A mechanical arm adaptive fractional order sliding mode control method, device and medium

Abstract

The embodiment of the application discloses a kind of mechanical arm adaptive fractional order sliding mode control method, equipment and medium. Based on the position vector, velocity vector and acceleration vector of mechanical arm, the corresponding dynamics model of mechanical arm is established;Based on the actual trajectory and expected trajectory of mechanical arm, a tracking error dynamic equation is established;Based on the position error and error boundary corresponding to different joints of mechanical arm respectively, an error function is constructed to limit the trajectory tracking error corresponding to mechanical arm in the preset range based on the error function;According to the tracking error dynamic equation and error function, the corresponding fractional order non-singular terminal sliding mode surface of mechanical arm is obtained to construct adaptive fractional order non-singular terminal sliding mode control;According to the comprehensive disturbance data in the dynamics model corresponding to mechanical arm, a nonlinear disturbance observer is constructed to feed forward compensation based on the nonlinear disturbance observer on the dynamics model corresponding to mechanical arm, to realize the control of mechanical arm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robots, and particularly relates to a mechanical arm adaptive fractional order sliding mode control method, device and medium. BACKGROUND

[0002] A mechanical arm is a highly nonlinear, strongly coupled complex system. In recent years, with the continuous progress of robot technology, more and more advanced mechanical arms are used in industrial production and home service and other fields. Due to the particularity of the working task of the mechanical arm, the control accuracy of the mechanical arm is continuously improved. The research on the control method of the mechanical arm has always been the focus of attention of researchers at home and abroad. Many advanced modern control methods have been applied to the precise operation of the mechanical arm, such as fuzzy control, neural network control, sliding mode control, etc.

[0003] The sliding mode control is characterized in that a very accurate dynamic model of the system is not required in the design process, and only the trajectory tracking error or position control error is used to reasonably design the sliding mode surface, and the sliding mode control has the characteristics of fast response and good robustness. As a practical control method, researchers apply the sliding mode control method to the control of the mechanical arm. However, due to the high-frequency chattering phenomenon in the control input, the application of the traditional SMC in the field of robots is limited, which affects the actual application performance of the robot. SUMMARY

[0004] The embodiment of the present application provides a mechanical arm adaptive fractional order sliding mode control method, device and medium, which is used to solve the following technical problems: in the prior art, due to the high-frequency chattering phenomenon in the control input, the application of the traditional SMC in the field of robots is limited, which affects the actual application performance of the robot.

[0005] The embodiment of the present application adopts the following technical scheme:

[0006] The embodiment of the present application provides a mechanical arm adaptive fractional order sliding mode control method. The method comprises the following steps: based on a position vector, a velocity vector and an acceleration vector of the mechanical arm, a corresponding dynamic model of the mechanical arm is established; based on an actual trajectory and an expected trajectory of the mechanical arm, a tracking error dynamic equation is established; based on a position error and an error boundary of each joint of the mechanical arm, an error function is constructed to limit the trajectory tracking error of the mechanical arm in a preset range based on the error function; according to the tracking error dynamic equation and the error function, a fractional order non-singular terminal sliding mode surface corresponding to the mechanical arm is obtained to construct an adaptive fractional order non-singular terminal sliding mode control; according to comprehensive disturbance data in the dynamic model corresponding to the mechanical arm, a nonlinear disturbance observer is constructed to perform feedforward compensation on the dynamic model corresponding to the mechanical arm based on the nonlinear disturbance observer, so as to control the mechanical arm.

[0007] The funnel function is adopted in the embodiment of the application to convert the original tracking error into a specified error, limit the trajectory tracking error in a preset range, and then construct an adaptive fractional order non-singular terminal sliding mode control, so as to effectively ensure the trajectory tracking accuracy of the robot arm and improve the transient and steady state performances of the system. In view of the model uncertainty and external disturbance of the robot arm system, a nonlinear disturbance observer is designed to compensate the disturbance of the system, so as to eliminate the influence of the disturbance on the operation performance of the robot arm, and effectively reduce the chattering phenomenon of the system.

[0008] In an implementation manner of the application, a dynamic model corresponding to the robot arm is established based on a position vector, a velocity vector and an acceleration vector of the robot arm, and specifically includes:

[0009] Based on a function

[0010]

[0011]

[0012] The dynamic model corresponding to the robot arm is obtained

[0013]

[0014] Wherein,

[0015] Wherein, q∈R n×1 is a position vector of a joint of the robot arm; is a velocity vector of the joint of the robot arm; is an acceleration vector of the joint of the robot arm; M(q)∈R n×n is a moment of inertia matrix of the robot arm; is a centrifugal force and Coriolis force matrix of the robot arm; G(q)∈R n×1 is a gravity term of the robot arm; τ is a control torque of the robot arm; τ d is a disturbance term of the robot arm; M0(q) is a certain quantity corresponding to the moment of inertia matrix of the robot arm; ΔM(q) is an uncertain quantity corresponding to the moment of inertia matrix of the robot arm; is a certain quantity corresponding to the centrifugal force and Coriolis force matrix of the robot arm; is an uncertain quantity corresponding to the centrifugal force and Coriolis force matrix of the robot arm; G0(q) is a certain quantity corresponding to the gravity term of the robot arm; ΔG(q) is an uncertain quantity corresponding to the gravity term of the robot arm.

[0016] In an implementation manner of the application, a tracking error dynamic equation is established based on an actual trajectory and an expected trajectory of the robot arm, and specifically includes: based on a trajectory tracking error function

[0017] e=q-q d ;

[0018] Obtain the tracking error dynamic equation

[0019]

[0020] Wherein, e is the trajectory tracking error; q d is the desired trajectory.

[0021] In an implementation form of the present application, based on the position error and error boundary corresponding to different joints of the robot arm respectively, an error function is constructed, specifically including:

[0022] Based on the function

[0023]

[0024] F μ = μ0exp(-υt) + μ ∞

[0025] An error function is constructed; wherein, e i , σ i (i = 1, 2, …, n) are the position error and conversion error of the i-th joint respectively; σ = [σ1, σ2, …, σ n ] T ; ||·|| is the Euclidean norm; μ0, μ ∞ are constants greater than 0, and μ0> μ ∞ ; F μ (0) = μ0+ μ ∞ is the maximum boundary of the initial error; is the steady-state error boundary, and υ>0.

[0026] In an implementation form of the present application, according to the tracking error dynamic equation and the error function, a fractional order non-singular terminal sliding mode surface corresponding to the robot arm is obtained, specifically including: based on the tracking error dynamic equation and the error function, a differential equation of the conversion error is obtained

[0027]

[0028]

[0029] Wherein, F = diag{f1,..., f n}, P = diag{p1,..., p n}, f i = F μ -||e i ||, p i = 1 / f i 2 , Based on the differential equation of the conversion error, a fractional order non-singular terminal sliding mode surface corresponding to the mechanical arm is obtained

[0030]

[0031] Wherein, 0 < alpha < 1, gamma > 0, All are real numbers,

[0032] In an implementation manner of the present application, a nonlinear disturbance observer is constructed according to the comprehensive disturbance data in the dynamic model corresponding to the mechanical arm, specifically including: constructing a function

[0033]

[0034]

[0035] Wherein, The observation value of the comprehensive disturbance term Z is an internal state variable of the observer, The observer to be designed nonlinear function, The observer gain coefficient; based on the preset observation error and the constructed function, a nonlinear disturbance observer is constructed to realize that the observation error asymptotically converges to 0.

[0036] In an implementation manner of the present application, based on the preset observation error and the constructed function, a nonlinear disturbance observer is constructed to realize that the observation error asymptotically converges to 0, specifically including: defining the preset observation error as

[0037]

[0038] In the case of Based on the preset observation error and the constructed function, the differential equation of the preset observation error is obtained

[0039]

[0040]

[0041] Based on the dynamic model corresponding to the mechanical arm, the constructed function and the differential equation of the preset observation error, the

[0042]

[0043] Define

[0044] By adjusting the coefficient C, the observation error asymptotically converges to 0.

[0045] In an implementation form of the application, the method further comprises: system modeling by FOMCON fractional order toolbox; and simulation verification by Matlab / simulink.

[0046] The embodiment of the application provides a mechanical arm adaptive fractional order sliding mode control device, comprising: at least one processor; and a memory in communication connection with the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to: establish a corresponding dynamics model of the mechanical arm based on a position vector, a velocity vector and an acceleration vector of the mechanical arm; establish a tracking error dynamic equation based on an actual trajectory and an expected trajectory of the mechanical arm; construct an error function based on a position error and an error boundary corresponding to different joints of the mechanical arm, to limit a corresponding trajectory tracking error of the mechanical arm in a preset range based on the error function; obtain a corresponding fractional order non-singular terminal sliding mode surface of the mechanical arm according to the tracking error dynamic equation and the error function, to construct an adaptive fractional order non-singular terminal sliding mode control; and construct a nonlinear disturbance observer based on comprehensive disturbance data in the corresponding dynamics model of the mechanical arm, to perform feedforward compensation on the corresponding dynamics model of the mechanical arm based on the nonlinear disturbance observer, to realize control on the mechanical arm.

[0047] The embodiment of the application provides a nonvolatile computer storage medium, which stores computer executable instructions, and the computer executable instructions are configured to: establish a corresponding dynamics model of a mechanical arm based on a position vector, a velocity vector and an acceleration vector of the mechanical arm; establish a tracking error dynamic equation based on an actual trajectory and an expected trajectory of the mechanical arm; construct an error function based on a position error and an error boundary corresponding to different joints of the mechanical arm, to limit a corresponding trajectory tracking error of the mechanical arm in a preset range based on the error function; obtain a corresponding fractional order non-singular terminal sliding mode surface of the mechanical arm according to the tracking error dynamic equation and the error function, to construct an adaptive fractional order non-singular terminal sliding mode control; and construct a nonlinear disturbance observer based on comprehensive disturbance data in the corresponding dynamics model of the mechanical arm, to perform feedforward compensation on the corresponding dynamics model of the mechanical arm based on the nonlinear disturbance observer, to realize control on the mechanical arm.

[0048] The at least one technical solution adopted by the embodiment of the present application can achieve the following beneficial effects: the funnel function is used to convert the original tracking error into a specified error, the trajectory tracking error is limited within a preset range, and then an adaptive fractional order non-singular terminal sliding mode control is constructed, so as to effectively ensure the trajectory tracking accuracy of the mechanical arm and improve the transient and steady-state performance of the system. In view of the model uncertainty and external disturbance of the mechanical arm system, a nonlinear disturbance observer is designed to compensate for the disturbance of the system, so as to eliminate the influence of the disturbance on the operation performance of the mechanical arm, and effectively reduce the sliding mode gain coefficient and the chattering phenomenon of the system. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative labor. In the drawings:

[0050] Figure 1 A flow chart of a mechanical arm adaptive fractional order sliding mode control method is provided for the embodiment of the present application.

[0051] Figure 2 A funnel error function basic characteristic diagram is provided for the embodiment of the present application.

[0052] Figure 3 A mechanical arm control system structure block diagram is provided for the embodiment of the present application.

[0053] Figure 4 A structure diagram of a mechanical arm adaptive fractional order sliding mode control device is provided for the embodiment of the present application. DETAILED DESCRIPTION

[0054] The embodiment of the present application provides a mechanical arm adaptive fractional order sliding mode control method, device and medium.

[0055] In order to enable those skilled in the art to better understand the technical solutions in the present application, the technical solutions in the embodiments of the present application will be described clearly and completely in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor should be within the scope of protection of the present application.

[0056] Robotic arm is a highly nonlinear, strong coupling complex system. In recent years, with the continuous progress of robot technology, more and more advanced robotic arms are used in industrial production and home service and other fields. Due to the particularity of the working task of the robotic arm, the control accuracy of the robotic arm is continuously improved. The research on the control method of the robotic arm has always been the focus of researchers at home and abroad. Many advanced modern control methods have been applied to the precise operation of the robotic arm, such as fuzzy control, neural network control, sliding mode control, etc.

[0057] The sliding mode control has the characteristics of fast response and good robustness, because it does not need to provide a very accurate dynamic model of the system in the design process, and only needs to use the trajectory tracking error or position control error to reasonably design the sliding mode surface. As a practical control method, domestic researchers apply the sliding mode control method to the control of the robotic arm. However, due to the existence of high-frequency chattering phenomenon in the control input, the application of traditional SMC in the field of robots is limited, which affects the actual application performance of the robot.

[0058] In order to solve the above problems, the embodiment of the present application provides a robotic arm adaptive fractional order sliding mode control method, device and medium. The funnel function is used to convert the original tracking error into a specified error, and the trajectory tracking error is limited in a predetermined range, and then an adaptive fractional order non-singular terminal sliding mode control is constructed, which effectively ensures the trajectory tracking accuracy of the robotic arm and improves the transient and steady state performance of the system. In view of the model uncertainty and external disturbance existing in the robotic arm system, a nonlinear disturbance observer is designed to compensate the disturbance of the system, so as to eliminate the influence of the disturbance on the operation performance of the robotic arm, and effectively reduce the sliding mode gain coefficient and reduce the chattering phenomenon of the system.

[0059] The technical solutions provided by the embodiments of the present application will be described in detail below with reference to the drawings.

[0060] Figure 1 A flowchart of a robotic arm adaptive fractional order sliding mode control method provided by the embodiment of the present application is shown in FIG. 1. Figure 1 As shown in FIG. 1, the robotic arm adaptive fractional order sliding mode control method comprises the following steps:

[0061] S101, based on the position vector, velocity vector and acceleration vector of the robotic arm, a corresponding dynamics model of the robotic arm is established.

[0062] In an embodiment of the present application, the dynamics model of the N-joint rigid robotic arm considering external disturbance is

[0063]

[0064] However, in the process of engineering application, the model parameters of the mechanical arm often have uncertainty, and the accurate mathematical model cannot be realized, so the embodiments of the application obtain

[0065]

[0066] The dynamics model of the mechanical arm can be rewritten as

[0067]

[0068] wherein,

[0069] q∈Rn×1 is a position vector of a joint of the mechanical arm; is a velocity vector of the joint of the mechanical arm; is an acceleration vector of the joint of the mechanical arm; M(q)∈Rn×n is a rotational inertia matrix of the mechanical arm; is a centrifugal force and Coriolis force matrix of the mechanical arm; G(q)∈Rn×1 is a gravity term of the mechanical arm; τ is a control torque of the mechanical arm; τ d is a disturbance term of the mechanical arm; M0(q) is a deterministic quantity corresponding to the rotational inertia matrix of the mechanical arm; ΔM(q) is an uncertain quantity corresponding to the rotational inertia matrix of the mechanical arm; is a deterministic quantity corresponding to the centrifugal force and Coriolis force matrix of the mechanical arm; is an uncertain quantity corresponding to the centrifugal force and Coriolis force matrix of the mechanical arm; G0(q) is a deterministic quantity corresponding to the gravity term of the mechanical arm; ΔG(q) is an uncertain quantity corresponding to the gravity term of the mechanical arm.

[0070] Fractional calculus is an extension of integer order, and there are three commonly used definitions in the control field: Grunwald-Letnikov (GL) type, Riemann-Liouville (RL) type and Caputo type. The Caputo type has the same characteristics as the initial condition definition and integer order, and is widely used in the engineering field.

[0071] The Caputo type fractional differential form is as follows:

[0072]

[0073] wherein f(t) is a continuous equation, and Γ() is a Gamma function. u-1<α≤u, u∈N.

[0074] The Caputo type fractional integral form is as follows:

[0075]

[0076] The following Caputo type fractional differential operation is correct, that is,

[0077]

[0078] where α, β ∈ R, α ≥ β ≥ 0.

[0079] Non-autonomous fractional order system There is an equilibrium point x(t) = 0, and it is assumed that there is a Lyapunov function V(t, x(t)) that satisfies the following conditions:

[0080] κ1(||x(t)||)≤V(t,x(t))≤κ2(||x(t)||) (7)

[0081]

[0082] where f(t, x(t)) satisfies the Lipschitz condition, κ1, κ2, κ3 are all normal numbers. Then the system is asymptotically stable.

[0083] S102, based on the actual trajectory of the mechanical arm and the desired trajectory, a tracking error dynamic equation is established.

[0084] In an embodiment of the present application, in order to improve the transient and steady state performance of the mechanical arm and improve the control accuracy of the mechanical arm, an adaptive fractional order non-singular terminal sliding mode control method for a specified performance mechanical arm is proposed, which can ensure that the mechanical arm quickly tracks the desired motion trajectory.

[0085] Define the trajectory tracking error as

[0086] e = q - q d

[0087] The tracking error dynamic equation is obtained as

[0088]

[0089] where q d is the desired trajectory.

[0090] S103, based on the position error and error boundary corresponding to different joints of the mechanical arm, an error function is constructed to limit the trajectory tracking error of the mechanical arm within a predetermined range based on the error function.

[0091] In order to avoid the singularity problem of the traditional specified performance method, an improved funnel function is used in the embodiment of the present application, which eliminates the requirement of the original funnel function for the number of systems and has higher practicability. The improved funnel error function σ i is defined as:

[0092]

[0093] F μ =μ0exp(-υt)+μ ∞ (15b)

[0094] Among them, e i σ i (i = 1, 2, ..., n) represent the position error and transformation error of the i-th joint, respectively; define σ = [σ1, σ2, ..., σn]. n ] T ;||·|| represents the Euclidean norm; μ0, μ ∞ It is a constant greater than 0, and μ0 > μ ∞ ;F μ (0)=μ0+μ ∞ This represents the maximum boundary of the initial error; For steady-state error boundary, υ>0. Figure 2 This is a schematic diagram illustrating the basic characteristics of a Funnel error function provided in an embodiment of this application. Figure 2 As shown, the horizontal axis represents time, and the vertical axis represents the maximum boundary of the initial error.

[0095] S104. Based on the tracking error dynamic equation and error function, obtain the fractional-order non-singular terminal sliding surface corresponding to the robotic arm, so as to construct an adaptive fractional-order non-singular terminal sliding control.

[0096] In one embodiment of this application, the differential equation of the conversion error is obtained based on the tracking error dynamic equation and the error function.

[0097]

[0098]

[0099] Where F = diag{f1,...,f n}, P = diag{p1,...,p n}, f i =F μ -||e i ||,p i =1 / f i 2 ,

[0100] Based on the differential equation of the transformation error, the fractional-order non-singular terminal sliding surface corresponding to the robotic arm is obtained.

[0101]

[0102] Where 0 < α < 1, γ > 0, All are real numbers.

[0103] Since there is an observation error in the nonlinear disturbance observer, the embodiments of the present application make the following assumptions:

[0104]

[0105] wherein,

[0106] According to formula (16), formula (17) and formula (18), the final control law of the control system is designed as

[0107]

[0108]

[0109]

[0110] wherein, In order to eliminate the influence of the observation error on the actual control performance, the adaptive law of is designed as

[0111]

[0112] In order to prove the stability of the system, the Lyapunov function is selected as

[0113]

[0114] The α-order fractional derivative of both sides of formula (24) is obtained, and the following formula is obtained

[0115]

[0116] Substituting formula (19), formula (20) and formula (23) into formula (20), the following formula is obtained

[0117]

[0118] Therefore, according to the Lyapunov stability theory, it can be concluded that s and are bounded, and the sliding surface s can reach the equilibrium point in a finite time. When the sliding surface s reaches 0, we can obtain

[0119]

[0120] The 1-α-order fractional integral of both sides is obtained, and the following formula is obtained

[0121]

[0122] The Lyapunov function is selected as

[0123]

[0124] Differentiate equation (29) and substitute equation (28) to get

[0125]

[0126] Therefore, it can be concluded that the conversion error σ will tend to the equilibrium point, so that the tracking error e will be strictly limited within the specified performance boundary, thus completing the proof.

[0127] S105, according to the comprehensive disturbance data in the dynamic model corresponding to the mechanical arm, construct a nonlinear disturbance observer, and feed forward compensate the dynamic model corresponding to the mechanical arm based on the nonlinear disturbance observer, to realize the control of the mechanical arm.

[0128] In an embodiment of the present application, the uncertainty existing in the mechanical arm model and the external disturbance are taken as comprehensive disturbance terms, a nonlinear disturbance observer is designed to feed forward compensate the disturbance of the system, so as to eliminate the influence of the disturbance on the operation performance of the mechanical arm, and effectively reduce the chattering gain coefficient of the system and reduce the chattering phenomenon of the system.

[0129] The function is constructed

[0130]

[0131] Wherein, is the observation value of the comprehensive disturbance term , z is the internal state variable of the observer, is the nonlinear function to be designed in the observer, is the gain coefficient of the observer. And satisfy:

[0132]

[0133] Define the observation error as:

[0134]

[0135] Assume Combined with equations (9) and (10), we can get

[0136]

[0137] Substitute equation (2) and equation (9) into equation (12) to get

[0138]

[0139] Here, define and as

[0140]

[0141] Therefore, by selecting the ideal coefficient c, the observation error is asymptotically convergent to 0.

[0142] In an embodiment of the present application, simulation verification is performed by Matlab / simulink, and a FOMCON fractional order toolbox is used for system modeling and control design. Figure 3 A mechanical arm control system structure block diagram is provided for an embodiment of the present application. As shown in the figure, a conversion error is first constructed, a sliding mode surface is constructed, and a fractional order non-singular terminal sliding mode control is established. Since the system has uncertainty, a nonlinear disturbance observer is established to process the error of the uncertainty. An embodiment of the present application performs a trajectory tracking simulation experiment on a 2-DOF mechanical arm, and the specific dynamic parameters are as follows: Figure 3

[0143]

[0144]

[0145]

[0146] Wherein, v = 13.33, q 01 = 8.98, q 02 = 8.75, g = 9.8. The initial position and velocity of the 2-DOF mechanical arm are: q(0) = [0.7, 0.1] T , The given tracking trajectory is: q d = [cos(πt), sin(πt)] T , the simulated friction and external disturbance is The values of the controller parameters in the embodiment of the present application are: c = 300, υ = 1, μ0 = 0.4, μ ∞ = 0.01, γ = 1, α = 0.05.

[0147] The embodiment of the present application converts the original tracking error into a specified error through a funnel function, limits the trajectory tracking error within a preset range, and then constructs an adaptive fractional order non-singular terminal sliding mode control, effectively ensuring the trajectory tracking accuracy of the mechanical arm and improving the transient and steady-state performance of the system. In view of the model uncertainty and external disturbance of the mechanical arm system, a nonlinear disturbance observer is designed to compensate for the disturbance of the system, thereby eliminating the influence of the disturbance on the operation performance of the mechanical arm, and effectively reducing the sliding mode gain coefficient and the chattering phenomenon of the system.

[0148] Figure 4 A structure schematic diagram of a mechanical arm adaptive fractional order sliding mode control device is provided for an embodiment of the present application. As shown in the figure, Figure 4 ​The illustrated mechanical arm adaptive fractional order sliding mode control device comprises:

[0149] at least one processor; and

[0150] a memory in communication connection with the at least one processor; wherein

[0151] the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to:

[0152] establish a dynamics model corresponding to the mechanical arm based on a position vector, a velocity vector and an acceleration vector of the mechanical arm;

[0153] establish a tracking error dynamic equation based on an actual trajectory and an expected trajectory of the mechanical arm;

[0154] construct an error function based on a position error and an error boundary corresponding to different joints of the mechanical arm respectively, to limit the trajectory tracking error corresponding to the mechanical arm within a preset range based on the error function;

[0155] obtain a fractional order non-singular terminal sliding mode surface corresponding to the mechanical arm according to the tracking error dynamic equation and the error function, to construct an adaptive fractional order non-singular terminal sliding mode control;

[0156] construct a nonlinear disturbance observer based on comprehensive disturbance data in the dynamics model corresponding to the mechanical arm, to perform feedforward compensation on the dynamics model corresponding to the mechanical arm based on the nonlinear disturbance observer, to realize control of the mechanical arm.

[0157] The embodiments of the present application also include a non-volatile computer storage medium storing computer executable instructions, which are configured to:

[0158] establish a dynamics model corresponding to the mechanical arm based on a position vector, a velocity vector and an acceleration vector of the mechanical arm;

[0159] establish a tracking error dynamic equation based on an actual trajectory and an expected trajectory of the mechanical arm;

[0160] construct an error function based on a position error and an error boundary corresponding to different joints of the mechanical arm respectively, to limit the trajectory tracking error corresponding to the mechanical arm within a preset range based on the error function;

[0161] obtain a fractional order non-singular terminal sliding mode surface corresponding to the mechanical arm according to the tracking error dynamic equation and the error function, to construct an adaptive fractional order non-singular terminal sliding mode control;

[0162] According to comprehensive disturbance data in the dynamic model corresponding to the mechanical arm, a nonlinear disturbance observer is constructed, and feedforward compensation is performed on the dynamic model corresponding to the mechanical arm based on the nonlinear disturbance observer, so as to realize control on the mechanical arm.

[0163] The various embodiments in the present application are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the difference from other embodiments. In particular, for the device, equipment, and nonvolatile computer storage medium embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the method embodiment.

[0164] The above describes specific embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the acts or steps recited in the claims can be performed in a different order than the order in which they are recited and still achieve desirable results. In addition, the processes depicted in the figures do not necessarily require the particular order shown, or sequential order, to achieve the desired results. In certain implementations, multitasking and parallel processing can be advantageous or necessary.

[0165] The above only describes the embodiments of the present application and is not intended to limit the present application. The embodiments of the present application can be variously changed and modified by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the embodiments of the present application shall be included in the scope of the claims of the present application.

Claims

1. An adaptive fractional sliding mode control method for a robotic arm, characterized in that, The method includes: Based on the position vector, velocity vector, and acceleration vector of the robotic arm, a dynamic model corresponding to the robotic arm is established. Based on the actual trajectory and the expected trajectory of the robotic arm, a dynamic equation for the tracking error is established; Based on the position errors and error boundaries corresponding to different joints of the robotic arm, an error function is constructed to limit the trajectory tracking error of the robotic arm within a preset range. Based on the tracking error dynamic equation and the error function, the fractional-order non-singular terminal sliding surface corresponding to the robotic arm is obtained, so as to construct an adaptive fractional-order non-singular terminal sliding mode control. Based on the comprehensive disturbance data in the dynamic model corresponding to the robotic arm, a nonlinear disturbance observer is constructed to perform feedforward compensation on the dynamic model corresponding to the robotic arm based on the nonlinear disturbance observer, so as to realize the control of the robotic arm. The step of obtaining the fractional-order non-singular terminal sliding surface corresponding to the robotic arm based on the tracking error dynamic equation and the error function specifically includes: Based on the tracking error dynamic equation and the error function, the differential equation of the conversion error is obtained. in, , , , , ; Based on the differential equation of the transformation error, the fractional-order non-singular terminal sliding surface corresponding to the robotic arm is obtained. in, , , All are real numbers. , For order is Fractional differential operators; The step of constructing a nonlinear disturbance observer based on the comprehensive disturbance data in the dynamic model corresponding to the robotic arm specifically includes: Constructor function in, For the comprehensive disturbance term The observed values, For the internal state variables of the observer, A nonlinear function needs to be designed for the observer. The observer gain coefficient; Based on the preset observation error and the constructed function, the nonlinear perturbation observer is constructed to achieve the asymptotic convergence of the observation error to 0.

2. The adaptive fractional sliding mode control method for a robotic arm according to claim 1, characterized in that, The establishment of the dynamic model of the robotic arm based on its position vector, velocity vector, and acceleration vector specifically includes: Based on functions ； The dynamic model corresponding to the robotic arm is obtained. ； in, ; in, This is the position vector of the robotic arm joint; The velocity vector of the robotic arm joint; This is the acceleration vector of the robotic arm joint; Let be the rotational inertia matrix of the robotic arm; The matrix of centrifugal force and Coriolis force of the robotic arm; For the mechanical arm's gravity term; This refers to the control torque of the robotic arm; This is the disturbance term for the robotic arm; This is a definite quantity corresponding to the rotational inertia matrix of the robotic arm; The uncertainty is the moment of inertia matrix of the robotic arm. These are the definite quantities corresponding to the centrifugal force and Coriolis force matrices of the robotic arm; These are the uncertainties corresponding to the centrifugal force and Coriolis force matrices of the robotic arm; This is a definite quantity corresponding to the gravity term of the robotic arm; This represents the uncertainty related to the gravity term of the robotic arm.

3. The adaptive fractional sliding mode control method for a robotic arm according to claim 2, characterized in that, The step of establishing a dynamic equation for tracking error based on the actual trajectory and the expected trajectory of the robotic arm specifically includes: Based on trajectory tracking error function ； The tracking error dynamic equation is obtained. ； in, For trajectory tracking error; This represents the desired trajectory.

4. The adaptive fractional sliding mode control method for a robotic arm according to claim 1, characterized in that, The error function is constructed based on the position errors and error boundaries corresponding to different joints of the robotic arm, specifically including: Based on functions Construct the error function; where, , (i=1,2,…,n) represent the position error and transformation error of the i-th joint, respectively; defined ; It is the Euclidean norm; , It is a constant greater than 0, and ; This represents the maximum boundary of the initial error; For steady-state error boundary, .

5. The adaptive fractional sliding mode control method for a robotic arm according to claim 1, characterized in that, The nonlinear perturbation observer, constructed based on the preset observation error and the constructed function, aims to achieve asymptotic convergence of the observation error to zero. Specifically, this includes: Define the preset observation error as exist In this case, based on the preset observation error and the constructed function, the differential equation of the preset observation error is obtained. Based on the dynamic model corresponding to the robotic arm, the constructed function, and the differential equation of the preset observation error, the following is obtained: definition , By adjusting the coefficient C, the observation error can be asymptotically converged to 0.

6. The adaptive fractional sliding mode control method for a robotic arm according to claim 1, characterized in that, The method further includes: System modeling is performed using the FOMCON fractional-order toolbox; and Simulation verification was performed using Matlab / Simulink.

7. An adaptive fractional-order sliding mode control device for a robotic arm, the device being capable of executing the adaptive fractional-order sliding mode control method for a robotic arm as described in any one of claims 1-6, the device comprising: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the at least one processor to: Based on the position vector, velocity vector, and acceleration vector of the robotic arm, a dynamic model corresponding to the robotic arm is established. Based on the actual trajectory and the expected trajectory of the robotic arm, a dynamic equation for the tracking error is established; Based on the position errors and error boundaries corresponding to different joints of the robotic arm, an error function is constructed to limit the trajectory tracking error of the robotic arm within a preset range. Based on the tracking error dynamic equation and the error function, the fractional-order non-singular terminal sliding surface corresponding to the robotic arm is obtained, so as to construct an adaptive fractional-order non-singular terminal sliding mode control. Based on the comprehensive disturbance data in the dynamic model corresponding to the robotic arm, a nonlinear disturbance observer is constructed to perform feedforward compensation on the dynamic model corresponding to the robotic arm based on the nonlinear disturbance observer, so as to realize the control of the robotic arm.

8. A non-volatile computer storage medium storing computer-executable instructions, said computer storage medium being capable of executing the adaptive fractional sliding mode control method for a robotic arm according to any one of claims 1-6, wherein the computer-executable instructions are configured as follows: Based on the position vector, velocity vector, and acceleration vector of the robotic arm, a dynamic model corresponding to the robotic arm is established. Based on the actual trajectory and the expected trajectory of the robotic arm, a dynamic equation for the tracking error is established; Based on the position errors and error boundaries corresponding to different joints of the robotic arm, an error function is constructed to limit the trajectory tracking error of the robotic arm within a preset range. Based on the tracking error dynamic equation and the error function, the fractional-order non-singular terminal sliding surface corresponding to the robotic arm is obtained, so as to construct an adaptive fractional-order non-singular terminal sliding mode control. Based on the comprehensive disturbance data in the dynamic model corresponding to the robotic arm, a nonlinear disturbance observer is constructed to perform feedforward compensation on the dynamic model corresponding to the robotic arm based on the nonlinear disturbance observer, so as to realize the control of the robotic arm.

Images