Flexible arm and flexible joint space robot adaptive switching control method

Abstract

The invention discloses an adaptive switching control method for a flexible arm and flexible joint space robot. The adaptive switching control method comprises the following steps: S1, establishing a dynamic model of the disturbed flexible arm and flexible joint space robot under alternating load; s2, a first quick change switching subsystem representing the flexibility of the arm lever is separated out, and a linear quadratic optimal switching vibration suppressor is designed for the first quick change switching subsystem; s3, the disturbed flexible joint space robot model under the alternating load is decomposed into a slow change switching subsystem representing mechanical arm trajectory tracking and a second quick change switching subsystem representing joint elasticity; s4, designing a torque proportion-differential feedback switching vibration suppressor for the second quick-change switching subsystem, and S5, designing an adaptive switching controller for the slow-change switching subsystem by combining an average residence time method and a composite sliding-mode observer, and realizing angular velocity signal recognition of joints and trajectory tracking of a mechanical arm under the alternating load working condition.

Description

Technical Field

[0001] The 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 to perform ultra-precision tasks in extreme cosmic environments, such as sampling on the surface of asteroids, refueling spacecraft on orbit, and construction and maintenance of large space facilities. When performing tasks, space robots are inevitably subject to environmental interference factors such as solar light pressure, strong radiation, microgravity, and planetary gravitational perturbations, which seriously affect the stability, accuracy, and safety of the space robot system. On the other hand, in order to capture large-mass target satellites and transmit torque between arms, the joints of space robots have greater flexibility. This flexibility feature is more hidden and more significant than the flexibility of the arms, which can easily lead to elastic vibration of the joint hinge, thereby greatly affecting the control stability of the system. In addition, many current adaptive control methods of space robots do not have transferability, and their adaptive laws are only applicable to small parameter perturbations, but are helpless in switching control of capturing and releasing large-mass satellites.

[0003] For example, the invention patent with publication number CN118789557B published "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: S1: Combining the assumed modal method, the law of conservation of momentum and the elastic joint assumption, the dynamic model of the space robot with disturbed flexible arms and flexible joints under alternating loads was established by applying the Lagrangian method; S2: Using singular perturbation technology, a fast-changing switching subsystem 1 that characterizes 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 a space robot with a disturbed flexible joint under alternating load is established. According to the singular perturbation technology based on the flexible compensator, the model of the space robot with a disturbed flexible joint 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 2 characterizing the elasticity of the joint. 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 slow-changing 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 under alternating load conditions.

[0006] Further: the specific implementation process of step S1 is: Combining the assumed modal method, the law of conservation of angular momentum and linear momentum, and the elastic joint assumption, the dynamic model of the disturbed flexible arm and flexible joint space robot under alternating load can be obtained by applying the Lagrangian method, 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 activated 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 arm angular displacement column vector, Representation 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 For vector Solve the first and second derivatives for time t respectively; and For vector The first and second derivatives of the derivatives solved for time t; Specifically, it is the driving motor rotor angular displacement column vector; is the rotation inertia matrix of the drive motor; is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint; is the stiffness coefficient matrix of the flexible arm, and are the first-order stiffness coefficient and the second-order stiffness coefficient of the flexible arm respectively.

[0007] Further: the specific implementation process of S2 is: Defining 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 symmetric and positive inertia switching matrix ,and is a positive definite matrix, and its inverse matrix can be expressed as: ; in, ; ; ; .

[0008] The rotation angle deviation of the flexible joint is defined as , is the arm angular displacement column vector, 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; It can be seen from this that 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 vibration mode of the flexible arm 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 corresponding to the system after eliminating the joint flexibility; ; ; ; ; 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; make , the dynamic equation of the fast-changing switching subsystem 1 corresponding to the flexible arm can be obtained, specifically: ; in, , , , and The matrices are and exist The matrix corresponding to the condition;

[0009] 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 fast-changing subsystem 1, For the 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 1 and output variables By solving the extreme value of the functional, we can find a control strategy that minimizes the energy consumption and maximizes the efficiency of the system, so as to improve the efficiency, stability and economy of the system.

[0010] Furthermore: the specific implementation process of S3 is: 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 equation of the space robot system with disturbed flexible joints under alternating loads can be obtained as follows: ; ; ; in, for The inertia switching matrix of the system is symmetric and positive definite under the condition; for Under the condition, the system includes the 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 activated state; is the output torque column vector of the joint motor; ; is the carrier attitude angular displacement; is the arm angular displacement column vector; is the column vector of the driving motor rotor angular displacement; is the rotation inertia matrix of the drive motor; is the joint equivalent stiffness coefficient matrix; From the dynamic equation of the disturbed flexible joint space robot system under alternating load, we can get: ; 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; Combining formulas 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 the space robot with flexible joints under alternating loads after stiffness enhancement is formed; Using the singular perturbation method based on flexible compensator, Decomposed into two parts: ; in, and They represent the fast-changing and slow-changing subsystem controllers of the disturbed flexible joint space robot under alternating loads respectively; Let the joint stiffness coefficient matrix The smallest element in is , let the singular perturbation factor for: ;make ,but Same dimension as the slowly varying component matrix; Combining formulas 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 angular displacement column vector of the driving motor rotor and the first-order derivative and the second-order derivative of the vector is infinitely close to the vector consisting of the angular displacement column vector of the arm and the first-order derivative and the second-order derivative of the vector ; Substitute the fast-changing switching subsystem 2 into the dynamic model of the disturbed flexible joint space robot system under the alternating load determined by S3, and let , the dynamic equation of the slow-changing switching subsystem that characterizes the robot trajectory tracking is obtained as: ; in, is the positive definite inertia switching matrix; To use Simplify and organize The resulting column vector; for About Time Find the second-order derivative, is the external disturbance vector.

[0011] Further: the specific implementation process of S4 is: 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.

[0012] Further: the specific implementation process of S5 is: The dynamic equation of the slowly changing switching subsystem characterizing the trajectory tracking of the manipulator obtained by decomposing the disturbed flexible joint space robot model under the alternating load in S3 is converted into the following form: ; in, , , , is the positive definite inertia switching matrix; To use Simplify and organize The resulting column vector is is the external disturbance vector; Then define the expected trajectory of the joint as , the joint trajectory tracking error is , is the arm angular displacement column vector, and the sliding surface can be further obtained as: ; in, is a diagonally positive definite matrix; In this regard, 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 Respectively represent sliding mode the first and second elements of ; For switching signals and any two moments ,make To this end, the switching signal is in the time interval The number of switching times on the and have Established, then they are called and For this purpose, the average dwell time and tremor bound of the switching signal are; In order not to lose generality, the present invention takes ,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 The estimate, for About Time Find the first-order derivative; When the disturbance estimation error Satisfies the boundedness condition: ; When the disturbance estimation error is a slow time-varying signal, that is: ; According to the dynamic equation of the slow-changing switching subsystem that characterizes the trajectory tracking of the robot arm, an adaptive sliding mode switching control law for the slow-changing subsystem based on the composite sliding mode alternating observer is designed to ensure the tracking error of the dynamic equation of the slow-changing switching subsystem that characterizes the trajectory tracking of the robot arm. Global asymptotic convergence; Choose the positive definite Lyapunov function as: ; in, , , ; Then Taking the derivative with respect to time t, we can obtain: ; 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 get: ; 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 slow 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 .

[0013] The beneficial effects of the present invention are: 1. For the slowly changing switching subsystem of the disturbed space robot under alternating load, a composite sliding mode switching observer is designed, which can simultaneously realize the alternating recognition of joint angular velocity signals and external disturbances; 2. For the slowly changing switching subsystem of the disturbed space robot under alternating load, an adaptive switching control method based on the average dwell time method and the composite sliding mode observer is designed to solve the influence of alternating load and external disturbance on the trajectory tracking performance of the robot arm; 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, which fully consider the current information and future change trend of the control torque transmitted by the joint joint to effectively suppress the elastic vibration of the arm and joint. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention and the technical solutions in the prior art, the drawings required for use in the embodiments and the description of the prior art will be briefly introduced below. 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 creative work.

[0015] Figure 1 It is a technical flow chart of the present invention; Figure 2 It is a structural diagram of a flexible arm and a flexible joint space robot under alternating load in the present invention; Figure 3 It is the switching signal of the alternating load; Figure 4 is the time response curve of the angular displacement of joint 1 when the flexible compensator is turned on; Figure 5 is the time response curve of the angular displacement of joint 2 when the flexible compensator is turned on; 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; Figure 7 This is the time response curve of the observed angular velocity of joint 1 when the flexible compensator is turned on; Figure 8 This is the time response curve of the observed angular velocity of joint 2 when the flexible compensator is turned on; Fig. 9 is the time response curve of the angular displacement of joint 1 under the condition of flexible compensator being closed; Fig.10 is the time response curve of the angular displacement of joint 2 when the flexible compensator is closed; Fig.11 is the time response curve of the angular displacement tracking error of joint 1 and joint 2 when the flexible compensator is closed; Fig.12 is the time response curve of the observed angular velocity of joint 1 under the condition of the flexible compensator being closed; Fig.13 This is the time response curve of the observed angular velocity of joint 2 when the flexible compensator is closed. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical scheme 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 only used to explain 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 ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0017] 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.

[0018] 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.

[0019] If not otherwise specified, all embodiments and optional embodiments of the present invention can be combined with each other to form a new technical solution.

[0020] See also Figure 1 and Figure 2 , respectively, are the technical flow chart of the present invention and the structural diagram of the flexible arm and flexible joint space robot under alternating load. The process includes the following steps: S1: Combining the assumed modal method, the law of conservation of momentum and the elastic joint assumption, the dynamic model of the space robot with disturbed flexible arms and flexible joints under alternating loads was established by applying the Lagrangian method; S2: Using singular perturbation technology, the fast-changing switching subsystem 1 that represents the flexibility of the arm is separated from the system model, and a linear quadratic optimal switching damper is designed for it; S3: According to the singular perturbation technique based on flexible compensator, it 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 slow-changing 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 under alternating load conditions.

[0021] Specifically: 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 dynamic model of the flexible arm and flexible joint space robot under alternating load can be obtained by applying the Lagrangian method: (1) (2) 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 activated 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 arm angular displacement column vector, Representation 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 For vector Solve the first and second derivatives for time t respectively; and For vector The first and second derivatives solved for time t; Specifically, it is the driving motor rotor angular displacement column vector; is the rotation inertia matrix of the drive motor; is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint; is the stiffness coefficient matrix of the flexible arm, and are the first-order stiffness coefficient and the second-order stiffness coefficient of the flexible arm respectively.

[0022] The specific implementation process of step S2 is: definition , ; In the formula , , for The sub-matrix of and for submatrix of ; because is a positive definite matrix, so its inverse matrix exists and can be expressed as: (3) in, ; ; ; ; The rotation angle deviation of the flexible joint is defined as , is the arm angular displacement column vector, 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; therefore, equations (1) and (2) can be expressed as: (4) (5) (6) 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) to (6) can be , , after sorting, we can get: (7) (8) In the formula, It represents the control torque corresponding to the system after eliminating the joint flexibility; ; ; ; ; 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 ; If you , the dynamic equation of the fast-changing switching subsystem 1 corresponding to the flexible arm is obtained as follows: (9) Among them, , , , and The matrices are and exist The matrix corresponding to the condition.

[0023] The following linear quadratic optimal switching damper is designed for the fast-changing switching subsystem 1: (10) In the formula, , is a symmetric positive definite matrix, represents the controller of fast-changing subsystem 1, For the matrix The unique solution of the corresponding Raccati equation; the performance index functional of the optimal vibration suppressor is selected as .

[0024] The specific implementation process of step S3 is: Ignore the influence of the flexible arm on the flexibility of the system, that is, let the modal coordinate vector of the flexible arm be , from equations (1)-(2), the dynamic equation of the disturbed flexible joint space robot system under alternating load is: (11) (12) (13) in, for The inertia switching matrix of the system is symmetric and positive definite under the condition; for Under the condition, the system includes the 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 activated state; is the output torque column vector of the joint motor; ; is the carrier attitude angular displacement; is the arm angular displacement column vector; is the column vector of the driving motor rotor angular displacement; is the rotation inertia matrix of the drive motor; is the joint equivalent stiffness coefficient matrix.

[0025] Combining equations (12) and (13), we can obtain (14) The control law of the joint motor is designed as: (15) in, is the joint flexibility compensation controller, is a diagonal, positive definite matrix; , is the identity matrix; is the control quantity to be designed; Combining formula (15) and (14), we can get: (16) in, is the stiffness reinforcement matrix; 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; Using the singular perturbation method based on flexible compensator, Decomposed into two parts: (17) in, and They represent the fast-changing and slow-changing subsystem controllers of the disturbed flexible joint space robot under alternating loads respectively; in, and They represent the fast-changing and slow-changing subsystem controllers of the disturbed flexible joint space robot under alternating loads respectively; Let the joint stiffness coefficient matrix The smallest element in is , let the singular perturbation factor for: ;make ,but Same dimension as the slowly varying component matrix; Combining equation (16) and equation (17), the dynamic equation of the fast-changing switching subsystem 2 can be derived as: (18) At this time, if , then the stiffness strengthening matrix and .

[0026] 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: (19) in, is the positive definite inertia switching matrix; To use Simplify and organize The resulting column vector; for About Time Find the second-order derivative, is the external disturbance vector.

[0027] The specific implementation process of S4 is: 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: (20) 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.

[0028] The specific implementation process of S5 is: The slow-changing switching subsystem shown in equation (19) can be written as follows: (twenty one) in, , , , is the positive definite inertia switching matrix; To use Simplify and organize The resulting column vector is is the external disturbance vector; Then define the expected trajectory of the joint as , the joint trajectory tracking error is , is the arm angular displacement column vector, and the sliding surface can be further obtained as: (twenty two) in, is a diagonally positive definite matrix.

[0029] In this regard, the adaptive sliding mode switching control law of the slow-varying subsystem is designed as follows: (twenty three) in, represents the estimate of the disturbance term; is the switching gain coefficient; , represents the standard symbolic function, and Respectively represent sliding mode The first and second elements of .

[0030] For switching signals and any two moments ,make To this end, the switching signal is in the time interval The number of switching times on the and have Established, then they are called and For this purpose, the average dwell time and the tremor bound of the switching signal are: ,Right now .

[0031] The design of the composite sliding mode alternating observer is: (twenty four) in, and is a diagonally positive definite matrix; is the joint angular velocity vector The estimate, for About Time Find the first-order derivative; Assumption 1 Perturbation estimation error Satisfies the boundedness condition: (25) Assumption 2 The disturbance is a slow time-varying signal, that is (26) Theorem 1 Considering the switching dynamics equation (19) of the slow-changing subsystem of the space robot with disturbed flexible joints under alternating load, the sliding mode switching control law (23) based on the adaptive observer (24) is designed to ensure the tracking error of the slow-changing subsystem (19) Global asymptotic convergence.

[0032] Choose the positive definite Lyapunov function as (27) in, , , ; Then Taking the derivative with respect to time t, we can obtain: (28) Combining equation (21) with equation (28), we can get (29) According to formula (23) and formula (29), we can get: (30) According to Assumption 1, equation (30) becomes: (31) Likewise, Taking the derivative with respect to time t, we get: (32) According to Assumption 2, equation (32) becomes: (33) Combining equation (21) and equation (24), we can get: (34) From formula (31) and formula (34), we can see that .

[0033] 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.

[0034] A specific embodiment of the present invention: like Figure 1 As shown, the control object of the present invention is a flexible arm and flexible joint space robot disturbed 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 centroid of For each module Relative to the world origin Position vector of module The quality is , the moment of inertia is ; For modules and The articulation center; is the carrier attitude angular displacement, For arm Angular displacement of joints; 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 turning angle is , equivalent stiffness coefficient .

[0035] by Figure 2 Taking the disturbed flexible arm and flexible joint space robot under the alternating load (satellite capture and release) as an example, the effectiveness of the adaptive switching control method proposed in the present invention is verified in MATLAB / Simulink. The expected trajectory (unit: radian) of the disturbed flexible joint space robot arm under the alternating load is , the initial position of the system (unit: radians) 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 load); when When , it means that the space robot has captured satellite P and merged with it (with load). 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.

[0036] Table 1 .

[0037] Table 2 .

[0038] Figures 4 to 8 It 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 the alternating load, the adaptive switching control method based on the flexible compensator designed in the present invention can ensure that the disturbed flexible arm and the flexible joint space robot arm rod are stable under the alternating load, and the desired trajectory is tracked 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 (such as Figure 7-8 As 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 a dual-time scale control role. 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 obvious 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 compensators designed for the disturbed flexible arm and flexible joint space robot under alternating loads.

[0039] The above is a very detailed description of one or more embodiments of the present invention, but the content is only a specific example of the present invention and cannot be considered to limit the scope of application of the present invention. Any other methods and changes proposed based on the content of 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 dynamic model of the space robot with disturbed flexible arms and flexible joints under alternating loads was established by applying the Lagrangian method; S2: Using singular perturbation technology, a fast-changing switching subsystem 1 that characterizes 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 a space robot with a disturbed flexible joint under alternating load is established. According to the singular perturbation technology based on the flexible compensator, the model of the space robot with a disturbed flexible joint 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 2 characterizing the elasticity of the joint. 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 slow-changing 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 under alternating load conditions.

2. The method for adaptive switching control of a flexible arm and flexible joint space robot according to claim 1, characterized in that: The specific implementation process of step S1 is: Combining the assumed modal method, the law of conservation of angular momentum and linear momentum, and the elastic joint assumption, the dynamic model of the disturbed flexible arm and flexible joint space robot under alternating load can be obtained by applying the Lagrangian method, 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, ; It 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 arm angular displacement column vector, Representation 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 For vector Solve the first and second derivatives for time t respectively; and For vector The first and second derivatives solved for time t; Specifically, it is the driving motor rotor angular displacement column vector; is the rotation inertia matrix of the drive motor; is the positive definite diagonal matrix representing the equivalent stiffness coefficient of the flexible joint; is the stiffness coefficient matrix of the flexible arm, and are the first-order stiffness coefficient and the second-order stiffness coefficient of the flexible arm respectively.

3. The method for adaptive switching control of a flexible arm and flexible joint space robot according to claim 1, characterized in that: The specific implementation process of S2 is: Defining 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 symmetric and positive inertia switching matrix ,and is a positive definite matrix, and its inverse matrix can be expressed as: ； in, ; ； ； ； The rotation angle deviation of the flexible joint is defined as , is the arm angular displacement column vector, 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; It can be seen from this that 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 vibration mode of the flexible arm 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 corresponding to the system after eliminating the joint flexibility; ； ； ； ； 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; make , the dynamic equation of the fast-changing switching subsystem 1 corresponding to the flexible arm can be obtained, specifically: ; in, , , , and The matrices are and exist The matrix corresponding to the condition; 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 fast-changing subsystem 1, For the matrix The unique solution of the corresponding Raccati equation; the performance index functional of the optimal vibration suppressor is selected as .

4. The method for adaptive switching control of a flexible arm and flexible joint space robot according to claim 1, 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 equation of the space robot system with disturbed flexible joints under alternating loads can be obtained as follows: ； ； ； in, for The inertia switching matrix of the system is symmetric and positive definite under the condition; for Under the condition, the system includes the 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 activated state; is the output torque column vector of the joint motor; ; is the carrier attitude angular displacement; is the arm angular displacement column vector; is the column vector of the driving motor rotor angular displacement; is the rotation inertia matrix of the drive motor; is the joint equivalent stiffness coefficient matrix; From the dynamic equation of the disturbed flexible joint space robot system under alternating load, we can get: ; 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; Combining formulas 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 the space robot with flexible joints under alternating loads after stiffness enhancement is formed; Using the singular perturbation method based on flexible compensator, Decomposed into two parts: ; in, and They represent the fast-changing and slow-changing subsystem controllers of the disturbed flexible joint space robot under alternating loads respectively; Let the joint stiffness coefficient matrix The smallest element in is , let the singular perturbation factor for: ;make ,but Same dimension as the slowly varying component matrix; Combining formulas With 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 composed of the driving motor rotor angular displacement column vector and the first-order derivative and second-order derivative of the vector is infinitely close to the vector composed of the arm angular displacement column vector and the first-order derivative and second-order derivative of the vector, that is, ; Substitute the fast-changing switching subsystem 2 into the dynamic model of the disturbed flexible joint space robot system under the alternating load determined by S3, and let , the dynamic equation of the slow-changing switching subsystem that characterizes the robot trajectory tracking is obtained as: ； in, is the positive definite inertia switching matrix; To use Simplify and organize The resulting column vector; for Taking the second-order derivative with respect to time t, is the external disturbance vector.

5. The method for adaptive switching control of a flexible arm and flexible joint space robot according to claim 1, 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.

6. The method for adaptive switching control of a flexible arm and flexible joint space robot according to claim 1, characterized in that: The specific implementation process of S5 is as follows: The dynamic equation of the slowly changing switching subsystem characterizing the trajectory tracking of the manipulator obtained by decomposing the disturbed flexible joint space robot model under the alternating load in S3 is converted into the following form: ； in, , , , is the positive definite inertia switching matrix; To use Simplify and organize The resulting column vector is is the external disturbance vector; Then define the expected trajectory of the joint as , the joint trajectory tracking error is , is the arm angular displacement column vector, and the sliding surface can be further obtained as: ; in, is a diagonally positive definite matrix; In this regard, 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 Respectively represent sliding mode the first and second elements of ; For switching signals and any two moments ,make To this end, the switching signal is in the time interval The number of switching times on the and have Established, then they are called and For this purpose, the average dwell time and tremor bound of the switching signal are; In order not to lose generality, the present invention takes ,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 The estimate, for About Time Find the first-order derivative; When the disturbance estimation error Satisfies the boundedness condition: ; When the disturbance estimation error is a slow time-varying signal, that is: ； According to the dynamic equation of the slow-changing switching subsystem that characterizes the trajectory tracking of the robot arm, an adaptive sliding mode switching control law for the slow-changing subsystem based on the composite sliding mode alternating observer is designed to ensure the tracking error of the dynamic equation of the slow-changing switching subsystem that characterizes the trajectory tracking of the robot arm. Global asymptotic convergence; Choose the positive definite Lyapunov function as: ； in, , , ; Then Taking the derivative with respect to time t, we can obtain: ； Will The derivative formula for time t is Combining, we can get: ; According to the above formula combined with the designed adaptive sliding mode switching control law of the slow-varying subsystem, we can get: ； 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 slow 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 .

Images