0104]

[0105] By taking the derivative of formula (3), we can get:

[0106]

[0107] Sports body B j The angular velocity of the moving body B i The angular velocity is expressed as:

[0108] w j =w i +w rj (5)

[0109] By taking the derivative of formula (5), we can get:

[0110]

[0111] Among them, h j Represents the rotary hinge H j The rotation vector in the inertial coordinate system, h j =A 0i h j ′;h j ′ represents the moving body B j Relative to the moving body B i The rotation vector of

[0112] Substituting formula (5) into formula (4), we have:

[0113]

[0114] Derivative of formula (4):

[0115]

[0116] Substituting equations (5) and (6) into equation (8), we can obtain:

[0117]

[0118] Combining equation (6) and equation (7), we can get:

[0119]

[0120] in,

[0121] Combining equation (6) and equation (9), we can get:

[0122]

[0123] Equations (10) and (11) are the kinematic relationships between rigid bodies;

[0124] For the space robot system of the central rigid body and the flexible sailboard, its kinematic relationship can be described as the recursive relationship between the velocity and acceleration of the rigid body and the flexible structure:

[0125]

[0126] in,

[0127] From the above derivation, the kinematic recursive relationship between the various moving bodies of the space rigid-flexible coupling robot is obtained. For a multi-body system, the relationship can be expressed as:

[0128]

[0129] Among them, i=i + (j) represents the moving body B j the internal body of

[0130]

[0131]

[0132] According to formula (13), the speed change of the system can be calculated as:

[0133]

[0134] The system dynamics equation is established based on Jourdain velocity variation principle:

[0135]

[0136] Among them, M i , f i ω , f i o , f i u They are called generalized mass matrix, generalized inertia force matrix, generalized external force matrix and generalized deformation force matrix respectively; ΔP is the virtual power of ideal constraint force and non-ideal constraint force;

[0137] Substituting equation (13) and equation (14) into equation (15), we can obtain:

[0138]

[0139] Using the joint coordinates of the robot and the modal coordinates of the flexible body as generalized variables, the dynamic model of the rigid-flexible coupling space robot is expressed as:

[0140]

[0141] The first equation of the spatial rigid-flexible coupling robot dynamics model (17) can be transformed into:

[0142]

[0143] Among them, q r is the generalized coordinate of the central rigid base and the rigid manipulator, q f is the generalized coordinate of the flexible sailboard, u is the control vector;

[0144] From the first line of formula (18), we get:

[0145]

[0146] Considering various uncertainties, formula (19) can be written as:

[0147]

[0148] Among them, d e is the external disturbance, and d is the collection of various disturbance forces that will affect the control accuracy of the robotic arm.

[0149] Formula (20) includes all disturbances to the base and the rigid manipulator. The effect of the control force on the system is also affected by the generalized inertia tensor, and the system has strong nonlinearity.

[0150] S2. Controller Design

[0151] In the space robot system, the uncertainty of the actual dynamic parameters, the interference force caused by the vibration of the flexible sailboard, and the disturbance of the external environment will affect the trajectory tracking accuracy of the robot arm joint. In order to improve the trajectory tracking performance of the robot arm, the present invention adopts a control strategy that combines sliding mode control with radial basis function (RBF) neural network. The sliding mode controller can guide the system state to the sliding surface and ensure that the state error gradually approaches zero, with good robustness. At the same time, the RBF neural network provides feedforward compensation by online estimating the interference force caused by the vibration of the flexible sailboard and the uncertainty of the system, further reducing the impact of system jitter and uncertainty on the controller, and significantly improving the control accuracy and system stability.

[0152] Define the non-singular terminal sliding surface:

[0153]

[0154] Where e = q r -q d is the tracking error vector of the system state, q d For a given desired trajectory, is the error change rate of system state tracking, 1<q / p<2, p and q are positive odd numbers;

[0155] By taking the derivative of the sliding mode function (21) and substituting the first line of (20) into it, we can get the expression:

[0156]

[0157] Where diag(*) means constructing a diagonal matrix with the elements in the vector as the main diagonal.

[0158] The following control law is designed for the space robot system:

[0159] u=u1+u2 (23)

[0160] make The equivalent control law u1 can be obtained:

[0161] u2=-Z 11 (k0s+diag(k1)sat(s)) (24)

[0162] in, is the estimation of uncertainty by RBF neural network;

[0163] Set the switching control law to:

[0164] u2=-Z 11 (k0s+diag(k1)sat(s)) (25)

[0165] Among them, k0 is a positive definite diagonal matrix; sat(*) is a saturation function, and the saturation boundary thickness is υ; k1 is the adaptive gain, and the designed adaptive law is:

[0166]

[0167] Among them, η>0 is the adaptive learning rate.

[0168] To ensure that the neural network can better learn uncertainty, set the adaptive law of the neural network:

[0169]

[0170] in, is the estimated weight of the RBF neural network; ζ is a positive definite diagonal matrix, which represents the learning rate of the neural network; h is the radial basis vector of the RBF neural network, which is a column vector. The i-th formula can be expressed as:

[0171]

[0172] Among them, x is the input signal of the neural network; b i is the basis function width; c i It is the data center of the neural node.

[0173] Controller stability analysis:

[0174] Assume the optimal estimated weight of the neural network is W * , then the uncertainty estimation error of the system is:

[0175]

[0176] Among them, ε * is the optimal approximation error, |ε * |≤ε N .

[0177] At the same time, define as well as Set the Lyapunov function to:

[0178]

[0179] By taking the derivative of formula (30), we can obtain:

[0180]

[0181] Substituting formula (23) into (22), we can obtain:

[0182]

[0183] Substituting equations (32) and (31) into equation (31), we have:

[0184]

[0185] in, Also because Therefore, formula (33) can be written as:

[0186]

[0187] Substituting formula (27) into formula (34), we have:

[0188]

[0189] Substituting formula (26) into formula (35), we have:

[0190]

[0191] According to the Lyapunov stability theorem, the designed non-singular terminal sliding mode can make the tracking error converge.

[0192] Simulation example:

[0193] To describe the relative motion of the joints in a multi-body space robot, according to Figure 3 A rigid body fixed coordinate system of the space robot system is established, where Z i Defined as the i-th joint J i The link parameters of the robot arm are defined as shown in Table 1, where a i , b i , I i is the corresponding vector in the coordinate system Σ i The dimensions of the two flexible sailboards are 5×2×0.025m, their elastic modulus is 3Gpa, Poisson's ratio is 0.3, and damping ratio is 0.1.

[0194] Table 1 Physical parameters of space robot system

[0195] Space Robot Base Connecting rod 1 Connecting rod 2 Connecting rod 3 Connecting rod 4 Connecting rod 5 Connecting rod 6 Mass m 400 30 25 10 8 6 8 <![CDATA[Centroid vector a ix > 0 0 0.2702 0 0 0 0 <![CDATA[Centroid vector a iy > 0 0 0 0 0 -0.0338 0 <![CDATA[Centroid vector a iz > 0 0.15 -0.2513 0.15 -0.35 0 0.075 <![CDATA[Body hinge vector b ix > 0 0 0.5598 0 0 0 0 <![CDATA[Body hinge vector b iy > 0 0 0 0 0 -0.0662 0 <![CDATA[Body hinge vector b iz > 0.5 0.15 -0.0487 0.15 -0.35 0 0.1595 <![CDATA[Moment of inertia I xx > 133 0.75 0.4630 0.21 0.4996 0.066 0.2061 <![CDATA[Moment of inertia I yy > 133 0.75 4.5265 0.21 0.4996 0.0344 0.2061 <![CDATA[Moment of inertia I zz > 133 0.375 4.2255 0.0588 0.0392 0.0520 0.0877 <![CDATA[Moment of inertia I xy > 0 0 0 0 0 0 0 <![CDATA[Moment of inertia I xz > 0 0 0.6575 0 0 0 0 <![CDATA[Moment of inertia I yz > 0 0 0 0 0 0 0

[0196] The initial base position, posture and manipulator joint angle of the space robot system are all 0 at the beginning. The control targets of the base position, posture and manipulator joint angle are set to [0.1, 0.1, 0.1, 30°, -30°, 40°, 45°, 45°, 47°, -38°, -46°, -37°] T The control parameter settings are shown in Table 2.

[0197] Table 2 Space robot system control parameters

[0198] parameter Numeric q 9 p 7 a diag([0.6,0.6,0.6,0.9,0.9,0.7,0.7,0.7,0.6,0.8,0.6]) <![CDATA[k0]]> diag([0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8]) η <![CDATA[5×10 4 ]]> ζ <![CDATA[8×10 5 ]]>

[0199] The main sources of uncertainty in the dynamics of the space robot are the unknown load at the end of the manipulator and the existing system disturbances. The external disturbance torques on the space base are assumed to be:

[0200] d base =0.15sin(0.5t)+0.5sin(0.01t) (37)

[0201] Assume that the disturbance torque on each rotating joint of the robot arm is:

[0202] d arm =0.04sin(0.5t)+0.02sin(0.01t) (38)

[0203] according to Figure 4 and Figure 5 As shown in the figure, the designed controller effectively realizes fast and stable tracking of the robot arm and the base, showing excellent tracking performance, and the tracking error is kept in a small range, which fully demonstrates that the controller has good dynamic response capability and high tracking accuracy.

[0204] At the same time, the powerful online learning ability of the RBF neural network enables it to effectively cope with the vibration of the flexible structure and various interferences from the external environment, thereby significantly improving the robustness and stability of the system. According to the experimental results, after 20 seconds, the neural network has basically completed the learning and compensation of external interference. Although the controller failed to completely eliminate the high-frequency vibration of the flexible sailboard, under the action of damping, the amplitude of the vibration gradually decreased and eventually stabilized. This process shows that the system exhibits good adaptability and vibration attenuation capabilities when dealing with the vibration of the flexible structure and interference from the external environment.

[0205] In summary, this control strategy combines the online learning ability of the RBF neural network to achieve effective estimation of the flexible structure vibration and external environmental interference, and overcomes the total disturbance and the estimation error of the neural network through adaptive gain, ensuring the stability and control accuracy of the system in complex task environments, and having strong robustness and task execution capabilities.

[0206] The embodiments of the present invention are described in detail above, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments are made without departing from the principles and spirit of the present invention, and still fall within the protection scope of the present invention.

Claims

1. A method for improving the accuracy of a rigid-flexible coupling space robot system, characterized in that: The following steps are involved: S1. Based on the recursive group set and velocity variation method, a dynamic model of a rigid-flexible coupling space robot system is established, wherein the rigid-flexible coupling space robot system includes a central rigid body base, a rigid link of a robotic arm, and a flexible sailboard; establishing the dynamic model specifically includes the following steps: S1.

1. Define the generalized coordinates of the system. For the central rigid body base, the generalized coordinates are defined as r1 and ψ1 are the position vector of the center of mass of the central rigid body base and the Euler angle vector expressed in the form of xyz respectively; for the rigid link of the robot arm, the generalized coordinate is defined as y i =q i (i=2,3...n+1); For the flexible sailboard, the generalized coordinates are defined as where a i is the modal coordinate of the flexible sailboard, q i is the rotation angle of the hinge; S1.

2. Define the moving body B i The generalized speed is as follows: Among them, v i and w i are the linear velocity and angular velocity of the moving body’s body coordinate system relative to the inertial coordinate system respectively; S1.3, get the rigid body B i and B j The motion relationship between i and B j Through the hinge H j connect, and Movement body B i The hinge point and sports body B j The hinge point The coordinate system at and Represents the transformation matrix of each hinge point relative to the floating coordinate system of the body. Here, the coordinate system of the hinge point is set to be the same as the floating coordinate system of the object, that is, Will and The transformation relationship between them is defined as R j , sports body B j The posture can be expressed as: Among them, C j =C j0 R j , C j0 represents the initial installation matrix of the two hinge points; Fixed coordinate system O of space robot system j x j y j z j The position relative to the inertial frame is expressed as: By taking the derivative of formula (3), we can get: Sports body B j The angular velocity of the moving body B i The angular velocity is expressed as: In j =in i +in rj (5) By taking the derivative of formula (5), we can get: Among them, h j Represents the rotary hinge H j The rotation vector in the inertial coordinate system, h j =A 0i h j ′;h j ' represents the moving body B j Relative to the moving body B i The rotation vector of Substituting formula (5) into formula (4), we have: Derivative of formula (4): Substituting equations (5) and (6) into equation (8), we can obtain: Combining equation (6) and equation (7), we can get: in, Combining equation (6) and equation (9), we can get: Equations (10) and (11) are the kinematic relationships between rigid bodies; S1.

4. The kinematic relationship between the central rigid body base and the flexible sailboard is obtained, which is the recursive relationship between the velocity and acceleration between the rigid body and the flexible structure: in, S1.

5. Obtain the kinematic recursive relationship between the various moving bodies of the space rigid-flexible coupling robot; for a multi-body system, the relationship can be expressed as: Among them, i=i + (j) represents the moving body B j the internal body of According to formula (13), the speed change of the system can be calculated as: The system dynamics equation is established based on Jourdain velocity variation principle: in, M i , f i ω , f i o , f i u They are called generalized mass matrix, generalized inertial force matrix, generalized external force matrix and generalized deformation force matrix respectively; ΔP is the virtual power of ideal constraint force and non-ideal constraint force; Substituting equation (13) and equation (14) into equation (15), we can obtain: Using the joint coordinates of the robot and the modal coordinates of the flexible body as generalized variables, the dynamic model of the rigid-flexible coupling space robot is expressed as: The first equation of the spatial rigid-flexible coupling robot dynamics model (17) can be transformed into: Among them, q r is the generalized coordinate of the central rigid base and the rigid manipulator, q f is the generalized coordinate of the flexible sailboard, u is the control vector; From the first line of formula (18), we get: Considering various uncertainties, formula (19) can be written as: Among them, d e is the external disturbance, d is the set of various disturbance forces that will affect the control accuracy of the manipulator; Formula (20) includes all disturbances to the central rigid base and the rigid manipulator. The effect of the control force on the system is also affected by the generalized inertia tensor, and the system has strong nonlinearity; S2, using the control strategy combining sliding mode control and radial basis function neural network to set the controller, the specific steps are as follows: S2.

1. Define the non-singular terminal sliding surface: Where e = q r -q d is the tracking error vector of the system state, q d For a given desired trajectory, is the error change rate of system state tracking, 1<q / p<2, p and q are positive odd numbers; By taking the derivative of the sliding mode function (21) and substituting the first line of (20) into it, we can get the expression: Among them, diag(*) means constructing a diagonal matrix with the elements in the vector as the main diagonal; S2.

2. Design the following control law for the space robot system: u=u1+u2 (23) make The equivalent control law u1 can be obtained: in, is the estimation of uncertainty by RBF neural network; Set the switching control law to: u2=-Z 11 (k0s+diag(k1)sat(s)) (25) Among them, k0 is a positive definite diagonal matrix; sat(*) is a saturation function, and the saturation boundary thickness is υ; k1 is the adaptive gain, and the designed adaptive law is: Among them, η>0 is the adaptive learning rate; S2.

3. Set the adaptive law of the neural network: in, is the estimated weight of the RBF neural network; ζ is a positive definite diagonal matrix, which represents the learning rate of the neural network; h is the radial basis vector of the RBF neural network, which is a column vector. The i-th formula can be expressed as: Among them, x is the input signal of the neural network; b i is the basis function width; c i It is the data center of the neural node.

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