Singular perturbation control method for flexible space robot based on decentralized neural network

Abstract

The present invention provides a method for controlling a flexible space robot under singular perturbation based on a decentralized neural network, comprising the following steps: establishing a system dynamics model; establishing a system dynamics model based on singular perturbation, including a slow-changing subsystem dynamics model and a fast-changing subsystem dynamics model, to achieve order reduction processing of the flexible space robot system; setting a dual time scale controller, including a fast-changing subsystem controller and a slow-changing subsystem controller; judging whether the system is a fast-changing subsystem or a slow-changing subsystem, and executing drive control. The present invention adopts singular perturbation technology, and the flexible space robot system is reduced to two independent subsystems at different time scales, thereby simplifying the system model structure, reducing the difficulty and complexity of control design, and improving versatility, tracking progress and stability.

Description

Technical Field

[0001] The invention relates to the technical field of space robot control, and in particular to a flexible space robot singular perturbation control method based on a decentralized neural network. Background Art

[0002] Flexible base and flexible arm space robot is a special robot with dual flexible structure, which can assist or replace astronauts to complete high-risk extravehicular missions. Flexible space robots serve in harsh environments with large temperature differences and strong radiation. Their dynamic models have the characteristics of parameter uncertainty, strong coupling, multi-modality and nonlinearity, which leads to the shortcomings of existing controllers, such as complex structure, poor real-time performance and low tracking accuracy. It is worth noting that, unlike ground robots, in an undamped high vacuum environment, the elastic deformation of the base of the flexible space robot and the modal vibration of the arm are difficult to attenuate, which has a great impact on the stability of the system. In view of this, the design of control schemes for flexible space robot systems has always been the focus of academic and industry attention. However, in previous extensive operation tasks, people usually regard space robots as multi-rigid body systems, while ignoring the flexible characteristics of the system, which makes it difficult for the original control scheme to achieve satisfactory control effects. On the other hand, the traditional centralized controller needs to coordinate the global state variables of the controlled system, which has the disadvantages of high dimension, complex structure and poor real-time performance, and consumes more onboard computing resources when solving. The decentralized control strategy does not need to know the global information of the system, but only needs the local information of the participating individuals and their adjacent nodes, so it shows better performance in terms of flexibility, real-time and reliability. Summary of the invention

[0003] The purpose of the present invention is to provide a singular perturbation control scheme to address the deficiencies in the above-mentioned background technology and solve the problems of complex controller structure, poor real-time performance and low tracking accuracy of flexible base and flexible arm space robot systems.

[0004] In order to achieve the above object, the present invention provides a method for controlling a flexible space robot under singular perturbation based on a decentralized neural network, comprising the following steps:

[0005] S1, establish the dynamic model of the flexible base and flexible arm space robot system;

[0006] S2, establish the dynamic model of the flexible base and flexible arm space robot system based on singular perturbation, including the slow-varying subsystem dynamic model and the fast-varying subsystem dynamic model. First, ignore the fast-varying time-scale variables to reduce the system dimension, and then introduce the boundary layer correction term to improve the approximation degree of the model, so as to achieve the order reduction processing of the flexible base and flexible arm space robot system;

[0007] S3, setting a dual time scale controller, including a fast-changing subsystem controller and a slow-changing subsystem controller;

[0008] S4, judge whether the flexible base and flexible arm space robot system is a fast-changing subsystem; if yes, use the fast-changing subsystem controller to execute control; if no, determine it is a slow-changing subsystem, and use the slow-changing subsystem controller to execute control; input the outputs of the two subsystem controllers to the subsequent driver, and after the data is stored, judge whether the running time has arrived, if not, continue to execute the loop judgment; if yes, the output result is end.

[0009] Furthermore, the dynamic equation of the flexible base and flexible arm space robot system in S1 is:

[0010]

[0011] in, is the symmetric, positive definite inertia matrix of the system; is the Coriolis force and centrifugal force vector of the system; q s =[θ0,θ1,θ2] T is the rigid generalized coordinate of the system; q f =[x b ,δ1,δ2] T is the flexible generalized coordinate of the system; K f =diag(k b ,k1,k2) is the stiffness matrix of the flexible system, τ=[u0,u1,u2] T is the control input of the system, u0 is the equivalent adjustment torque of the carrier attitude, u i (i=1,2) is the joint driver a i of control torque.

[0012] Furthermore, in S2, the system dynamics model is reduced in order based on singular perturbations to obtain a slow-varying subsystem that characterizes the carrier attitude stabilization and robot arm joint trajectory tracking, and a fast-varying subsystem that characterizes the elastic deformation of the base and the flexible vibration of the robot arm.

[0013] Furthermore, S2 specifically includes the following sub-steps:

[0014] S21, establish the dynamic model of the slow-changing subsystem;

[0015] Define the bending stiffness matrix K f The smaller element is k min , the singular perturbation factor is ε=(1 / k min ) 1 / 2 ; Introduce a new state variable ξ f , K ε (ε2 ξ f =q f ,K ε =ε 2 K f ), the dynamic equation of the slow-varying subsystem is obtained as:

[0016]

[0017] in, is the quantity corresponding to {··} when ε=0;

[0018] S22, establish the fast-changing subsystem dynamics model;

[0019] Introducing fast-changing time scale t f (εt f = t-t0) and boundary layer correction The dynamic equation of the fast-changing subsystem is obtained as follows:

[0020]

[0021] in, τ f It is the control input of the fast-changing subsystem;

[0022]

[0023] S23, combining the slow-changing subsystem dynamics model and the fast-changing subsystem dynamics model to obtain the singular perturbation model of the flexible base and flexible arm space robot system.

[0024] Furthermore, S3 specifically includes the following sub-steps:

[0025] S31, setting a slow-changing subsystem controller;

[0026] The slow-varying subsystem is further decomposed into the following three coupled subsystems:

[0027]

[0028] Among them, q si , and The vector q s , and The i-th (i=1,2,3) component of and The matrix and The ijth component of ;

[0029] Let x i =[x i1 ,xi2 ] T =[q si ,υ si ] T , then formula (15) can be rewritten as

[0030]

[0031] in,

[0032] definition With g i (q ri ) are as follows: With g i (q ri ,W ig ), the decentralized neural network trajectory tracking controller of the slow-varying subsystem is set as:

[0033]

[0034] in, and In order and The estimated value of and is the estimation error; is a positive constant; and f i (q i ,υ i ), g i (q i ) and cross-linking items The neural network estimate of ;

[0035] S32, setting a fast-changing subsystem controller;

[0036] Based on the negative feedback of the state variable, the PD feedback controller is set as:

[0037] τ f =-K f ζ(74)

[0038] Among them, K f ∈R 3×6 is the gain matrix;

[0039] S33, combining the fast-changing subsystem controller and the slow-changing subsystem controller;

[0040] According to the multiple time scale theory, the subsystem controllers obtained by S32 and S31 are combined to obtain the combined controller of the flexible base and flexible arm space robot system:

[0041]

[0042] The above scheme of the present invention has the following beneficial effects:

[0043] The invention provides a flexible space robot singular perturbation control method based on a decentralized neural network. The singular perturbation technology is adopted. The flexible space robot system is reduced to two independent subsystems at different time scales, thereby simplifying the system model structure and reducing the difficulty and complexity of the control design.

[0044] The present invention controls the corresponding subsystems individually through the subsystem controller, and the control accuracy and stability of each subsystem are not affected by other subsystems, making the control of the present invention more universal;

[0045] The present invention adopts the decentralized principle to further simplify the model structure of the slow-changing subsystem, combines the decentralized neural network technology to reconstruct the model of the second-order subsystem, solves the problem of uncertainty of system model parameters, and improves tracking accuracy;

[0046] The present invention utilizes a PD state feedback controller to effectively suppress the modal vibration of the flexible arm, thereby improving the stability of the control system without the need to accurately obtain the dynamic parameters of the model.

[0047] The present invention unifies the time scales of subsystem controllers under different time scales, adopts a combined control method to improve the reliability and flexibility of control, is easy to implement in engineering, and has good real-time performance;

[0048] Other beneficial effects of the present invention will be described in detail in the subsequent specific implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a flow chart of the method steps of the present invention;

[0050] Figure 2 This is a schematic diagram of the structure of the flexible base and flexible arm space robot system in the present invention;

[0051] Figure 3 It is the principle diagram of the singular perturbation control method of the present invention;

[0052] Figure 4 It is a schematic diagram of the structure of the slow-changing subsystem of the present invention. DETAILED DESCRIPTION

[0053] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0054] In the description of the present invention, for simplicity of explanation, the method or rule is depicted or described as a series of operations, and its purpose is neither to exhaustively list the experimental operations nor to limit the order of the experimental operations. For example, the experimental operations can be performed in various orders and / or simultaneously, and include other experimental operations that are not described again. In addition, the steps described are not all necessary for the methods and algorithms described herein. Those skilled in the art will recognize and understand that these methods and algorithms can be represented as a series of unrelated states through state diagrams or projects.

[0055] Embodiment 1:

[0056] See also Figure 1 Embodiment 1 of the present invention provides a method for controlling singular perturbations of a flexible base and flexible arm space robot system, comprising the following steps:

[0057] S1, establish the dynamic model of the flexible base and flexible arm space robot system.

[0058] See also Figure 2 The control object of this method is a flexible base and flexible arm space robot system, which consists of a flexible floating carrier, a rigid arm, a flexible arm, two revolute joints and two joint drivers, where link 1 is a rigid arm, link 2 is a flexible arm, and the revolute joints are driven by corresponding motors. The lengths of link 1 and link 2 are l1 and l2 respectively, the attitude angle of the carrier is θ0, the rotation angles of joint 1 and joint 2 are θ1 and θ1, OXY is the inertial coordinate system of the system, o i x i y i (i=0,1,2) is a mobile coordinate system fixed on the carrier or the robotic arm. m0 is the mass of the base, m1 is the mass of the rigid arm, ρ is the axial linear density of the flexible arm, EI is the bending stiffness of the flexible arm section; J0 is the moment of inertia of the base center, J1 is the moment of inertia of the rigid arm center; x b is the elastic displacement of the flexible base. This system has dynamic coupling between the carrier posture and the robotic arm joint. Solving this problem is the premise for achieving high-precision and high-stability control of the flexible space robot system.

[0059] The flexible link is treated as an Euler-Bernoulli cantilever beam. According to the assumed modal method, the elastic deformation of the flexible arm is:

[0060]

[0061] Among them, φ i (x2′) is the i-th order mode function; δ i (t) is the i-th order mode coordinate; n is the mode retention number.

[0062] Since the vibration mode of the flexible beam is mainly composed of low-order vibration modes, this embodiment intercepts the first two order modes for analysis, that is, n = 2, v(x2′, t) = φ1(x2′)δ1(t)+φ2(x2′)δ2(t). Among them, the i-th order mode function φ i The expression of (x2′) is:

[0063] φ i (x2′)=A i [cos(c i x2′)-cosh(c i x2′)]+[sin(c i x2′)-sinh(c i x2′)](2)

[0064] Among them, A i =-(sinc i l2+sinhc i l2) / (cosc i l2+coshc i l2);c i is the equivalent eigenfrequency of the i-th mode.

[0065] Combining the linear momentum conservation theorem with Lagrange's second-kind equation, the dynamic equation of the flexible arm and flexible base system can be derived as follows:

[0066]

[0067] in, is the symmetric, positive definite inertia matrix of the system; is the Coriolis force and centrifugal force vector of the system; q s =[θ0,θ1,θ2] T is the rigid generalized coordinate of the system; q f =[x b ,δ1,δ2] T is the flexible generalized coordinate of the system; K f =diag(k b ,k1,k2) is the stiffness matrix of the flexible system, τ=[u0,u1,u2] T is the control input of the system, u0 is the equivalent adjustment torque of the carrier attitude, u i (i=1,2) is the joint driver a i of control torque.

[0068] S2, establish the dynamic model of flexible base and flexible arm space robot system based on singular perturbation.

[0069] The motion system of the flexible base and flexible arm space robot includes the rigid trajectory tracking part of the posture and joints and the flexible vibration part of the base and arm. The motion states of the two cannot keep changing synchronously. In view of this, this method is based on the singular perturbation technology. It first ignores the fast time scale variables to reduce the system dimension, and then introduces the boundary layer correction term to improve the approximation of the model, thereby realizing the reduced-order processing of the flexible base and flexible arm space robot system. This method simplifies the system model structure, reduces the difficulty of controller setting, and saves onboard computing resources, such as Figure 3 shown.

[0070] S21, establish the dynamic model of the slow-varying subsystem.

[0071] Since the inertia matrix D is a symmetric positive definite matrix, its inverse matrix exists and can be expressed as

[0072]

[0073] in,

[0074] From formula (3), we can get and They are:

[0075]

[0076] Define the bending stiffness matrix K f The smaller element is k min , the singular perturbation factor is ε=(1 / k min ) 1 / 2 . Introducing a new state variable ξ f , K ε (ε 2 ξ f =q f ,K ε =ε 2 K f ), and substitute into equations (5) and (6), we have

[0077]

[0078] In order to obtain the dynamic model of the slow-varying subsystem of the flexible-base and flexible-arm space robot, let ε = 0, then equations (7) and (8) can be written as

[0079]

[0080] in, is the quantity corresponding to {··} when ε=0.

[0081] Solving equation (10)

[0082]

[0083] in, It is the control input of the slow-varying subsystem.

[0084] Substituting equation (11) into equation (9), the dynamic equation of the slow-varying subsystem is obtained as follows:

[0085]

[0086] S22, establish the fast-changing subsystem dynamics model.

[0087] In order to obtain the fast-changing subsystem, a fast-changing time scale t is introduced. f (εt f = t-t0) and boundary layer correction Substituting it into formula (8), we get

[0088]

[0089] Let ε = 0, and after rearranging equation (13), the dynamic equation of the fast-changing subsystem is obtained as follows:

[0090]

[0091] in, τ f It is the control input of the fast-changing subsystem.

[0092] Combining S21 and S22, the slow-changing subsystem model (12) and the fast-changing subsystem model (14) constitute the singular perturbation model of the flexible base and flexible arm space robot system.

[0093] In summary, this step is based on the multi-time scale characteristics of the flexible base and flexible arm space robot system, and reduces the order of its dynamic model through singular perturbation technology to obtain a slow-changing subsystem that characterizes the carrier attitude stabilization and the robot arm joint trajectory tracking, and a fast-changing subsystem that characterizes the elastic deformation of the base and the flexible vibration of the robot arm. Its advantage is that the complexity of the control system changes from the system level to the subsystem level, which simplifies the control system structure and algorithm complexity, and is easy to implement in engineering.

[0094] S3, set up dual time scale controller.

[0095] Based on the unique modular properties of the slow-varying subsystem, this method separates the local variables of the carrier posture and the robot arm joint module from its dynamic model, and obtains a set of three interconnected subsystems. Then, a subsystem tracking controller is set to stabilize it and eliminate the coupling effects between subsystems. Its advantage is that it changes the complexity of control from the subsystem level to the sub-order subsystem level, thereby further simplifying the control structure and reducing the complexity of the control algorithm. The core issue of the decentralized controller setting is how to solve the changes in the system dynamics matrix caused by the frequent reconstruction of the robot or the addition and removal of modules and eliminate the cross-linking effects between the subsystems, such as Figure 4 shown.

[0096] S31, set the slow-changing controller.

[0097] In order to achieve separate control of each subsystem, the slow-changing subsystem can be further decomposed into the following three coupled subsystems:

[0098]

[0099] Among them, q si , and The vector q s , and The i-th (i=1,2,3) component of and The matrix and The ijth component of .

[0100] To facilitate subsequent controller settings, define x i =[x i1 ,x i2 ] T =[q si ,υ si ] T , then formula (15) can be rewritten as

[0101]

[0102] in,

[0103] Setting 1: Reference trajectory x id , and are all bounded functions.

[0104] Define the trajectory tracking error e i1 =x i1 -xid and its derivatives From this we can get e i =[e i1 ,e i2 ] T and

[0105] The first-order filtering error is defined as:

[0106] s i =e i2 +c i e i1 (18)

[0107] Among them, c i Is a normal number.

[0108] Setting 2: The cross-link term satisfies the following bounded conditions

[0109]

[0110] Among them, δ i0 is a positive constant, δ ij (|s j |)≥0 is a continuous Lipschitz function.

[0111] From formula (17), we can get the subsystem error dynamics equation:

[0112]

[0113] definition and Sequentially e i1 、e i2 、e i and i The estimated value of . The following RBF neural network is used to sequentially calculate the nonlinear unknown term f i (q i ,υ i ), g i (q i ) and cross-linking items Make an approximation

[0114]

[0115] in, and are the ideal weights of the neural network. and The estimate, Φ ig (q i )and is the basis function, is the filtering error si Estimates.

[0116] The ideal weights of the neural network are defined as:

[0117]

[0118] Among them, Ω if ,Ω ig ,Ω ip , U if , U ig and U ip In order x i ,q i and The constraint set.

[0119] Setting 3: Ideal weights and Satisfy in sequence and Among them, M if 、M ig and M ip is an unknown constant.

[0120] The minimum approximation error of the neural network is defined as:

[0121]

[0122] in, This is a function to be defined later.

[0123] Setting 4: Approximation error w i1 and w i2 Satisfy in sequence and in and Is a normal number.

[0124] The state error observer is defined as

[0125]

[0126] Among them, 0<ε<<1, α i (ε)=[α i1 / ε,α i2 / ε 2 ] T .

[0127] The trajectory tracking controller of the second-order subsystem is defined as

[0128]

[0129] in, and In order and The estimated value of and is the estimation error; Is a normal number.

[0130] Estimated weights and and variables and The update law is designed as follows:

[0131]

[0132] Among them, γ if , γ ig , γ ip , γ iρ and γ iλ Is a normal number.

[0133] Defining weight estimation error and Substituting formula (29) into formula (28), we can get

[0134]

[0135] in,

[0136] Setting 5: φ i satisfy is an unknown positive constant.

[0137] Defining Observation Error and Combining equations (19) and (28), we can obtain the following observation error dynamic equation:

[0138]

[0139] Define the following variables

[0140]

[0141] According to setting 3, we can get

[0142]

[0143] Among them, b if Is a normal number.

[0144] Substituting equation (38) into equation (37), we can obtain

[0145]

[0146] make

[0147]

[0148] η i =[η i1 ,η i2 ] T (42)

[0149] Combining equations (40) to (42), we get

[0150]

[0151] make

[0152]

[0153] Among them, α i1 and α i2 Is a normal number.

[0154] Definition P i is a positive definite solution to the following Riccati equation

[0155]

[0156] Among them, P i =P i T .

[0157] Then formula (43) can be rewritten as

[0158]

[0159] For the second-order dynamic subsystem (15), under the premise that 1-5 is established, the adaptive update law shown in equations (31)-(35) is designed, and the controller (29) can ensure that the closed-loop subsystem is uniformly ultimately bounded and stable.

[0160] The proof is as follows:

[0161] Choose the positive definite Lyapunov function as

[0162]

[0163] in,

[0164]

[0165] V i1 Taking the derivative with respect to time t, we get

[0166]

[0167] Substituting equation (36) into equation (48), we get

[0168]

[0169] Combining the adaptive update laws (31) and (32), we can obtain

[0170]

[0171] Substituting equation (34) into equation (50), we get

[0172]

[0173] V i2 Taking the derivative with respect to time t, we get

[0174]

[0175] Due to δ ij (|s j |) is a Lipschitz function. According to the properties of the Lipschitz function, we get

[0176]

[0177] Where, L ij >0 is the Lipschitz constant.

[0178] Combining equations (52) and (53), we have

[0179]

[0180] Let μ j =[εc j 1], we can get

[0181]

[0182] because is a continuous function, so there exists a function Satisfy the following formula

[0183]

[0184] Combining equations (54)-(56), we can get

[0185]

[0186]

[0187] in, According to the properties of Young's inequality: 2ab≤a 2 / κ+κb 2 (κ>0), we get

[0188]

[0189] Substituting equations (58)-(60) into equation (57), we can obtain

[0190]

[0191] make

[0192]

[0193] Combining equations (51) and (61), we have

[0194]

[0195] Substituting equations (33) and (35) into equation (63), we can obtain

[0196]

[0197] make

[0198]

[0199] Choose a suitable ε to satisfy 0<ε≤ε * ,have

[0200]

[0201] in, η=[η1,η2,η3] T .

[0202] make

[0203]

[0204] Therefore, outside the constraint set Ω, It is negative

[0205]

[0206] Based on the Lyapunov stability theorem, the closed-loop subsystem is stable, so With ||η i || will also converge to the constraint set in turn and

[0207]

[0208] From formula (28), we can get Therefore It will also converge to the following constraint set

[0209]

[0210] Considering will converge to the following constraint set

[0211]

[0212] Therefore, the tracking error of the second-order subsystem is uniformly bounded and will converge to the following constraint set:

[0213]

[0214] The proof is complete.

[0215] S32, set the fast-change controller.

[0216] From the state equation of the fast-changing subsystem, it can be seen that the fast-changing subsystem is a linear function of the state variable. Therefore, we can consider using the idea of ​​negative feedback of the state variable to control it. The PD feedback controller is set as

[0217] τ δ =-K f ζ(74)

[0218] Among them, K f ∈R 3×6 is the gain matrix.

[0219] S33, combining the fast-changing controller and the slow-changing controller.

[0220] According to the multiple time scale theory, the combined controller of the flexible base and flexible arm space robot system can be obtained by combining the subsystem controllers obtained above:

[0221]

[0222] In summary, this step is based on the unique modular properties of the slow-varying subsystem, separating the local variables of the carrier posture and the robot arm joint module from its dynamic model, obtaining a set of three interconnected subsystems, and then designing a subsystem tracking controller to stabilize it and eliminate the coupling effect between subsystems. Its advantage is that it changes the complexity of the control system from the subsystem level to the sub-order subsystem level, thereby further simplifying the control system structure and reducing the complexity of the control algorithm.

[0223] S4, determining and distinguishing the robotic arm system into a slow-changing subsystem and a fast-changing subsystem.

[0224] This method uses singular perturbation technology to decompose the flexible base and flexible arm space robot system, and then judges whether the system is a fast-changing subsystem. If yes, the fast-changing subsystem control module (controller) is used to perform corresponding control; if no, it can be determined to be a slow-changing subsystem, and then the slow-changing subsystem control module (controller) is used to perform corresponding control. Then, the outputs of the two subsystem control modules (controllers) are input to the subsequent drive module, and then the data is stored, and then it is judged whether the running time has arrived. If not, the loop judgment is continued; if yes, the output result is the end.

[0225] The following is a specific case to further illustrate the effect of this method:

[0226] The physical parameters of the flexible base and flexible arm space robot system controlled by this method are shown in Table 1. The initial shape and position of the selected system is q(0) = [0.2, 0.3, 0.7] rad, the expected trajectory in the operation space is q(t) = [0.1, 0.5, 0.5] rad, and the simulation time is t = 30 s.

[0227] Table 1: Physical parameters of the flexible base and flexible arm space robot system

[0228] <![CDATA[m0]]> <![CDATA[m1]]> ρ <![CDATA[l0]]> <![CDATA[l1]]> <![CDATA[l2]]> <![CDATA[J0]]> <![CDATA[J1]]> EI <![CDATA[k b ]]> 60kg 6kg 2kg / m 1m 3m 3m <![CDATA[30kg·m 2 ]]> <![CDATA[3kg·m 2 ]]> <![CDATA[100N·m 2 ]]> 500N·m

[0229] The singular perturbation control method is written in Matlab language and generates .m files. The program design idea and execution process are Figure 1 The control parameters of the system are shown in Table 2.

[0230] Table 2: Control parameters of flexible base and flexible arm space robot system

[0231]

[0232]

[0233] When running the program, the system is first reduced to a dual-time-scale subsystem through singular perturbation technology, and then controlled in sequence by the dual-time-scale subsystem controller. When the combined controller based on the decentralized neural network is turned on, the carrier attitude stabilization and joint trajectory tracking can be achieved, and the elastic deformation of the flexible base and the modal vibration of the flexible arm can also be effectively suppressed.

[0234] Based on the same inventive concept, this embodiment further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the aforementioned control method is implemented.

[0235] The computer readable medium includes, but is not limited to, any type of disk (including floppy disk, hard disk, optical disk, CD-ROM, and magneto-optical disk), ROM, RAM, EPROM (Erasable Programmable Read-Only Memory), EEPROM, flash memory, magnetic card or optical card. In other words, the readable medium includes any medium that can store or transmit information in a readable form by a device (such as a computer).

[0236] The computer-readable storage medium provided in this embodiment has the same inventive concept and the same beneficial effects as the aforementioned method, and will not be described in detail here.

[0237] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A singular perturbation control method for a flexible space robot based on a decentralized neural network, characterized in that: The steps include: S1, establish the dynamic model of the flexible base and flexible arm space robot system; S2, establish the dynamic model of the flexible base and flexible arm space robot system based on singular perturbation, including the slow-varying subsystem dynamic model and the fast-varying subsystem dynamic model. First, ignore the fast-varying time-scale variables to reduce the system dimension, and then introduce the boundary layer correction term to improve the approximation degree of the model, so as to achieve the order reduction processing of the flexible base and flexible arm space robot system; S3, setting a dual time scale controller, including a fast-changing subsystem controller and a slow-changing subsystem controller; S4, judge whether the flexible base and flexible arm space robot system is a fast-changing subsystem; if yes, use the fast-changing subsystem controller to execute control; if no, determine it is a slow-changing subsystem, and use the slow-changing subsystem controller to execute control; input the outputs of the two subsystem controllers to the subsequent driver, and after the data is stored, judge whether the running time has arrived, if not, continue to execute the loop judgment; if yes, the output result is end.

2. The method for controlling a flexible space robot under singular perturbation based on a decentralized neural network according to claim 1, characterized in that: In S2, the system dynamics model is reduced based on singular perturbations to obtain a slow-changing subsystem that characterizes the carrier attitude stabilization and robot arm joint trajectory tracking, and a fast-changing subsystem that characterizes the elastic deformation of the base and the flexible vibration of the robot arm.

3. The method for controlling a flexible space robot under singular perturbation based on a decentralized neural network according to claim 2, characterized in that: S2 specifically includes the following sub-steps: S21, establish the dynamic model of the slow-changing subsystem; S22, establish the fast-changing subsystem dynamics model; S23, combining the slow-changing subsystem dynamics model and the fast-changing subsystem dynamics model to obtain the singular perturbation model of the flexible base and flexible arm space robot system.

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