An adaptive switching control method for a flexible arm and flexible joint space robot

Abstract

The present invention discloses an adaptive switching control method for a flexible arm and flexible joint space robot, comprising the following steps: S1: establishing a dynamic model of a disturbed flexible arm and flexible joint space robot under an alternating load; S2: isolating a fast-changing switching subsystem 1 that characterizes the flexibility of the arm, and designing a linear quadratic optimal switching damper for it; S3: decomposing the model of the disturbed flexible joint space robot under an alternating load into a slow-changing switching subsystem that characterizes the trajectory tracking of the robot arm and a fast-changing switching subsystem 2 that characterizes the elasticity of the joint; S4: designing a torque proportional-differential feedback switching damper for the fast-changing switching subsystem 2; and S5: designing an adaptive switching controller for the slow-changing switching subsystem by combining an average dwell time method and a composite sliding mode observer to realize angular velocity signal recognition of the joint and trajectory tracking of the robot arm under an alternating load condition.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control of space robots, and in particular to an adaptive switching control method for a flexible arm and flexible joint space robot. Background Art

[0002] Space robots can replace astronauts in performing ultra-precise tasks in extreme cosmic environments, such as sampling asteroid surfaces, refueling spacecraft on-orbit, and constructing and maintaining large space facilities. While performing their missions, space robots are inevitably subject to environmental interference factors such as solar pressure, strong radiation, microgravity, and planetary gravitational perturbations, which can severely impact the stability, precision, and safety of the space robot system. Furthermore, to capture large-mass target satellites and transmit torque between arms, space robots require significant joint flexibility. This flexibility, more subtle and significant than arm flexibility, can easily lead to elastic vibrations in the joints, significantly impacting the system's maneuverability. Furthermore, many current adaptive control methods for space robots lack transferability; their adaptive laws are only applicable to small parameter perturbations and are incapable of controlling the switching between the capture and release of large-mass satellites.

[0003] For example, the invention patent with publication number CN118789557B published a "A decentralized fault-tolerant control method for a flexible joint space robot without speed feedback", but this method does not take into account the alternating load and arm flexibility characteristics; this application uses an adaptive switching control strategy designed by the average residence time method and a composite sliding mode alternating observer to overcome the unresolved problem of load alternation. Summary of the Invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art; to this end, the present invention proposes an adaptive switching control method and system for a flexible arm and flexible joint space robot, which is used to solve the technical problem of load alternation that has not been solved by the prior art.

[0005] To achieve the above object, the present invention provides a method for adaptive switching control of a flexible arm and flexible joint space robot, comprising the following steps:

[0006] S1: Combining the assumed modal method, the law of conservation of momentum, and the elastic joint assumption, the Lagrangian method is applied to establish the dynamic model of the space robot with a disturbed flexible arm and flexible joints under alternating loads;

[0007] S2: Using singular perturbation techniques, a fast-changing switching subsystem representing the flexibility of the arm is separated from the dynamic model of the flexible arm and flexible joint space robot under alternating loads described in S1, and a linear quadratic optimal switching vibration suppressor is designed for it.

[0008] S3: Based on the dynamic model of the flexible arm and flexible joint space robot under alternating load described in S1, a model of the flexible joint space robot under alternating load is established. According to the singular perturbation technology based on flexible compensator, the model of the flexible joint space robot under alternating load is decomposed into a slow-changing switching subsystem characterizing the trajectory tracking of the robot arm and a fast-changing switching subsystem II characterizing the joint elasticity.

[0009] S4: For the fast-changing switching subsystem 2, a torque proportional-differential feedback switching vibration suppressor is designed to eliminate the elastic vibration of the joint and ensure the stability of the movement;

[0010] S5: For the slow-varying switching subsystem, an adaptive switching controller is designed by combining the average dwell time method and the composite sliding mode observer to realize the angular velocity signal recognition of the joint and the trajectory tracking of the robot arm under alternating load conditions.

[0011] Furthermore: the specific implementation process of step S1 is:

[0012] Combining the assumed modal method, the conservation laws of angular momentum and linear momentum, and the elastic joint assumption, the Lagrangian method can be used to obtain the dynamic model of the flexible arm and flexible joint space robot under alternating loads, as follows:

[0013] ;

[0014] ;

[0015] in, is the symmetric and positive definite inertia switching matrix of the system, ; is the switching column vector of the system including Coriolis force and centrifugal force, ; is the external disturbance vector, ; Is a segment switching function , and in a finite index set Any value between When the matrix and In the active state, the matrix The corresponding vector is ; is the output torque column vector of the joint motor, ; , is the carrier attitude angular displacement, is the column vector of the arm angular displacement, Represents a vector The transposed matrix of is the modal coordinate vector of the flexible arm, and are the first-order and second-order modal coordinates of the flexible arm, respectively; and is a vector Solve the first and second derivatives of time t separately; and is a vector The first and second derivatives of the time t are solved; Specifically, it is the column vector of the driving motor rotor angular displacement; is the rotational inertia matrix of the drive motor; is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint; is the flexible arm stiffness coefficient matrix, and are the first-order stiffness coefficient and second-order stiffness coefficient of the flexible arm, respectively.

[0016] Furthermore: the specific implementation process of S2 is:

[0017] Define the matrix

[0018] ;

[0019] ;

[0020] In the formula 、 、 for The sub-matrix of and for submatrix of ;

[0021] Since the dynamic model of the flexible arm and flexible joint space robot under alternating load in S1 contains the system symmetry and positive definite inertia switching matrix ,and is a positive definite matrix, and its inverse matrix can be expressed as:

[0022] ;

[0023] in, ;

[0024] ;

[0025] ;

[0026] .

[0027] The rotational deviation of the flexible joint is defined as , is the column vector of the arm angular displacement, is the column vector of the driving motor rotor angular displacement; take the singular perturbation factor , and are the first-order stiffness coefficient and the second-order stiffness coefficient of the flexible arm respectively; then the new vector 、 and the new matrix 、 , is the modal coordinate vector of the flexible arm, is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint, is the stiffness coefficient matrix of the flexible arm;

[0028] Based on this, the dynamic model of the flexible arm and flexible joint space robot under the alternating load in S1 can be expressed as follows:

[0029] ;

[0030] ;

[0031] ;

[0032] At this time, only the influence of the flexible arm vibration mode on the flexibility of the space robot system is considered, and the above formula is 、 , we can get the following formula:

[0033] ; ;

[0034] in, It represents the control torque of the system after eliminating the joint flexibility;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] Defining fast-changing time scales and correction parameters and ; Considering that the slow variables in the fast-changing system can be equivalent to constants, we have , where t is the time variable;

[0040] make , we can obtain the dynamic equation of the fast-changing switching subsystem 1 corresponding to the flexible arm, specifically:

[0041] ;

[0042] in, , , , and The matrices and exist The matrix corresponding to the conditions;

[0043] Finally, the following linear quadratic optimal switching damper is designed for the fast-changing switching subsystem 1 as shown below:

[0044] ;

[0045] in, 、 is a symmetric positive definite matrix, represents the controller of fast-changing subsystem 1, is a matrix The unique solution of the corresponding Raccati equation; the performance index functional of the optimal vibration suppressor is selected as , which describes the control torque of the fast-changing subsystem and output variables By solving the extreme value of the functional, we can find a control strategy that can minimize the energy consumption and maximize the efficiency of the system, so as to improve the efficiency, stability and economy of the system.

[0046] Furthermore: the specific implementation process of S3 is:

[0047] According to the dynamic model of the flexible arm and flexible joint space robot under the alternating load in S1, the influence of the flexible arm on the flexibility of the system is neglected, that is, the modal coordinate vector of the flexible arm is , the dynamic equations of the flexible joint space robot system under alternating loads can be obtained as follows:

[0048] ;

[0049] ;

[0050] ;

[0051] in, for The inertia switching matrix of the system is symmetric and positive under the condition; for Under these conditions, the system includes switching column vectors of Coriolis force and centrifugal force; is the column vector of the control torque actually transmitted by the flexible joint; is the external disturbance vector; is a piecewise switching function and in a finite set of indices Any value between When the matrix and is in an active state; is the output torque column vector of the joint motor; ; is the carrier attitude angular displacement; is the column vector of the arm angular displacement; is the column vector of the driving motor rotor angular displacement; is the rotational inertia matrix of the drive motor; is the joint equivalent stiffness coefficient matrix;

[0052] The dynamic equation of the flexible joint space robot system under alternating load can be obtained:

[0053] ;

[0054] The control law of the joint motor is designed as:

[0055] ;

[0056] in, is the joint flexibility compensation controller, is a diagonal, positive definite matrix; , is the identity matrix; is the control quantity to be designed;

[0057] Combined formula And the control law formula of the joint motor, we can get:

[0058] ;

[0059] in, is the stiffness reinforcement matrix;

[0060] According to the dynamic equations and formulas of the disturbed flexible joint space robot system under the determined alternating load The dynamic model of a space robot with flexible joints subjected to disturbances under alternating loads after stiffness enhancement is constructed.

[0061] Using the singular perturbation method based on flexible compensator, Deconstructed into two parts:

[0062] ;

[0063] in, and They represent the fast-changing and slow-changing subsystem controllers of the flexible joint space robot under alternating loads;

[0064] Let the joint stiffness coefficient matrix The smallest element in , let the singular perturbation factor for: ;make ,but Same dimension as the slowly varying component matrix;

[0065] Combined formula With the formula , the dynamic equation of the fast-changing switching subsystem 2 can be derived as: ;

[0066] At this time, , then the stiffness strengthening matrix , and the vector consisting of the driving motor rotor angular displacement column vector and the first-order derivative and second-order derivative of this vector is infinitely close to the vector consisting of the arm angular displacement column vector and the first-order derivative and second-order derivative of this vector ;

[0067] Substitute the fast-changing switching subsystem 2 into the dynamic model of the flexible joint space robot system under the alternating load determined by S3, and let , the dynamic equation of the slowly changing switching subsystem that characterizes the trajectory tracking of the manipulator is obtained as:

[0068] ;

[0069] in, is the positive definite inertia switching matrix; To utilize Simplify and organize The column vector obtained after for About time Find the second-order derivative, is the external disturbance vector.

[0070] Furthermore, the specific implementation process of S4 is as follows:

[0071] For the fast-changing switching subsystem 2 in S3, in order to eliminate the nonlinear vibration caused by the flexible joint, the torque proportional-differential feedback switching vibration suppressor is designed as follows:

[0072] ;

[0073] in, and is the diagonal coefficient matrix;

[0074] is the singular perturbation factor;

[0075] is the column vector of the control torque actually transmitted by the flexible joint, express The first derivative with respect to time t.

[0076] Furthermore, the specific implementation process of S5 is as follows:

[0077] The dynamic equation of the slowly varying switching subsystem representing the trajectory tracking of the manipulator obtained from the decomposition of the disturbed flexible joint space robot model under the alternating load obtained in S3 is converted into the following form:

[0078] ;

[0079] in, , , , is the positive definite inertia switching matrix; To utilize Simplify and organize The column vector obtained after is the external disturbance vector;

[0080] Then define the expected trajectory of the joint as , the joint trajectory tracking error is , is the column vector of the arm angular displacement, and the sliding surface can be further obtained as:

[0081] ;

[0082] in, is a diagonally positive definite matrix;

[0083] Therefore, the adaptive sliding mode switching control law of the slow-varying subsystem is designed as follows:

[0084] ;

[0085] in, represents the estimate of the disturbance term; is the switching gain coefficient; , represents the standard symbolic function, and Represents sliding mode the first and second elements of ;

[0086] For switching signals and any two moments ,make To this end, the switching signal is The number of switching times on the and have If established, then we call them and For this purpose, the average dwell time and chatter bound of the switching signal are;

[0087] In order not to lose generality, the present invention takes ,Right now ;

[0088] The design of the composite sliding mode alternating observer is:

[0089] ;

[0090] in, and is a diagonally positive definite matrix; is the joint angular velocity vector Estimates, for About time Find the first-order derivative;

[0091] When the disturbance estimation error Satisfy the boundedness condition:

[0092] ;

[0093] When the disturbance estimation error is a slow time-varying signal, that is:

[0094] ;

[0095] According to the dynamic equations of the slow-varying switching subsystem that characterizes the trajectory tracking of the manipulator, an adaptive sliding mode switching control law for the slow-varying subsystem based on the composite sliding mode alternating observer is designed to ensure the tracking error of the dynamic equations of the slow-varying switching subsystem that characterizes the trajectory tracking of the manipulator. Global asymptotic convergence;

[0096] Choose the positive definite Lyapunov function as:

[0097] ;

[0098] in, , , ;

[0099] Then Taking the derivative with respect to time t, we can get:

[0100] ;

[0101] Will The derivative formula for time t is Combining, we can get:

[0102] ;

[0103] Combining the above formula with the designed adaptive sliding mode switching control law of the slow-varying subsystem, we can obtain:

[0104] ;

[0105] Therefore, the control method expressed in the above formula has two states. One is when the disturbance estimation error satisfies the boundedness condition, that is, ; The other is when the disturbance estimation error is a slow time-varying signal, that is: ;

[0106] When the disturbance estimation error satisfies the boundedness condition:

[0107] ;

[0108] Likewise, Derivative with respect to time t:

[0109] ;

[0110] According to another state, that is, when the disturbance estimation error is a slowly time-varying signal:

[0111] ;

[0112] Combined with the composite sliding mode alternating observer and , we can get: ;

[0113] From the above formula and It can be seen that .

[0114] The beneficial effects of the present invention are:

[0115] 1. For the slowly varying switching subsystem of a disturbed space robot under alternating loads, a composite sliding mode switching observer is designed to simultaneously identify the alternating joint angular velocity signals and external disturbances.

[0116] 2. For the slowly varying switching subsystem of a space robot subjected to alternating loads, an adaptive switching control method based on the average dwell time method and a composite sliding mode observer was designed to address the effects of alternating loads and external disturbances on the robot's trajectory tracking performance.

[0117] 3. For the fast-changing switching subsystems 1 and 2 of the disturbed space robot under alternating loads, a linear quadratic optimal switching damper and a torque proportional-differential feedback switching damper are designed, respectively. These dampers fully consider the current information and future variation trends of the control torque transmitted by the joint, effectively suppressing the elastic vibrations of the arm and joints. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] In order to more clearly illustrate the embodiments of the present invention and the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments and the description of the prior art. Obviously, the drawings described below are only some implementation methods recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0119] Figure 1 It is a technical flow chart of the present invention;

[0120] Figure 2 It is a structural diagram of the flexible arm and flexible joint space robot under alternating load in the present invention;

[0121] Figure 3 It is the switching signal of alternating load;

[0122] Figure 4 is the time response curve of the angular displacement of joint 1 when the flexible compensator is turned on;

[0123] Figure 5 This is the time response curve of the angular displacement of joint 2 when the flexible compensator is turned on;

[0124] Figure 6 The time response curve of the angular displacement tracking error of joint 1 and joint 2 when the flexible compensator is turned on;

[0125] Figure 7 This is the time response curve of the observed angular velocity of joint 1 when the flexible compensator is turned on;

[0126] Figure 8 This is the time response curve of the observed angular velocity of joint 2 when the flexible compensator is turned on;

[0127] Figure 9 is the time response curve of the angular displacement of joint 1 when the flexible compensator is closed;

[0128] Figure 10 is the time response curve of the angular displacement of joint 2 when the flexible compensator is closed;

[0129] Figure 11 is the time response curve of the angular displacement tracking error of joint 1 and joint 2 when the flexible compensator is closed;

[0130] Figure 12 is the time response curve of the observed angular velocity of joint 1 under the condition of flexible compensator closed;

[0131] Figure 13 This is the time response curve of the observed angular velocity of joint 2 when the flexible compensator is closed. DETAILED DESCRIPTION

[0132] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is described and illustrated below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention. Based on the embodiments provided by the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present invention.

[0133] Obviously, the drawings described below are only some examples or embodiments of the present invention. For ordinary technicians in this field, the present invention can be applied to other similar scenarios based on these drawings without any creative work.

[0134] In addition, it can be understood that although the efforts made in this development process may be complex and lengthy, for ordinary technicians in the field related to the contents disclosed in the present invention, some design, manufacturing or production changes based on the technical contents disclosed in the present invention are just conventional technical means and should not be understood as the contents disclosed in the present invention are insufficient.

[0135] Unless otherwise specified, all embodiments and optional embodiments of the present invention can be combined with each other to form new technical solutions.

[0136] See also Figure 1 and Figure 2 , respectively, are a technical flow chart of the present invention and a structural diagram of a flexible arm and a flexible joint space robot under alternating loads. The process includes the following steps:

[0137] S1: Combining the assumed modal method, the law of conservation of momentum, and the elastic joint assumption, the Lagrangian method is applied to establish the dynamic model of the space robot with a disturbed flexible arm and flexible joints under alternating loads;

[0138] S2: Using singular perturbation techniques, we separate the fast-changing switching subsystem 1 that characterizes the arm's flexibility from the system model and design a linear quadratic optimal switching damper for it.

[0139] S3: Based on the singular perturbation technique based on flexible compensators, it is decomposed into a slow-changing switching subsystem that characterizes the trajectory tracking of the manipulator and a fast-changing switching subsystem that characterizes the joint elasticity;

[0140] S4: For the fast-changing switching subsystem 2, a torque proportional-differential feedback switching vibration suppressor is designed to eliminate the elastic vibration of the joint and ensure the stability of the movement;

[0141] S5: For the slow-varying switching subsystem, an adaptive switching controller is designed by combining the average dwell time method and the composite sliding mode observer to realize the angular velocity signal recognition of the joint and the trajectory tracking of the robot arm under alternating load conditions.

[0142] Specifically:

[0143] The specific implementation process of step S1 is:

[0144] Combining the assumed modal method, the conservation laws of angular momentum and linear momentum, and the elastic joint assumption, the dynamic model of the flexible arm and flexible joint space robot under alternating load can be obtained by applying the Lagrangian method:

[0145] (1)

[0146] (2)

[0147] in, is the symmetric and positive definite inertia switching matrix of the system, ; is the switching column vector of the system including Coriolis force and centrifugal force, ; is the external disturbance vector, ; Is a segment switching function , and in a finite index set Any value between When the matrix and In the active state, the matrix The corresponding vector is ; is the output torque column vector of the joint motor, ; , is the carrier attitude angular displacement, is the column vector of the arm angular displacement, Represents a vector The transposed matrix of is the modal coordinate vector of the flexible arm, and are the first-order and second-order modal coordinates of the flexible arm, respectively; and is a vector Solve the first and second derivatives of time t separately; and is a vector The first and second derivatives of the solution for time t; Specifically, it is the column vector of the driving motor rotor angular displacement; is the rotational inertia matrix of the drive motor; is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint; is the flexible arm stiffness coefficient matrix, and are the first-order stiffness coefficient and second-order stiffness coefficient of the flexible arm, respectively.

[0148] The specific implementation process of step S2 is:

[0149] definition , Where 、 、 for The sub-matrix of and for submatrix of ;

[0150] because is a positive definite matrix, so its inverse matrix exists and can be expressed as:

[0151] (3)

[0152] in, ;

[0153] ;

[0154] ;

[0155] ;

[0156] The rotational deviation of the flexible joint is defined as , is the column vector of the arm angular displacement, is the column vector of the driving motor rotor angular displacement; take the singular perturbation factor , and are the first-order stiffness coefficient and the second-order stiffness coefficient of the flexible arm respectively; then the new vector 、 and the new matrix 、 , is the modal coordinate vector of the flexible arm, is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint, is the stiffness coefficient matrix of the flexible arm; based on this, equations (1) and (2) can be expressed as:

[0157] (4)

[0158] (5)

[0159] (6)

[0160] At this time, if only the influence of the flexible arm vibration mode on the flexibility of the space robot system is considered, the equations (4)-(6) can be made 、 , we can get:

[0161] (7)

[0162] (8)

[0163] Where, It represents the control torque of the system after eliminating the joint flexibility;

[0164] ;

[0165] ;

[0166] ;

[0167] ;

[0168] Defining fast-changing time scales and correction parameters and ; Considering that the slow variables in the fast-changing system can be equivalent to constants, we have ;

[0169] If the order , the dynamic equation of the fast-changing switching subsystem 1 corresponding to the flexible arm is:

[0170] (9) Among them, , , , and The matrices and exist The matrix corresponding to the conditions.

[0171] Design the following linear quadratic optimal switching damper for the fast-changing switching subsystem 1:

[0172] (10)

[0173] Where, 、 is a symmetric positive definite matrix, represents the controller of fast-changing subsystem 1, is a matrix The unique solution of the corresponding Raccati equation; the performance index functional of the optimal vibration suppressor is selected as .

[0174] The specific implementation process of step S3 is:

[0175] Ignoring the influence of the flexible arm on the flexibility of the system, let the modal coordinate vector of the flexible arm be , from equations (1)-(2), the dynamic equation of the flexible joint space robot system under alternating load is:

[0176] (11)

[0177] (12)

[0178] (13)

[0179] in, for The inertia switching matrix of the system is symmetric and positive under the condition; for Under these conditions, the system includes switching column vectors of Coriolis force and centrifugal force; is the column vector of the control torque actually transmitted by the flexible joint; is the external disturbance vector; is a piecewise switching function and in a finite set of indices Any value between When the matrix and is in an active state; is the output torque column vector of the joint motor; ; is the carrier attitude angular displacement; is the column vector of the arm angular displacement; is the column vector of the driving motor rotor angular displacement; is the rotational inertia matrix of the drive motor; is the joint equivalent stiffness coefficient matrix.

[0180] Combining equations (12) and (13), we can obtain (14)

[0181] The control law of the joint motor is designed as:

[0182] (15)

[0183] in, is the joint flexibility compensation controller, is a diagonal, positive definite matrix; , is the identity matrix; is the control quantity to be designed;

[0184] Combining formula (15) and (14), we can get:

[0185] (16)

[0186] in, is the stiffness reinforcement matrix;

[0187] The dynamic model of the flexible joint space robot system under alternating load determined by S3 and formula (16) constitute the dynamic model of the flexible joint space robot under alternating load after stiffness enhancement;

[0188] Using the singular perturbation method based on flexible compensator, Deconstructed into two parts:

[0189] (17)

[0190] in, and They represent the fast-changing and slow-changing subsystem controllers of the flexible joint space robot under alternating loads;

[0191] in, and They represent the fast-changing and slow-changing subsystem controllers of the flexible joint space robot under alternating loads;

[0192] Let the joint stiffness coefficient matrix The smallest element in , let the singular perturbation factor for: ;make ,but Same dimension as the slowly varying component matrix;

[0193] Combining Equation (16) and Equation (17), the dynamic equation of the fast-changing switching subsystem 2 can be derived as:

[0194] (18)

[0195] At this time, if , then the stiffness strengthening matrix and .

[0196] Substitute the fast-changing switching subsystem 2 in S3 into the dynamic model (11) of the disturbed flexible joint space robot system under the alternating load determined by S3, and let , the dynamic equation of the slow-changing subsystem of the disturbed space robot under alternating load is obtained as follows:

[0197] (19)

[0198] in, is the positive definite inertia switching matrix; To utilize Simplify and organize The column vector obtained after for About time Find the second-order derivative, is the external disturbance vector.

[0199] The specific implementation process of S4 is as follows:

[0200] For the fast-changing switching subsystem 2 in S3, in order to eliminate the nonlinear vibration caused by the flexible joint, the torque proportional-differential feedback switching vibration suppressor is designed as follows:

[0201] (20)

[0202] in, and is the diagonal coefficient matrix;

[0203] is the singular perturbation factor;

[0204] is the column vector of the control torque actually transmitted by the flexible joint, express The first derivative with respect to time t.

[0205] The specific implementation process of S5 is as follows:

[0206] The slow-changing switching subsystem shown in formula (19) can be written as follows:

[0207] (twenty one)

[0208] in, , , , is the positive definite inertia switching matrix; To utilize Simplify and organize The column vector obtained after is the external disturbance vector;

[0209] Then define the expected trajectory of the joint as , the joint trajectory tracking error is , is the column vector of the arm angular displacement, and the sliding surface can be further obtained as:

[0210] (twenty two)

[0211] in, is a diagonally positive definite matrix.

[0212] Therefore, the adaptive sliding mode switching control law of the slow-varying subsystem is designed as follows: (twenty three)

[0213] in, represents the estimate of the disturbance term; is the switching gain coefficient; , represents the standard symbolic function, and Represents sliding mode The first and second elements of .

[0214] For switching signals and any two moments ,make To this end, the switching signal is The number of switching times on the and have If established, then we call them and For this purpose, the average dwell time and chatter bound of the switching signal are taken as ,Right now .

[0215] The design of the composite sliding mode alternating observer is:

[0216] (twenty four)

[0217] in, and is a diagonally positive definite matrix; is the joint angular velocity vector Estimates, for About time Find the first-order derivative;

[0218] Assumption 1 Perturbation estimation error Satisfy the boundedness condition:

[0219] (25)

[0220] Assumption 2 The disturbance is a slow time-varying signal, that is (26)

[0221] Theorem 1 Considering the switching dynamics equation (19) of the slow-changing subsystem of a space robot with a disturbed flexible joint under alternating load, the sliding mode switching control law (23) based on the adaptive observer (24) is designed to ensure that the tracking error of the slow-changing subsystem (19) is Global asymptotic convergence.

[0222] Choose the positive definite Lyapunov function as (27)

[0223] in, , , ;

[0224] Then Taking the derivative with respect to time t, we can get:

[0225] (28)

[0226] Combining formula (21) and formula (28), we can get (29)

[0227] According to formula (23) and formula (29), we can get:

[0228] (30)

[0229] According to Assumption 1, Equation (30) becomes:

[0230] (31)

[0231] Likewise, Taking the derivative with respect to time t, we get:

[0232] (32)

[0233] According to Assumption 2, Equation (32) becomes:

[0234] (33)

[0235] Combining equations (21) and (24), we can obtain:

[0236] (34)

[0237] From formula (31) and formula (34), we can see that .

[0238] because yes function, according to the Lyapunov stability criterion, the designed control scheme can ensure the tracking error of the slow-varying subsystem (19) The global convergence is asymptotic and the system has good robustness.

[0239] A specific embodiment of the present invention:

[0240] like Figure 1 As shown, the control object of the present invention is a flexible arm and flexible joint space robot under alternating load. The system consists of a floating carrier , flexible arm It consists of three modules: and between and and They are all connected by flexible joints; the symbols in the figure are defined as: is the world coordinate system of the system, For split The local coordinate system of the space robot system is In-plane motion, For modules The axis of symmetry; is the total center of mass of the system, is the center of mass of the carrier, and it is related to the center of rotation of the carrier coincide, For arm The center of mass; For each module Relative to the world coordinate system origin Position vector of module The quality of , the moment of inertia is ; For modules and The articulation center; is the carrier attitude angular displacement, For arm Joint angular displacement; and The distance between , and The distance between , The axial length is Flexible joints The moment of inertia of the internal motor rotor is , the corner is , equivalent stiffness coefficient .

[0241] by Figure 2 Taking the disturbed flexible arm and flexible joint space robot under alternating load (satellite capture and release) as an example, the effectiveness of the adaptive switching control method proposed in this invention is verified in MATLAB / Simulink. The expected trajectory (unit: radian) of the disturbed flexible joint space robot arm under alternating load is , the initial position of the system (unit: radian) is 、 The external disturbance of the system is (Unit: N·m). The system inertia parameters are shown in Table 1, and the control method parameters are shown in Table 2. Switching signal like Figure 3 As shown, when When , it means that the space robot has not captured the spacecraft P (no payload); when When , it means that the space robot has captured satellite P and merged with it into one (with payload). As shown in Table 1 below, the mass of the captured satellite is (or moment of inertia ) and the mass of the space robot (or moment of inertia ) ratio is as high as 20%, which can be regarded as a large-mass satellite.

[0242] Table 1

[0243] .

[0244] Table 2

[0245] .

[0246] Figures 4 to 8 This is the time response curve of the relevant output of the space robot when the flexible compensator is turned on; Figures 9 to 13 is the time response curve of the relevant output of the space robot under the condition of the flexible compensator being closed; from the simulation results, it can be found that under the action of alternating load, the adaptive switching control method based on the flexible compensator designed in this invention can ensure that the disturbed flexible arm and the flexible joint space robot arm are stable under alternating load and can track the desired trajectory with high precision (such as Figure 4-6 ), and the proposed angular velocity observer can accurately identify the actual angular velocity signal of the joint (as shown in Figure 7-8As shown in ); When the flexible compensator is closed, the equivalent stiffness of the space robot joint is too low, and the singular perturbation strategy is difficult to play the role of dual-time scale control. Therefore, the designed adaptive switching control method cannot achieve the tracking control of the disturbed flexible arm and the flexible joint space robot arm under alternating load (as shown in Figure 9-11 As shown in the figure, there is a persistent and significant deviation between the actual trajectory of the arm and the expected trajectory, and the angular velocity observer cannot accurately identify the actual angular velocity signal of the joint (such as Figure 12-13 The simulation results show the correctness and feasibility of the adaptive switching control method based on flexible compensator designed for the flexible arm and flexible joint space robot under alternating load.

[0247] The above description of one or more embodiments of the present invention is very detailed. However, the description is only a specific example of the present invention and should not be considered to limit the scope of application of the present invention. All other methods and modifications proposed based on the present invention should fall within the scope of patent protection of the present invention.

Claims

1. A method for adaptive switching control of a flexible arm and flexible joint space robot, characterized in that: The steps include: S1: Combining the assumed modal method, the law of conservation of momentum, and the elastic joint assumption, the Lagrangian method is applied to establish the dynamic model of the space robot with a disturbed flexible arm and flexible joints under alternating loads; S2: Using singular perturbation techniques, a fast-changing switching subsystem representing the flexibility of the arm is separated from the dynamic model of the flexible arm and flexible joint space robot under alternating loads described in S1, and a linear quadratic optimal switching vibration suppressor is designed for it. S3: Based on the dynamic model of the flexible arm and flexible joint space robot under alternating load described in S1, a model of the flexible joint space robot under alternating load is established. According to the singular perturbation technology based on flexible compensator, the model of the flexible joint space robot under alternating load is decomposed into a slow-changing switching subsystem characterizing the trajectory tracking of the robot arm and a fast-changing switching subsystem II characterizing the joint elasticity. S4: For the fast-changing switching subsystem 2, a torque proportional-differential feedback switching vibration suppressor is designed to eliminate the elastic vibration of the joint and ensure the stability of the movement; S5: For the slowly varying switching subsystem, an adaptive switching controller is designed by combining the average dwell time method and the composite sliding mode observer to realize the angular velocity signal recognition of the joint and the trajectory tracking of the manipulator under alternating load conditions; The specific implementation process of step S1 is: Combining the assumed modal method, the conservation laws of angular momentum and linear momentum, and the elastic joint assumption, the Lagrangian method can be used to obtain the dynamic model of the flexible arm and flexible joint space robot under alternating loads, as follows: ； ； in, is the symmetric and positive definite inertia switching matrix of the system, ; is the switching column vector of the system including Coriolis force and centrifugal force, ; is the external disturbance vector, ; Is a segment switching function , and in a finite index set Any value between When the matrix and In the active state, the matrix The corresponding vector is ; is the output torque column vector of the joint motor, ; , is the carrier attitude angular displacement, is the column vector of the arm angular displacement, Represents a vector The transposed matrix of is the modal coordinate vector of the flexible arm, and are the first-order and second-order modal coordinates of the flexible arm, respectively; and is a vector Solve the first and second derivatives of time t separately; and is a vector The first and second derivatives of the solution for time t; Specifically, it is the column vector of the driving motor rotor angular displacement; is the rotational inertia matrix of the drive motor; is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint; is the flexible arm stiffness coefficient matrix, and are the first-order stiffness coefficient and second-order stiffness coefficient of the flexible arm, respectively.

2. The adaptive switching control method of a flexible arm and flexible joint space robot according to claim 1 is characterized in that: The specific implementation process of S2 is as follows: Define the matrix ； ； In the formula 、 、 for The sub-matrix of and for submatrix of ; Since the dynamic model of the flexible arm and flexible joint space robot under alternating load in S1 contains the system symmetry and positive definite inertia switching matrix ,and is a positive definite matrix, and its inverse matrix can be expressed as: ； in, ; ； ； ； The rotational deviation of the flexible joint is defined as , is the column vector of the arm angular displacement, is the column vector of the driving motor rotor angular displacement; take the singular perturbation factor , and are the first-order stiffness coefficient and the second-order stiffness coefficient of the flexible arm respectively; then the new vector 、 and the new matrix 、 , is the modal coordinate vector of the flexible arm, is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint, is the stiffness coefficient matrix of the flexible arm; Based on this, the dynamic model of the flexible arm and flexible joint space robot under the alternating load in S1 can be expressed as follows: ； ； ； At this time, only the influence of the flexible arm vibration mode on the flexibility of the space robot system is considered, and the above formula is 、 , we can get the following formula: ； ； in, It represents the control torque of the system after eliminating the joint flexibility; ； ； ； ； Defining fast-changing time scales and correction parameters ; for exist The corresponding amount and ; Considering that the slow variables in the fast-changing system can be equivalent to constants, we have , where t is the time variable; make , we can obtain the dynamic equation of the fast-changing switching subsystem 1 corresponding to the flexible arm, specifically: ； in, , , , and The matrices and exist The matrix corresponding to the conditions; Finally, the following linear quadratic optimal switching damper is designed for the fast-changing switching subsystem 1 as shown below: ； in, 、 is a symmetric positive definite matrix, represents the controller of the fast-changing switching subsystem 1, is a matrix The unique solution of the corresponding Raccati equation; the performance index functional of the optimal vibration suppressor is selected as .

3. The adaptive switching control method of a flexible arm and flexible joint space robot according to claim 2 is characterized in that: The specific implementation process of S3 is as follows: According to the dynamic model of the flexible arm and flexible joint space robot under the alternating load in S1, the influence of the flexible arm on the flexibility of the system is neglected, that is, the modal coordinate vector of the flexible arm is , the dynamic equations of the flexible joint space robot system under alternating loads can be obtained as follows: ； ； ； in, for The inertia switching matrix of the system is symmetric and positive under the condition; for Under these conditions, the system includes switching column vectors of Coriolis force and centrifugal force; is the column vector of the control torque actually transmitted by the flexible joint; is the external disturbance vector; is a piecewise switching function and in a finite set of indices Any value between When the matrix and is in an active state; is the output torque column vector of the joint motor; ; is the carrier attitude angular displacement; is the column vector of the arm angular displacement; is the column vector of the driving motor rotor angular displacement; is the rotational inertia matrix of the drive motor; is the joint equivalent stiffness coefficient matrix; The dynamic equation of the flexible joint space robot system under alternating load can be obtained: ； The control law of the joint motor is designed as: ； in, is the joint flexibility compensation controller, is a diagonal, positive definite matrix; , is the identity matrix; is the control quantity to be designed; Combined formula And the control law formula of the joint motor, we can get: ； in, is the stiffness reinforcement matrix; According to the dynamic equations and formulas of the disturbed flexible joint space robot system under the determined alternating load The dynamic model of a space robot with flexible joints subjected to disturbances under alternating loads after stiffness enhancement is constructed. Using the singular perturbation method based on flexible compensator, Deconstructed into two parts: ； in, and They represent the fast-changing and slow-changing subsystem controllers of the flexible joint space robot under alternating loads; Let the joint stiffness coefficient matrix The smallest element in , let the singular perturbation factor for: ;make ,but Same dimension as the slowly varying component matrix; Combined formula With the formula , the dynamic equation of the fast-changing switching subsystem 2 can be derived as: ； At this time, , then the stiffness strengthening matrix , and the vector consisting of the driving motor rotor angular displacement column vector and the first-order derivative and second-order derivative of this vector is infinitely close to the vector consisting of the arm angular displacement column vector and the first-order derivative and second-order derivative of this vector, that is, ; Substitute the fast-changing switching subsystem 2 into the dynamic model of the flexible joint space robot system under the alternating load determined by S3, and let , the dynamic equation of the slowly changing switching subsystem that characterizes the trajectory tracking of the manipulator is obtained as: ； in, is the positive definite inertia switching matrix; To utilize Simplify and organize The column vector obtained after for About time Find the second-order derivative, is the external disturbance vector.

4. The adaptive switching control method of a flexible arm and flexible joint space robot according to claim 3 is characterized in that: The specific implementation process of S4 is as follows: For the fast-changing switching subsystem 2 in S3, in order to eliminate the nonlinear vibration caused by the flexible joint, the torque proportional-differential feedback switching vibration suppressor is designed as follows: ； in, and is the diagonal coefficient matrix; is the singular perturbation factor; is the column vector of the control torque actually transmitted by the flexible joint, express The first derivative with respect to time t.

5. The adaptive switching control method of a flexible arm and flexible joint space robot according to claim 4 is characterized in that: The specific implementation process of S5 is as follows: The dynamic equation of the slowly varying switching subsystem representing the trajectory tracking of the manipulator obtained from the decomposition of the disturbed flexible joint space robot model under the alternating load obtained in S3 is converted into the following form: ； in, , , , is the positive definite inertia switching matrix; To utilize Simplify and organize The column vector obtained after is the external disturbance vector; Then define the expected trajectory of the joint as , the joint trajectory tracking error is , is the column vector of the arm angular displacement, and the sliding surface can be further obtained as: ； in, is a diagonally positive definite matrix; Therefore, the adaptive sliding mode switching control law of the slow-varying subsystem is designed as follows: ； in, represents the estimate of the disturbance term; is the switching gain coefficient; , represents the standard symbolic function, and Represents sliding mode the first and second elements of ; For switching signals and any two moments ,make To this end, the switching signal is The number of switching times on the and have If established, then we call them and For this purpose, the average dwell time and chatter bound of the switching signal are; In order to avoid loss of generality, ,Right now ; The design of the composite sliding mode alternating observer is: ； in, and is a diagonally positive definite matrix; is the joint angular velocity vector Estimates, for About time Find the first-order derivative; When the disturbance estimation error Satisfy the boundedness condition: ； When the disturbance estimation error is a slow time-varying signal, that is: ； According to the dynamic equations of the slow-varying switching subsystem that characterizes the trajectory tracking of the manipulator, an adaptive sliding mode switching control law for the slow-varying subsystem based on the composite sliding mode alternating observer is designed to ensure the tracking error of the dynamic equations of the slow-varying switching subsystem that characterizes the trajectory tracking of the manipulator. Global asymptotic convergence; Choose the positive definite Lyapunov function as: ； in, , , ; Then Taking the derivative with respect to time t, we can get: ； Will The derivative formula for time t is Combining, we can get: ; Combining the above formula with the designed adaptive sliding mode switching control law of the slow-varying subsystem, we can obtain: ； Therefore, the control method expressed in the above formula has two states. One is when the disturbance estimation error satisfies the boundedness condition, that is, ; The other is when the disturbance estimation error is a slow time-varying signal, that is: ; When the disturbance estimation error satisfies the boundedness condition: ； Likewise, Derivative with respect to time t: ； According to another state, that is, when the disturbance estimation error is a slowly time-varying signal: ； Combined with the composite sliding mode alternating observer and , we can get: ； From the above formula and It can be seen that .

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