Self-adaptive preset performance control method based on disturbance observer

Abstract

The embodiment of the invention relates to a self-adaptive preset performance control method based on a disturbance observer. The method comprises the steps that a mechanical arm system dynamic model is established; a preset performance function is constructed, the preset performance function comprises a lower bound performance function and an upper bound performance function, and the angular displacement error of the mechanical arm is restrained through the lower bound performance function and the upper bound performance function which are located in the same direction; under the constraint of the lower bound performance function and the upper bound performance function, introducing a barrier function to constrain the angular displacement error of each joint of the mechanical arm, and determining the control error of each joint of the mechanical arm based on the barrier function; the non-linear disturbance observer is used for estimating external disturbance of the mechanical arm system, and a disturbance estimation result is obtained; and a controller is designed based on the control error and the disturbance estimation result, external disturbance of the mechanical arm system is compensated in real time through the controller, and actions of all joints of the mechanical arm are controlled. The angular displacement error overshoot can be well controlled, and the stability of the mechanical arm system is improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of robotic arm systems, and in particular to an adaptive preset performance control method based on a disturbance observer. Background Art

[0002] In actual industrial production, in order to meet high-standard operation requirements, the automatic control of the robot arm is very important. However, since the robot arm will inevitably be restricted by different external disturbance conditions during operation, it is necessary to pre-set performance constraints on the robot arm system to ensure that the robot arm can meet the operation requirements in actual operation.

[0003] In the prior art, most of them impose performance constraints on the robot system by adopting a preset performance function of the decaying exponential type to achieve the preset performance control of the robot. Although this preset performance function of the decaying exponential type can ensure the steady-state performance of the output error of the robot system in most cases, it cannot control the overshoot of the angular displacement error well, resulting in poor transient performance of the robot system. In addition, most of them use a simple scaling processing method to deal with the external disturbance of the system, which cannot accurately compensate for the disturbance error, which is not conducive to the robustness and stability of the robot system.

[0004] Therefore, it is necessary to provide a new technical solution to improve one or more problems existing in the above solutions.

[0005] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the invention

[0006] The purpose of the embodiments of the present disclosure is to provide an adaptive preset performance control method based on a disturbance observer, which can well control the overshoot of the angular displacement error and improve the transient performance of the robotic arm system.

[0007] According to an embodiment of the present disclosure, there is provided an adaptive preset performance control method based on a disturbance observer, comprising:

[0008] Establish the dynamic model of the robotic arm system;

[0009] Constructing a preset performance function, wherein the preset performance function includes a lower bound performance function and an upper bound performance function, and utilizing the lower bound performance function and the upper bound performance function located in the same direction to constrain the angular displacement error of the robotic arm;

[0010] Under the constraints of the lower bound performance function and the upper bound performance function, a barrier function is introduced to constrain the angular displacement error of each joint of the robotic arm, and the control error of each joint of the robotic arm is determined based on the barrier function;

[0011] Designing a nonlinear disturbance observer, using the nonlinear disturbance observer to estimate the external disturbance of the robot arm system, and obtaining a disturbance estimation result;

[0012] A controller is designed based on the control error and the disturbance estimation result, and the controller is used to compensate for the external disturbance of the robotic arm system in real time and control the movements of the joints of the robotic arm.

[0013] In an exemplary embodiment of the present disclosure, the dynamic model of the robotic arm system is expressed as:

[0014]

[0015] Where M(q) represents the inertia matrix of the robot arm, represents the Coriolis force matrix of the robot arm, G(q) represents the gravity term of the robot arm, d represents the preset external disturbance, represents the friction term, τ represents the control input torque of the robot system, q represents the angular displacement of the robot, q n represents the angular displacement of the nth joint of the robot arm, represents the angular velocity of the robot arm, represents angular acceleration.

[0016] In an exemplary embodiment of the present disclosure, the lower bound performance function and the upper bound performance function are expressed as:

[0017]

[0018] Among them, ρ l (t) represents the lower bound performance function, ρ l,0 represents the initial performance lower bound, ρ l,0 >0,ρ l,∞ represents the steady-state lower performance boundary, ρ l,∞ >0,λ l represents the first performance attenuation coefficient, ρ u (t) represents the upper bound performance function, ρ u,0 represents the initial performance upper bound, ρ u,0 >0,ρ u,∞ represents the upper bound of steady-state performance, ρ u,∞ >0,λ u represents the second performance attenuation coefficient, t represents the time, δ represents the initial error threshold, e(0) represents the angular displacement error of the manipulator at time t=0, sgn(·) represents the sign function,

[0019] In an exemplary embodiment of the present disclosure, the method of constraining the angular displacement error of the robot arm by using the lower bound performance function and the upper bound performance function located in the same direction includes:

[0020] According to the initial error threshold, the initial performance lower bound, the steady-state lower bound performance boundary, the initial performance upper bound and the steady-state upper bound performance boundary are restricted by formula (3) so that the lower bound performance function and the upper bound performance function are located in the same direction;

[0021] The formula (3) is expressed as:

[0022]

[0023] Among them, |δ| represents the absolute value of the initial error threshold, |ρ l,0 | represents the absolute value of the lower bound of the initial performance, |ρ l,∞ | represents the absolute value of the steady-state lower performance boundary, |ρ u,0 | represents the absolute value of the upper bound of the initial performance, |ρ u,∞ | represents the absolute value of the steady-state upper performance boundary.

[0024] In an exemplary embodiment of the present disclosure, in the step of constraining the angular displacement error of the robot arm using the lower bound performance function and the upper bound performance function located in the same direction, the constraint is performed by formula (4):

[0025]

[0026] Where e(t) represents the angular displacement error of the robotic arm system at time t, ρ l (t) represents the lower bound performance function, ρ u (t) represents the upper bound performance function.

[0027] In an exemplary embodiment of the present disclosure, the introduction of a barrier function to constrain the angular displacement error of each joint of the robotic arm system includes:

[0028] The barrier function is designed based on the barrier function theory, and the barrier function is expressed as:

[0029]

[0030] Among them, z i represents the barrier function variable, e i represents the angular displacement error of the i-th joint of the robotic arm system, ρ l,i represents the lower bound performance function corresponding to the angular displacement error of the i-th joint, ρ u.i represents the upper bound performance function corresponding to the angular displacement error of the i-th joint;

[0031] Under the constraints of the lower bound performance function and the upper bound performance function, the angular displacement error of the i-th joint is derived according to the barrier function and formula (4) to satisfy the following formula (6):

[0032]

[0033] Among them, e i (t) represents the angular displacement error of the i-th joint at time t, e i (0) represents the angular displacement error of the i-th joint at time t = 0, ρ l,i (t) represents the lower bound performance function corresponding to the angular displacement error of the i-th joint at time t, ρ u,i (t) represents the upper bound performance function corresponding to the angular displacement error of the i-th joint at time t.

[0034] In an exemplary embodiment of the present disclosure, in the step of determining the control error of each joint of the robotic arm based on the barrier function, the control error is expressed as:

[0035]

[0036] Among them, s i represents the control error corresponding to the i-th joint, z i represents the barrier function variable corresponding to the i-th joint, Indicates z i The derivative of i is a constant, and Λ i >0.

[0037] In an exemplary embodiment of the present disclosure, the nonlinear disturbance observer is expressed as:

[0038]

[0039] Where w represents the state of the nonlinear disturbance observer, represents the derivative of w, L(q) represents the preset gain matrix, τ represents the control torque vector of the robot, V represents the Coriolis force matrix of the robot, G represents the gravity term of the robot, and F v represents the friction term, q represents the angular displacement of the robot arm, q n represents the angular displacement of the nth joint of the robot arm, represents the angular velocity of the robot arm, represents a positive definite matrix, M represents the inertia matrix of the robot arm, represents the angular acceleration, represents the disturbance estimation result.

[0040] In an exemplary embodiment of the present disclosure, in the step of designing a controller based on the disturbance estimation result, the controller is represented as:

[0041]

[0042] Where τ represents the control input torque, represents the disturbance estimation result, represents parameter estimation, represents the parameter adaptation rate, φ represents a smooth and continuous positive definite function, c represents the setting parameter, c>0, Representation Matrix The minimum eigenvalue of represents the transpose of χ, χ represents a vector, s represents the control error of the robot, s=[s1,s2,…,s n ]∈R n ,s n represents the nth element of s, γ represents the setting parameter, γ>0, σ represents the setting parameter, σ>0.

[0043] In an exemplary embodiment of the present disclosure, the adaptive preset performance control method based on disturbance observer further includes:

[0044] Construct a quadratic Lyapunov candidate function:

[0045]

[0046] Where V represents the quadratic Lyapunov candidate function, s T represents the transpose of s, m represents a positive boundary constant, represents the parameter estimation error, θ represents the preset parameter, represents the positive boundary constant, λ min (L(q)) represents the minimum eigenvalue of the preset gain matrix L(q), represents the disturbance estimation error, d represents the preset external disturbance, express The transpose of

[0047] Calculating the derivative of the quadratic Lyapunov candidate function, we get:

[0048]

[0049] in, represents the derivative of the quadratic Lyapunov candidate function, M represents the inertia matrix of the manipulator, represents the derivative of χ, represents the derivative of the angular displacement error, represents the derivative of T, T represents a variable, Λ represents any positive constant, represents the preset expected angular acceleration;

[0050] The stability of the nonlinear disturbance observer is verified using the derivative of the quadratic Lyapunov candidate function.

[0051] The technical solution provided by the present disclosure may have the following beneficial effects:

[0052] In the embodiments of the present disclosure, on the one hand, the angular displacement error of the robotic arm is constrained by using a lower bound performance function and an upper bound performance function located in the same direction, and under the constraint of the preset performance function, a barrier function is further introduced to constrain the angular displacement error of each joint of the robotic arm, which is beneficial to better control the overshoot of the angular displacement error and improve the transient performance of the robotic arm system. On the other hand, the control error of each joint of the robotic arm is determined based on the barrier function, and the external disturbance of the robotic arm system is accurately estimated by using a nonlinear disturbance observer to obtain the disturbance estimation result. The controller is designed based on the control error and the disturbance estimation result of the robotic arm to achieve real-time compensation for the external disturbance of the robotic arm system and control the movement of each joint of the robotic arm, thereby improving the robustness and stability of the robotic arm system.

[0053] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0055] Figure 1 A flowchart showing the steps of an adaptive preset performance control method based on a disturbance observer in an exemplary embodiment of the present disclosure;

[0056] Figure 2 A simulation schematic diagram showing an error overshoot phenomenon in a preset performance function used in the prior art in an exemplary embodiment of the present disclosure;

[0057] Figure 3 Schematic diagram showing the simulation results of constraining the angular displacement error using the preset performance function designed by the present application in the exemplary embodiment of the present disclosure Figure 1 ;

[0058] Figure 4Schematic diagram showing the simulation results of constraining the angular displacement error using the preset performance function designed by the present application in the exemplary embodiment of the present disclosure Figure 2 ;

[0059] Figure 5 Schematic diagram showing the simulation results of estimating the external disturbance of the manipulator system using the nonlinear disturbance observer designed in the present application in the exemplary embodiment of the present disclosure Figure 1 ;

[0060] Figure 6 Schematic diagram showing the simulation results of estimating the external disturbance of the manipulator system using the nonlinear disturbance observer designed in the present application in the exemplary embodiment of the present disclosure Figure 2 . DETAILED DESCRIPTION

[0061] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0062] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0063] In this example implementation, an adaptive preset performance control method based on a disturbance observer is first provided. Figure 1 As shown in , the method may include the following steps:

[0064] Step S101: Establishing a dynamic model of the robotic arm system;

[0065] Step S102: constructing a preset performance function, wherein the preset performance function includes a lower bound performance function and an upper bound performance function, and utilizing the lower bound performance function and the upper bound performance function located in the same direction to constrain the angular displacement error of the robot arm;

[0066] Step S103: Under the constraints of the lower bound performance function and the upper bound performance function, a barrier function is introduced to constrain the angular displacement error of each joint of the robotic arm, and the control error of each joint of the robotic arm is determined based on the barrier function;

[0067] Step S104: designing a nonlinear disturbance observer, and using the nonlinear disturbance observer to estimate the external disturbance of the manipulator system to obtain a disturbance estimation result;

[0068] Step S105: designing a controller based on the control error of the robotic arm and the disturbance estimation result, and utilizing the controller to compensate for the external disturbance of the robotic arm system in real time and control the movements of the joints of the robotic arm.

[0069] In the embodiments of the present disclosure, on the one hand, the angular displacement error of the robotic arm is constrained by using a lower bound performance function and an upper bound performance function located in the same direction, and under the constraint of the preset performance function, a barrier function is further introduced to constrain the angular displacement error of each joint of the robotic arm, which is beneficial to better control the overshoot of the angular displacement error and improve the transient performance of the robotic arm system. On the other hand, the control error of each joint of the robotic arm is determined based on the barrier function, and the external disturbance of the robotic arm system is accurately estimated by using a nonlinear disturbance observer to obtain the disturbance estimation result. The controller is designed based on the control error and the disturbance estimation result of the robotic arm to achieve real-time compensation for the external disturbance of the robotic arm system and control the movement of each joint of the robotic arm, thereby improving the robustness and stability of the robotic arm system.

[0070] It should be noted that, in the dynamic model of the robotic arm system established in this embodiment, the robotic arm includes multiple joints. By constraining the angular displacement error of the entire robotic arm and the angular displacement error of each joint of the robotic arm, the output error of the robotic arm system can be more accurately controlled and the transient performance of the robotic arm system can be improved.

[0071] Below, each step of the above method in this example implementation will be described in more detail.

[0072] Specifically, in step S101, the total kinetic energy and total potential energy of the robotic arm system can be analyzed according to the Lagrange formula method, and the control torque of each joint of the robotic arm can be solved by using the rotation law in combination with the mechanical model of the pneumatic artificial muscle to obtain the dynamic model of the robotic arm system, wherein the dynamic model of the robotic arm system is expressed as:

[0073]

[0074] Where M(q) represents the inertia matrix of the robot arm, represents the Coriolis force matrix of the robot arm, G(q) represents the gravity term of the robot arm, d represents the preset external disturbance, represents the friction term, τ represents the control input torque of the robot system, q represents the angular displacement of the robot, q n represents the angular displacement of the nth joint of the robot arm, represents the angular velocity of the robot arm, represents angular acceleration.

[0075] It should be noted that establishing a dynamic model of a robotic arm system is a conventional technical method in this field and will not be described in detail here.

[0076] In this embodiment, the following assumption 1 is given: the preset desired angular displacement q d = Among them, q dn represents the expected angular displacement of the nth joint of the robot. Then, by setting the preset expected angular displacement q d The corresponding angular displacement error can be obtained by subtracting it from the angular displacement q of the robotic arm in the system, including the angular displacement error of the entire robotic arm and the angular displacement errors of each joint of the robotic arm.

[0077] It should be noted that, for the dynamic model of the robotic arm system established above, the angular displacement error of the robotic arm can be controlled within a specified performance range to ensure that the robotic arm moves accurately along a preset motion trajectory.

[0078] It should be explained that, in order to illustrate the difference between the preset performance function proposed in this application and the preset performance function used in the prior art, Figure 2 A simulation schematic diagram of the error overshoot phenomenon of the preset performance function used in the prior art is given in the figure. The performance change direction of this attenuation exponential preset performance function is opposite, and its upper performance limit and lower performance limit are located in opposite directions respectively. It can also be understood that the upper performance limit and the lower performance limit are located on both sides of the x-axis, which may cause the angular displacement error to overshoot in the same direction or different directions, resulting in poor transient performance of the system.

[0079] In step S102, the lower bound performance function and the upper bound performance function of the preset performance function constructed in this embodiment are expressed as:

[0080]

[0081] Among them, ρ l (t) represents the lower bound performance function, ρ l,0 represents the initial performance lower bound, ρ l,0 >0,ρ l,∞ represents the steady-state lower performance boundary, ρ l,∞ >0,λ l represents the first performance attenuation coefficient, ρ u(t) represents the upper bound performance function, ρ u,0 represents the initial performance upper bound, ρ u,0 >0,ρ u,∞ represents the upper bound of steady-state performance, ρ u,∞ >0,λ u represents the second performance attenuation coefficient, t represents the time, δ represents the initial error threshold, e(0) represents the angular displacement error of the manipulator at time t=0, sgn(·) represents the sign function,

[0082] For example, the step of constraining the angular displacement error of the robot arm by using the lower bound performance function and the upper bound performance function located in the same direction in step S102 further includes the following steps:

[0083] The initial performance lower bound, the steady-state lower bound performance boundary, the initial performance upper bound and the steady-state upper bound performance boundary are restricted according to the initial error threshold so that the lower bound performance function and the upper bound performance function are located in the same direction.

[0084] Specifically, in the step of limiting the initial performance lower bound, the steady-state lower bound performance boundary, the initial performance upper bound and the steady-state upper bound performance boundary according to the initial error threshold, the limiting is performed by formula (3):

[0085]

[0086] Among them, |δ| represents the absolute value of the initial error threshold, |ρ l,0 | represents the absolute value of the lower bound of the initial performance, |ρ l,∞ | represents the absolute value of the steady-state lower performance boundary, |ρ u,0 | represents the absolute value of the upper bound of the initial performance, |ρ u,∞ | represents the absolute value of the steady-state upper performance boundary.

[0087] The above introduces the absolute value of the initial error threshold |δ| to the parameter |ρ l,0 |、|ρ l,∞ |、|ρ u,0 |、|ρ u,∞ | is restricted so that the preset lower bound ρ l (t) and the preset upper bound ρ u (t) is always in the same direction at any time t. The same direction here can be understood as the direction approaching positive infinity along the x-axis, so as to ensure that after the angular displacement error at any time is constrained, the angular displacement error can be prevented from overshooting, thereby improving the transient performance of the robotic arm system.

[0088] Specifically, in the above step of using the lower bound performance function and the upper bound performance function located in the same direction to constrain the angular displacement error of the robot arm, the constraint is performed by formula (4):

[0089]

[0090] Where e(t) represents the angular displacement error of the robotic arm system at time t, ρ l (t) represents the lower bound performance function, ρ u (t) represents the upper bound performance function.

[0091] By designing the preset performance function ρ represented by the above formula (2) to formula (4) l (t) and ρ u (t) is used to constrain the angular displacement error, which is beneficial to better control the overshoot of the angular displacement error and improve the transient performance of the robotic arm system.

[0092] refer to Figure 3 and Figure 4 , which shows a schematic diagram of the simulation results of the preset performance function designed in this embodiment constraining the angular displacement error. It can be seen that Figure 3 It is shown that in the case of e(0)≥0, Figure 4 It is shown that when e(0)<0, the overshoot phenomenon of the angular displacement error can be prevented, thereby improving the transient performance of the robot system.

[0093] In this embodiment, in order to ensure that the angular displacement error falls uniformly within the set In this paper, the barrier function is further introduced, and the barrier function is used to constrain the angular displacement errors of each joint of the robotic arm system to ensure that the angular displacement errors fall uniformly within the set In. The above i (0) represents the angular displacement error of the i-th joint at time t = 0, e i (t) represents the angular displacement error of the i-th joint at time t, e i is the angular displacement error of the i-th joint at any time.

[0094] For example, the step of introducing a barrier function in step S103 to constrain the angular displacement errors of the joints of the robotic arm system includes:

[0095] The barrier function is designed based on the barrier function theory, and the barrier function is expressed as:

[0096]

[0097] Among them, z i represents the barrier function variable, ei represents the angular displacement error of the i-th joint of the robotic arm system, ρ l,i represents the lower bound performance function corresponding to the angular displacement error of the i-th joint, ρ u.i represents the upper bound performance function corresponding to the angular displacement error of the i-th joint;

[0098] Under the constraints of the lower bound performance function and the upper bound performance function, the angular displacement error of the i-th joint is derived according to the barrier function and formula (4) to satisfy the following formula (6):

[0099]

[0100] Among them, e i (t) represents the angular displacement error of the i-th joint at time t, e i (0) represents the angular displacement error of the i-th joint at time t = 0, ρ l,i (t) represents the lower bound performance function corresponding to the angular displacement error of the i-th joint at time t, ρ u,i (t) represents the upper bound performance function corresponding to the angular displacement error of the i-th joint at time t.

[0101] It should be noted that, under the constraints of the preset performance function, in order to make the angular displacement error of the i-th joint derived from the barrier function and formula (4) satisfy formula (6), the following prerequisites need to be met first:

[0102] The first prerequisite is: i (0) must satisfy the following formula (12):

[0103]

[0104] Among them, e i (0) represents the angular displacement error of the i-th joint at time t = 0, ρ l,i (0) represents the lower bound performance function corresponding to the angular displacement error of the i-th joint at time t = 0, ρ u,i (0) represents the upper bound performance function corresponding to the angular displacement error of the i-th joint at time t = 0;

[0105] The second prerequisite is to ensure that the barrier function variable z i Bounded.

[0106] This ensures that the angular displacement error e of the i-th joint at any time i (t) will never reach the boundary ρ l,i (t) and ρ u,i (t), thereby implementing corresponding performance constraints on the angular displacement errors of each joint of the robot arm and achieving more stable dynamic control.

[0107] It should be noted that, in order to enable the controller to more accurately control the movement of the robotic arm, the control error of the robotic arm is further introduced in this embodiment, and in the step of determining the control error of each joint of the robotic arm based on the barrier function, the control error is expressed as:

[0108]

[0109] Among them, s i represents the control error corresponding to the i-th joint, z i represents the barrier function variable corresponding to the i-th joint, Indicates z i The derivative of i is a constant, and Λ i >0

[0110] In this embodiment, in order to compensate for the influence of the external disturbance d on the robot system, a nonlinear disturbance observer is further designed.

[0111] In step S104, the nonlinear disturbance observer designed in this embodiment is expressed as:

[0112]

[0113] Where w represents the state of the nonlinear disturbance observer, represents the derivative of w, L(q) represents the preset gain matrix, τ represents the control torque vector of the robot, V represents the Coriolis force matrix of the robot, G represents the gravity term of the robot, and F v represents the friction term, q represents the angular displacement of the robot arm, q n represents the angular displacement of the nth joint of the robot arm, represents the angular velocity of the robot arm, represents a positive definite matrix, M represents the inertia matrix of the robot arm, represents the angular acceleration, represents the disturbance estimation result.

[0114] According to the nonlinear disturbance observer designed above, the following assumption 2 is given: There exists a positive constant Make

[0115] The following Theorem 1 is introduced: For any external disturbance d that satisfies Assumption 2, if the preset gain matrix of the nonlinear disturbance observer is positive definite (L(q)>0), then the nonlinear disturbance observer can exponentially estimate the external disturbance d of the manipulator system and obtain an accurate disturbance estimation result.

[0116] The following formula (13) and formula (14) show that the nonlinear disturbance observer designed by this embodiment can accurately estimate the disturbance estimation result: The proof process:

[0117] First, according to the preset external disturbance d and the disturbance estimation result observed by the nonlinear disturbance observer Get the disturbance estimation error

[0118] Then, the perturbation estimation error Taking the derivative, we get:

[0119]

[0120] in, represents the derivative of the disturbance estimation error, represents the derivative of the disturbance estimation result, represents a positive definite matrix, represents the derivative of the nonlinear disturbance observer state;

[0121] Then, consider the Lyapunov candidate function For the Lyapunov candidate function V d Taking the derivative, we get:

[0122]

[0123] Among them, λ min (L(q)) represents the minimum eigenvalue of the preset gain matrix L(q), represents the derivative of the Lyapunov candidate function, express The transpose of

[0124] Since the preset gain matrix L(q)>0, we know that λ min (L(q))>0, so we can get: That is, as time t increases, the disturbance estimation error It approaches to 0, which indicates that the nonlinear disturbance observer designed in this embodiment can accurately estimate the external disturbance of the manipulator system.

[0125] refer to Figure 5 and Figure 6 , which shows a schematic diagram of simulation results of the nonlinear disturbance observer designed in this embodiment estimating the external disturbance of the manipulator system. Figure 5It can be seen that the actual disturbance curve and the disturbance estimation result are shown. The actual disturbance curve represents the preset external disturbance. When the preset external disturbance is a constant external disturbance, that is, d = 1.2, the disturbance estimation result obtained by using the nonlinear disturbance observer is At time t = 1s, it is already very close to the preset external disturbance d. Figure 6 It can be seen from , when the preset external disturbance is a time-varying external disturbance, that is, When the nonlinear disturbance observer is used to estimate the disturbance, Close to the preset external disturbance d.

[0126] In this embodiment, based on the accurate estimation of external disturbances by the above-mentioned nonlinear disturbance observer, in order to compensate for the impact of constant / time-varying external disturbances on the performance of the robotic arm system and ensure that the angular displacement error remains within the performance range specified by the above-mentioned preset performance function, a controller is further designed, and the controller parameters need to be adaptively updated over time.

[0127] In step S104, the controller designed in this embodiment is expressed as:

[0128]

[0129] Where τ represents the control input torque, represents the disturbance estimation result, represents parameter estimation, represents the parameter adaptation rate, φ represents a smooth and continuous positive definite function, c represents the setting parameter, c>0, Representation Matrix The minimum eigenvalue of represents the transpose of χ, χ represents a vector, s represents the column vector of the control error of the robot, s=[s1,s2,…,s n ]∈R n ,s n represents the nth element of s, γ represents the setting parameter, γ>0, σ represents the setting parameter, σ>0. In the above controller, since ∥s∥ 2 φ≥0 and Heng established.

[0130] The controller can update the controller parameters in real time according to the real-time estimated disturbance estimation results, the control error of the robot arm and the adaptively updated parameter estimation, so as to control the robot arm system and regulate the movements of the joints of the robot arm in real time.

[0131] In one embodiment, the adaptive preset performance control method based on the disturbance observer proposed in this embodiment further includes a stability analysis process, which may include the following steps:

[0132] Construct a quadratic Lyapunov candidate function:

[0133]

[0134] Where V represents the quadratic Lyapunov candidate function, represents the transpose of s, m represents a positive boundary constant, represents the parameter estimation error, θ represents the preset parameter, represents the positive boundary constant, λ min (L(q)) represents the minimum eigenvalue of the preset gain matrix L(q), represents the disturbance estimation error, d represents the preset external disturbance, express The transpose of

[0135] Calculating the derivative of the quadratic Lyapunov candidate function, we get:

[0136]

[0137] in, represents the derivative of the quadratic Lyapunov candidate function, M is M(q), represents the inertia matrix of the manipulator, represents the derivative of χ, represents the derivative of the angular displacement error, represents the derivative of T, T represents a variable, Λ represents any positive constant, represents the preset expected angular acceleration;

[0138] The stability of the nonlinear disturbance observer is verified using the derivative of the quadratic Lyapunov candidate function.

[0139] It should be noted that before constructing the quadratic Lyapunov candidate function, it is necessary to solve the barrier function variable z according to formula (5): i The derivative of It can be expressed as:

[0140]

[0141] in, χ i represents the i-th element of vector X, ti Represents a variable, e i is the angular displacement error of the i-th joint at any time, Indicates e i The derivative of Represents ρ l,i The derivative of Represents ρ u,i The derivative of

[0142] Furthermore, due to the control error Substitute formula (15) into the control error s of the robot arm i In the expression of i Taking the derivative, we can get the derivative of the control error as:

[0143]

[0144] in, Indicates the control error s i The derivative of Represents χ i The derivative of Indicates t i The derivative of express The derivative of

[0145] The above expression (16) can be rewritten into a compact form as shown in the following expression (17):

[0146]

[0147] Among them, Λ=diag{Λ1,Λ2,…,Λ n}∈R n×n , χ=diag{χ1,χ2,…,χ n}∈R n×n ,diag{Λ1,Λ2,…,Λ n} represents {Λ1,Λ2,…,Λ n}, diag{χ1,χ2,…,χ n} represents {χ1,χ2,…,χ n}, e=[e1,e2,…,e n ]∈R n , T=[t1,t2,…,t n ]∈R n , represents the derivative of the column vector s of the control error.

[0148] For example, the step of verifying the stability of the nonlinear disturbance observer using the derivative of the quadratic Lyapunov candidate function includes:

[0149] Based on the dynamic model of the robotic arm system, according to Young's inequality:

[0150]

[0151] Among them, ||s|| represents the norm of s, ||χ|| represents the norm of χ, express The norm of , ||Ξ|| represents the norm of Ξ, represents a positive boundary constant, represents a positive constant;

[0152] Substituting formula (18) into formula (11), we obtain:

[0153]

[0154] in, represents the derivative of the quadratic Lyapunov candidate function, φ represents a smooth and continuous positive definite function, θ represents a preset parameter, represents a positive boundary constant, represents a positive constant;

[0155] Substituting the controller's control input torque τ into the equation (19) get:

[0156]

[0157] Wherein, c represents the set parameter;

[0158] Substituting formula (20) into formula (19), we obtain:

[0159]

[0160] in, represents the derivative of the quadratic Lyapunov candidate function, and γ represents the setting parameter;

[0161] The controller parameter adaptation rate Substituting into formula (21), we get:

[0162]

[0163] in, Derivatives representing the number of candidate functions of the quadratic Lyapunov form;

[0164] Based on formula (22) The following formula (23) is satisfied. Substituting formula (23) into formula (22), formula (24) can be obtained to verify the stability of the nonlinear disturbance observer;

[0165] Among them, formula (23) and formula (24) are respectively expressed as:

[0166]

[0167] Among them, θ 2 represents the square of θ;

[0168]

[0169] Where κ = min{2c m ,σ},

[0170] From formula (24), we can know that This shows that the nonlinear disturbance observer is convergent, proving the stability of the nonlinear disturbance observer.

[0171] In addition, it should be noted that the controller designed in this embodiment can be used to control the angular displacement error of the robot system to meet the preset performance of the preset performance function. According to formula (24), the quadratic Lyapunov candidate function V is bounded, so the control error s of the robot is i and parameter estimation error are bounded, because So the parameter estimates is also bounded; because So the barrier function variable z i and the derivative of the barrier function variable are bounded; because Therefore, the angular displacement error e of the i-th joint at any time is i Bounded and satisfied This ensures that the controller designed by this embodiment can control the angular displacement error of the robot arm system to meet the preset performance specified by the preset performance function.

[0172] In addition, it should be noted that this embodiment further provides an explanation of the boundedness of all closed-loop signals. l,i , u,i , e i are all bounded, and since So the element x i and variable t i are all bounded; and due to the limitation of formula (14) And the derivative of the barrier function variable Bounded, so is also bounded, so Ξ and φ are both bounded, and we can further know that the control input torque τ and parameter adaptation rate are all bounded, so it can be shown that all closed-loop signals are bounded.

[0173] It should also be noted that in the above description, the following conditions must also be met:

[0174] Assumption 3: There exists a positive constant Make

[0175] Property 1: Matrix It is a skew-symmetric array.

[0176] Property 2: There are some positive boundary constants m , Make

[0177] It should be noted that, although the steps of the method in the present disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in this specific order, or that all the steps shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step for execution, and / or one step may be decomposed into multiple steps for execution, etc. In addition, it is also easy to understand that these steps may be, for example, executed synchronously or asynchronously in multiple modules / processes / threads.

[0178] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. An adaptive preset performance control method based on disturbance observer, characterized in that: include: Establish the dynamic model of the robotic arm system; Constructing a preset performance function, wherein the preset performance function includes a lower bound performance function and an upper bound performance function, and utilizing the lower bound performance function and the upper bound performance function located in the same direction to constrain the angular displacement error of the robotic arm; Under the constraints of the lower bound performance function and the upper bound performance function, a barrier function is introduced to constrain the angular displacement error of each joint of the robotic arm, and the control error of each joint of the robotic arm is determined based on the barrier function; Designing a nonlinear disturbance observer, using the nonlinear disturbance observer to estimate the external disturbance of the robot arm system, and obtaining a disturbance estimation result; A controller is designed based on the control error and the disturbance estimation result, and the controller is used to compensate for the external disturbance of the robotic arm system in real time and control the movements of the joints of the robotic arm.

2. The adaptive preset performance control method based on disturbance observer according to claim 1, characterized in that: The dynamic model of the robotic arm system is expressed as: Where M(q) represents the inertia matrix of the robot arm, represents the Coriolis force matrix of the robot arm, G(q) represents the gravity term of the robot arm, d represents the preset external disturbance, represents the friction term, τ represents the control input torque of the robot system, q represents the angular displacement of the robot, q n represents the angular displacement of the nth joint of the robot arm, represents the angular velocity of the robot arm, represents angular acceleration.

3. The adaptive preset performance control method based on disturbance observer according to claim 2 is characterized in that: The lower bound performance function and the upper bound performance function are expressed as: Among them, ρ l (t) represents the lower bound performance function, ρ l,0 represents the initial performance lower bound, ρ l,0 >0,ρ l,∞ represents the steady-state lower performance boundary, ρ l,∞ >0,λ l represents the first performance attenuation coefficient, ρ u (t) represents the upper bound performance function, ρ u,0 represents the initial performance upper bound, ρ u,0 >0,ρ u,∞ represents the upper bound of steady-state performance, ρ u,∞ >0,λ u represents the second performance attenuation coefficient, t represents the time, δ represents the initial error threshold, e(0) represents the angular displacement error of the manipulator at time t=0, sgn(·) represents the sign function, 4. The adaptive preset performance control method based on disturbance observer according to claim 3 is characterized in that: The method of constraining the angular displacement error of the robot arm by using the lower bound performance function and the upper bound performance function located in the same direction includes: According to the initial error threshold, the initial performance lower bound, the steady-state lower bound performance boundary, the initial performance upper bound and the steady-state upper bound performance boundary are restricted by formula (3) so that the lower bound performance function and the upper bound performance function are located in the same direction; The formula (3) is expressed as: Among them, |δ| represents the absolute value of the initial error threshold, |ρ l,0 | represents the absolute value of the lower bound of the initial performance, |ρ l,∞ | represents the absolute value of the steady-state lower performance boundary, |ρ u,0 | represents the absolute value of the upper bound of the initial performance, |ρ u,∞ | represents the absolute value of the steady-state upper performance boundary.

5. The adaptive preset performance control method based on disturbance observer according to claim 4 is characterized in that: In the step of constraining the angular displacement error of the robot arm by using the lower bound performance function and the upper bound performance function located in the same direction, the constraint is performed by formula (4): Where e(t) represents the angular displacement error of the robotic arm system at time t, ρ l (t) represents the lower bound performance function, ρ u (t) represents the upper bound performance function.

6. The adaptive preset performance control method based on disturbance observer according to claim 5, characterized in that: The barrier function is introduced to constrain the angular displacement error of each joint of the robotic arm system, including: The barrier function is designed based on the barrier function theory, and the barrier function is expressed as: Among them, z i represents the barrier function variable, e i represents the angular displacement error of the i-th joint of the robotic arm system, ρ l,i represents the lower bound performance function corresponding to the angular displacement error of the i-th joint, ρ u.i represents the upper bound performance function corresponding to the angular displacement error of the i-th joint; Under the constraints of the lower bound performance function and the upper bound performance function, the angular displacement error of the i-th joint is derived according to the barrier function and formula (4) to satisfy the following formula (6): Among them, e i (t) represents the angular displacement error of the i-th joint at time t, e i (0) represents the angular displacement error of the i-th joint at time t = 0, ρ l,i (t) represents the lower bound performance function corresponding to the angular displacement error of the i-th joint at time t, ρ u,i (t) represents the upper bound performance function corresponding to the angular displacement error of the i-th joint at time t.

7. The adaptive preset performance control method based on disturbance observer according to claim 6, characterized in that: In the step of determining the control error of each joint of the robotic arm based on the barrier function, the control error is expressed as: Among them, s i represents the control error corresponding to the i-th joint, z i represents the barrier function variable corresponding to the i-th joint, Indicates z i The derivative of i is a constant, and Λ i >0.

8. The adaptive preset performance control method based on disturbance observer according to claim 2, characterized in that: The nonlinear disturbance observer is expressed as: Where w represents the state of the nonlinear disturbance observer, represents the derivative of w, L(q) represents the preset gain matrix, τ represents the control torque vector of the robot, V represents the Coriolis force matrix of the robot, G represents the gravity term of the robot, and F v represents the friction term, q represents the angular displacement of the robot arm, q n represents the angular displacement of the nth joint of the robot arm, represents the angular velocity of the robot arm, represents a positive definite matrix, M represents the inertia matrix of the robot arm, represents the angular acceleration, represents the disturbance estimation result.

9. The adaptive preset performance control method based on disturbance observer according to claim 8, characterized in that: In the step of designing a controller based on the control error of the robotic arm and the disturbance estimation result, the controller is expressed as: Where τ represents the control input torque, represents the disturbance estimation result, represents parameter estimation, represents the parameter adaptation rate, φ represents a smooth and continuous positive definite function, c represents the setting parameter, c>0, Representation Matrix The minimum eigenvalue of represents the transpose of χ, χ represents a vector, s represents the control error of the robot, s=[s1,s2,…,s n ]∈R n ,s n It is the nth element of s, representing the control error corresponding to the nth joint of the robot arm, γ represents the setting parameter, γ>0, σ represents the setting parameter, σ>0.

10. The adaptive preset performance control method based on disturbance observer according to claim 9, characterized in that: The adaptive preset performance control method based on disturbance observer also includes: Construct a quadratic Lyapunov candidate function: Where V represents the quadratic Lyapunov candidate function, represents the transpose of s, m represents a positive boundary constant, represents the parameter estimation error, θ represents the preset parameter, represents the positive boundary constant, λ min (L(q)) represents the minimum eigenvalue of the preset gain matrix L(q), represents the disturbance estimation error, d represents the preset external disturbance, express The transpose of Calculating the derivative of the quadratic Lyapunov candidate function, we get: in, represents the derivative of the quadratic Lyapunov candidate function, M represents the inertia matrix of the manipulator, represents the derivative of χ, represents the derivative of the angular displacement error, represents the derivative of T, T represents a variable, Λ represents any positive constant, represents the preset expected angular acceleration; The stability of the nonlinear disturbance observer is verified using the derivative of the quadratic Lyapunov candidate function.

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