A flexible robot arm control method and system based on fractional order complementary sliding mode

Abstract

The application relates to a flexible mechanical arm control method and system based on a fractional order complementary sliding mode, and the method comprises the following steps: constructing a flexible mechanical arm dynamics model according to mechanical arm related parameters, a hypothetical modal method and a Lagrange method; decoupling the flexible mechanical arm dynamics model according to a singular perturbation method to generate a slow variable subsystem model and a fast variable subsystem model; establishing a super-helix extended state observer according to the slow variable subsystem model and generating an observed disturbance value; generating a fractional order complementary sliding mode control law according to a flexible mechanical arm position tracking error; generating a trajectory tracking control law according to a tracking differentiator, the observed disturbance value and the fractional order complementary sliding mode control law; generating a vibration suppression control law according to the fast variable subsystem model, a super-helix algorithm and a mechanical arm end vibration amount; and combining the trajectory tracking control law and the vibration suppression control law to generate a total control law. The control precision is improved through the fractional order complementary sliding mode, and chattering is effectively suppressed.

Description

Technical Field

[0001] This invention relates to the field of industrial production technology, and in particular to a flexible robotic arm control method and system based on fractional-order complementary sliding mode. Background Technology

[0002] Flexible robotic arms, with their advantages of being lightweight and highly efficient, are widely used in modern industry and aerospace. However, their modeling is complex and highly coupled. This strong coupling manifests as elastic vibrations occurring simultaneously with movement. These elastic vibrations possess infinite-dimensional modes, making it difficult to accurately establish a coupled system model. Due to model uncertainties and the influence of external disturbances, the motion control of flexible robotic arms has always been a research hotspot. Against this backdrop, improving the control accuracy and disturbance resistance of flexible robotic arms has significant theoretical and practical value.

[0003] During the movement of a flexible robotic arm, it is necessary to suppress its elastic vibration while tracking the trajectory to ensure that the control of the robotic arm can achieve high precision and a certain degree of disturbance rejection capability. Existing control methods for flexible robotic arms mainly design controllers based on the coupled dynamic equations of the flexible robotic arm, typically employing PID control, sliding mode control, and fuzzy control. Wu Min et al. used active disturbance rejection control (ADRC) to track the trajectory. Although this control strategy considers the coupling characteristics of the flexible robotic arm, its control method is simplistic and lacks specificity in the control objective, resulting in poor robustness of the control system. Despite considering the influence of coupling factors, it essentially suppresses vibration indirectly through the coupling effect, rather than directly suppressing it. Furthermore, this method complicates controller design, increases computational load, and relatively prolongs the vibration suppression time.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] Therefore, the technical problem to be solved by this invention is to overcome the poor robustness of existing control systems due to their single control method and lack of specific control objectives. Although the influence of coupling factors is considered, vibration suppression is essentially achieved indirectly through coupling effects rather than directly suppressing vibration. Furthermore, this increases the complexity of controller design, computational load, and relatively prolonged vibration suppression time.

[0006] To address the aforementioned technical problems, a first aspect of the present invention provides a flexible robotic arm control method based on fractional-order complementary sliding modes, the method comprising:

[0007] Obtain relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-effector load mass, robotic arm rotation angle, and robotic arm end-effector vibration.

[0008] A dynamic model of the flexible robotic arm is constructed based on the relevant parameters of the robotic arm, the hypothetical modal method, and the Lagrange method.

[0009] The dynamic model of the flexible robotic arm is decoupled according to the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model.

[0010] A superspiral expansion state observer is established based on the slow-varying subsystem model, and observation perturbation values ​​are generated.

[0011] A fractional-order complementary sliding surface is generated based on the position tracking error of the flexible robotic arm;

[0012] Differentiating the fractional-order complementary sliding surface generates the fractional-order complementary sliding mode control law;

[0013] A trajectory tracking control law is generated based on the tracking differentiator, the observed disturbance value, and the fractional-order complementary sliding mode control law.

[0014] A vibration suppression control law is generated based on the fast-change subsystem model, the super-helical algorithm, and the vibration amount at the end of the robotic arm.

[0015] The trajectory tracking control law and the vibration suppression control law are combined to generate the overall control law.

[0016] In one embodiment of the present invention, the formula for the slowly varying subsystem model is as follows:

[0017] θ s && =J(u s +w s -H 1s )

[0018] in, Where N 11s N 12s N 21s N 22s For N s The matrix elements, θ s u is an estimate of θ. s w is the control variable for the slow-varying subsystem. s For external disturbances, H 1s =H1.

[0019] In one embodiment of the present invention, the formula for the fast-changing subsystem model is as follows:

[0020]

[0021] Where d is a positive real number, z f =zz s , t p =t / μ, K s For the new state variable, u f For the control quantity of the fast variable subsystem, F 11s is a coefficient.

[0022] In one embodiment of the present invention, the formula for the superspiral expansion state observer is as follows:

[0023]

[0024] Where z1, z2, and z3 are the estimated values ​​of x1, x2, and x3, respectively, and u a For auxiliary feedback quantities, β1 > 0, k3 > 0, k4 > 0.

[0025] In one embodiment of the present invention, the formula for the fractional-order complementary sliding mode control law is as follows:

[0026] u0 = u eq +u sw

[0027] Among them, u eq For the equivalent control law, u sw To switch control laws.

[0028] In one embodiment of the present invention, the formula of the trajectory tracking control law is as follows:

[0029]

[0030] Where u0 is the fractional-order complementary sliding mode control law, and z3 is the observation. N 11s N 12s N 21s， N 22s For N s Matrix elements.

[0031] In one embodiment of the present invention, the formula for the vibration suppression control law is as follows:

[0032]

[0033] Among them, GB f GA f Let x be the parameter matrix. f s1 is the state variable, k5 and k6 are parameters, and s1 is the sliding mode variable.

[0034] The second aspect of the present invention provides a flexible robotic arm control system based on fractional-order complementary sliding mode, applied to a method proposed in any one of the first aspects above, the system comprising: a data acquisition module, a model construction module, a first calculation module, and a second calculation module;

[0035] The data acquisition module is configured to acquire relevant parameters of the robotic arm, including: robotic arm length, end-effector load mass, robotic arm rotation angle, and end-effector vibration.

[0036] The model building module is configured to: construct a dynamic model of the flexible manipulator based on the relevant parameters of the manipulator, the assumed modal method, and the Lagrange method; and decouple the dynamic model of the flexible manipulator based on the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model.

[0037] The first calculation module is configured to: establish a superspiral expansion state observer based on the slow-varying subsystem model and generate observed disturbance values; generate a fractional-order complementary sliding mode surface based on the position tracking error of the flexible robotic arm; differentiate the fractional-order complementary sliding mode surface to generate a fractional-order complementary sliding mode control law; and generate a trajectory tracking control law based on the tracking differentiator, the observed disturbance values, and the fractional-order complementary sliding mode control law.

[0038] The second calculation module is configured to: generate a vibration suppression control law based on the fast-change subsystem model, the super-helical algorithm, and the vibration amount at the end of the robotic arm; and combine the trajectory tracking control law and the vibration suppression control law to generate a total control law.

[0039] A third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method described in the first aspect or any possible implementation thereof.

[0040] A fourth aspect of the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect or any possible implementation thereof.

[0041] The technical solution of the present invention has the following advantages compared with the prior art:

[0042] The present invention discloses a flexible robotic arm control method and system based on fractional-order complementary sliding mode. By replacing the original nonlinear error feedback control with fractional-order complementary sliding mode, the control accuracy is improved, thereby achieving better trajectory tracking performance and effectively suppressing chattering. Attached Figure Description

[0043] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0044] Figure 1 This is a flowchart of a flexible robotic arm control method and system based on fractional-order complementary sliding mode provided by the present invention;

[0045] Figure 2 This is a schematic diagram of a flexible robotic arm control method based on fractional-order complementary sliding mode and a flexible robotic arm model in the system provided by the present invention.

[0046] Figure 3 This invention provides a flexible robotic arm control method based on fractional-order complementary sliding mode and a combined control output curve diagram in the system.

[0047] Figure 4 This invention provides a flexible robotic arm control method based on fractional-order complementary sliding mode and a traditional active disturbance rejection control output curve in the system.

[0048] Figure 5 This invention provides a flexible robotic arm control method based on fractional-order complementary sliding mode and a combined control output curve in the system;

[0049] Figure 6 This invention provides a flexible robotic arm control method based on fractional-order complementary sliding mode and a traditional active disturbance rejection control output curve in the system;

[0050] Figure 7 The present invention provides a system architecture diagram of a flexible robotic arm control method and system based on fractional-order complementary sliding mode. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0052] Furthermore, the described embodiments are merely some, not all, of the embodiments of this application. The components of the embodiments of this application described and illustrated herein can typically be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0053] Reference Figure 1As shown, this invention provides a flexible robotic arm control method based on fractional-order complementary sliding mode, the method comprising:

[0054] S100: Obtain relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-effector load mass, robotic arm rotation angle, and robotic arm end-effector vibration.

[0055] In step S100, the selected research object is a single-link flexible robotic arm, one end of which is connected to the motor shaft and the other end is connected to the load. Its model is referenced. Figure 2 As shown, XOY is the fixed coordinate system, xoy is the reference coordinate system, L is the length of the robotic arm, m is the end load mass of the robotic arm, u(t) is the driving torque, ω(x,t) is the elastic deformation of any point P on the robotic arm at x at time t, and θ(t) is the rotation angle of the robotic arm.

[0056] S200: Construct a dynamic model of the flexible robotic arm based on the relevant parameters of the robotic arm, the assumed modal method, and the Lagrange method;

[0057] In step S200, the selected research object is a single-link flexible robotic arm, one end of which is connected to the motor shaft and the other end is connected to the load. Its model is referenced. Figure 2 As shown, XOY is the fixed coordinate system, xoy is the reference coordinate system, L is the length of the robotic arm, m is the end load mass of the robotic arm, u(t) is the driving torque, ω(x,t) is the elastic deformation of any point P on the robotic arm at x at time t, and θ(t) is the rotation angle of the robotic arm.

[0058] Based on the relevant parameters of the robotic arm, the assumed modal method, and the Lagrange method, a dynamic model of the flexible robotic arm is constructed. The calculation formula for the dynamic model of the robotic arm is as follows:

[0059]

[0060] Where M is the positive definite mass matrix, H is the cross-coupling matrix, C is the damping matrix, K is the stiffness matrix, F is the coefficient matrix, and q = [q1 q2 … q n ] T The modal coordinates are used to describe the elastic vibration of the flexible robotic arm. w represents the external disturbance, and |w| < d, where d is a positive real number, u is the system input, and θ is the rotation angle of the robotic arm.

[0061] Since M is positive definite, let N = M. -1 Multiplying both sides of equation (1) by N and expanding, we get:

[0062] θ && =-N 11 H1-N 12 H2-N 12 Cq& -N 12 Kq+N 11 (u+w) (2);

[0063] q && =-N 12 H2-N 22 H2-N 22 Cq & -N 22 Kq+N 21 (u+w) (3);

[0064] S300: Decouple the dynamic model of the flexible manipulator according to the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model;

[0065] In step S300, the formula for the slowly varying subsystem model is as follows:

[0066] θ s && =J(u s +w s -H 1s (4);

[0067] in, Where N 11s N 12s N 21s N 22s For N s The matrix elements, θ s u is an estimate of θ. s w is the control variable for the slow-varying subsystem. s For external disturbances, H 1s =H1. The formula for the rapidly changing subsystem model is as follows:

[0068]

[0069] Where d is a positive real number, z f =zz s , t p =t / μ, K s For the new state variable, u f For the control quantity of the fast variable subsystem, F 11s is a coefficient.

[0070] In practical applications, parameters are introduced based on singular perturbation theory. λ=min{k i}, i = 1, 2, ..., n, introduce a new state variable K s =μ 2 K, z = q / μ 2Substituting into equations (2) and (3), we get:

[0071]

[0072]

[0073] Let the perturbation parameter μ = 0, and obtain the slow variable component according to equations (6) and (7).

[0074]

[0075] 0 = -N 21s H 1s -N 22s H 2s -N 22s K s z s +N 21s (u s +w s (9);

[0076] Among them, the components with the subscript 's' are the slowing quantities. According to equation (9):

[0077]

[0078] Substituting equation (10) into equation (8), we obtain the slow-varying subsystem model, w s =w, because w s Since the change is slow, it can be assumed to exist only in slowly varying subsystems. Because θ and q have different time characteristics, a fast timescale t is introduced. p = t / μ, at this time scale, the slow variable can be considered a constant, that is:

[0079]

[0080]

[0081] Let z f =zz s Substituting equation (7), and combining equations (6), (7), (11), and (12), we obtain the model of the flexible robotic arm's fast-change subsystem.

[0082] S400: Establish a superspiral expansion state observer based on the slow-varying subsystem model and generate observed perturbation values;

[0083] In step S400, the formula for the superspiral expansion state observer is as follows:

[0084]

[0085] Where z1, z2, and z3 are the estimated values ​​of x1, x2, and x3, respectively, and ua For auxiliary feedback quantities, β1 > 0, k3 > 0, k4 > 0.

[0086] In practical applications, the tracking differentiator performs differentiation on the input signal to avoid abrupt changes in the input quantity, thus buffering the input signal and facilitating the system to quickly track the input signal.

[0087] The algorithm is shown in equation (14):

[0088]

[0089] Where v is the input signal, v1 is the tracking signal of v, v2 is the derivative signal of v1, r0 is the velocity factor, h0 is the filter factor, and fhan is the fastest control synthesis function to prevent overshoot during tracking. The specific form of the fhan function is shown in equation (15):

[0090]

[0091] For slowly varying subsystems:

[0092]

[0093] Where x1 = θ, f = J(w s -H 1s ).

[0094] Define the extended states x3 = f and h = f & Then equation (16) can be expressed as:

[0095]

[0096] Where h satisfies the following conditions:

[0097] |h|≤L h (18);

[0098] Design slip amount:

[0099] σ=c1e1+e2 (19);

[0100] Where c1 > 0, e i =x i -z i , i = 1, 2. The constructed superspiral expansion state observer is shown in equation (13). From equations (17) and (13), the estimation error of the superspiral expansion state observer is:

[0101]

[0102] Differentiating equation (19) yields:

[0103]

[0104] Based on the superhelical algorithm, design u a :

[0105]

[0106] Substituting equation (22) into equation (21), we obtain equation (23):

[0107]

[0108] For equation (23), the neighborhood U∈i at the origin 2 Construct an inner Lyapunov function V(η) that satisfies Where (η)∈U{0}, 0<α1<1. Then the system is locally finite-time stable, and reaches V(η)=0 in time. Where η(0) is the initial value of η.

[0109] If equation (18) holds and the error system satisfies the Lipchitz condition, then by setting an appropriate gain k... i (i = 1, 2, 3, 4), so that the zero point of system (23) is the equilibrium point, and the designed auxiliary feedback quantity u a It can be guaranteed that σ converges to zero in a finite time and the estimation error asymptotically converges to zero.

[0110] The following proof uses z σ Replaces e3.

[0111] To prove the convergence of σ, we design the Lyapunov function:

[0112]

[0113] in,

[0114] When σ≠0, differentiating equation (24) yields:

[0115]

[0116] in,

[0117] definition:

[0118]

[0119] in,

[0120] Set an appropriate k i ,satisfy:

[0121] Ω1-Δ1>0, Ω2-Δ2>0 (27);

[0122] Combining equations (25) and (27), we get:

[0123]

[0124] From λ min (P)||ζ|| 2 ≤V σ ≤λ max (P)||ζ|| 2 and |σ|≤||ζ|| 2 have to:

[0125]

[0126] The convergence time is:

[0127]

[0128] Where σ converges in finite time and z σ It converges to zero.

[0129] From equations (19) and (20), we get:

[0130]

[0131] If the Lipchitz condition is satisfied, the error system is asymptotically stable.

[0132] S500: Generates fractional-order complementary sliding surfaces based on the position tracking error of the flexible robotic arm;

[0133] In step S500, the fractional-order calculus operator is defined:

[0134]

[0135] Where a and t are the upper and lower limits of the integral operator, respectively, α is the order of its calculus, 0 < α < 1, and R(α) is the real part of α.

[0136] The position tracking error of the flexible robotic arm is:

[0137] e = x d -x1 (33);

[0138] Where, x d Let x1 be the expected value. Fractional-order complementary sliding modes employ a fractional-order generalized sliding surface S. g complementary sliding surfaces S of fractional order c The combined design defines the two sliding surfaces as follows:

[0139] S g =Dα e+2λe+λ 2 D -α e (34);

[0140] S c =D a e-λ 2 D -α e (35);

[0141] Where λ>0. Then the fractional-order complementary sliding surface is:

[0142] S = S g +S c =2(D α e+λe) (36);

[0143] S600: Differentiate the fractional-order complementary sliding surface to generate a fractional-order complementary sliding mode control law;

[0144] In step S600, the formula for the fractional-order complementary sliding mode control law is as follows:

[0145] u0 = u eq +u sw

[0146] Among them, u eq For the equivalent control law, u sw To switch control laws.

[0147] In practical applications, taking the α-th derivative of both sides of equations (34) and (35) yields:

[0148] D α S g -D α S c =2λ(D α e+λe)=λS (37);

[0149] Fractional-order complementary sliding mode control laws can make the slow-varying subsystem model satisfy Lyapunov stability.

[0150] Define Lyapunov functions:

[0151]

[0152] When t≥t0 The following relationships hold true:

[0153]

[0154] Where x(t)∈R n It is a vector that is a differentiable function.

[0155] Combining equations (37) and (39), taking the first derivative of equation (38) yields:

[0156]

[0157] The control law of FOCSMC is:

[0158] u0 = u eq +u sw (41);

[0159] Among them, u eq For the equivalent control law, u sw To switch control laws.

[0160] S700: Generates a trajectory tracking control law based on the tracking differentiator, the observed disturbance value, and the fractional-order complementary sliding mode control law;

[0161] In step S700, the formula for the trajectory tracking control law is as follows:

[0162]

[0163] Where u0 is the fractional-order complementary sliding mode control law, and z3 is the observation. N 11s N 12s N 21s N 22s For N s Matrix elements.

[0164] In practical application scenarios, u is designed respectively. eq and u sw :

[0165]

[0166] u sw =j -1 ρD 2-2α tanh(S) (44);

[0167] Where ρ is the compensation coefficient and ρ > 0. From equations (40), (41), (43), and (44), we get:

[0168] D α V1≤-ρS tanh(S)≤0 (45);

[0169] The Lyapunov stability is satisfied. Therefore, the output of the active disturbance rejection controller is as shown in equation (45).

[0170] S800: Generates a vibration suppression control law based on the fast-change subsystem model, the super-helical algorithm, and the vibration amount at the end of the robotic arm;

[0171] In step S800, the formula for the vibration suppression control law is as follows:

[0172]

[0173] Among them, GB f GA f Let x be the parameter matrix. f s1 is the state variable, k5 and k6 are parameters, and s1 is the sliding mode variable.

[0174] In practical applications, the state-space expression of the rapid-change subsystem of the flexible robotic arm, derived from equation (5), is as follows:

[0175]

[0176] in,

[0177] For the fast-changing subsystem, a sliding mode controller is designed to suppress vibrations in the flexible robotic arm. The sliding surface is designed as follows:

[0178] s1=Gx f (48);

[0179] Where G > 0. The reaching law is designed using the superspiral algorithm. To avoid chattering caused by the sign function sgn(s) in the reaching law, the tanh(s) function is used instead of sgn(s).

[0180] The final approach law design is as follows:

[0181]

[0182] Where k5 > 0, k6 > 0.

[0183] Equation (46) is obtained from equations (42) and (48).

[0184] S900: Combine the trajectory tracking control law and the vibration suppression control law to generate the overall control law.

[0185] In step S900, for the flexible robotic arm system, the combined control output is obtained by combining equations (42) and (46):

[0186] u(t)=u s (t)+u f (t) (50);

[0187] Among them, u s (t) is the trajectory tracking control output, controlling the rigid motion of the robotic arm, u f (t) is the vibration suppression control output, which controls the elastic vibration of the robotic arm.

[0188] Under the condition that all the above conditions are met, the improved active disturbance rejection controller and super-helical sliding mode controller can stabilize the slow-changing and fast-changing subsystems respectively, and the combined control of the two subsystems can stabilize the closed loop of the original system.

[0189] To verify the performance of the designed combined controller compared to the traditional sliding mode controller using the constant velocity reaching law, simulations were performed in MATLAB. Considering its first-order vibration mode, Table 1 shows the parameters of the flexible robotic arm, and Table 2 shows the controller parameters.

[0190] Table 1:

[0191] parameter numerical values unit length 1.5 m width 0.1 m thickness 0.07 m density <![CDATA[2.81×10 3 ]]> <![CDATA[kg / m 3 ]]> End quality 4 kg elastic modulus <![CDATA[0.72×10 11 ]]> <![CDATA[N / m 2 ]]> Moment of inertia 1 <![CDATA[kg / m 2 ]]>

[0192] Table 2:

[0193]

[0194] To verify the trajectory tracking performance of the combined control, a desired signal θ is applied to the flexible robotic arm. d =sin(t), with an initial state of θ0 = 0.5 rad, which, under combined control, enables the system to track the desired trajectory more quickly; refer to Figure 3 The figure shown is the combined control output curve, referencing... Figure 4 The figure shows the output curve of a traditional active disturbance rejection control system. Figure 3 and Figure 4 It can be seen that, due to the filtering characteristics and slow energy transfer of fractional-order calculus operators, the control effect of fractional-order complementary sliding mode can be improved, making the control output curve of combined control smoother. In contrast, traditional active disturbance rejection control suffers from chattering. Therefore, combined control can suppress elastic vibration more quickly.

[0195] To verify the vibration suppression performance of the combined control, a sudden disturbance was introduced at the 5th second of the point-to-point tracking of the flexible robotic arm, with an initial state of θ0 = 0.5 rad. Under the combined control, the desired trajectory can be tracked faster. Furthermore, the STESO-based combined control can recover tracking of the desired trajectory more quickly after being disturbed; refer to... Figure 5 The figure shown is the combined control output curve, referencing... Figure 6 The figure shows the output curve of a traditional active disturbance rejection control system. Figure 5 and Figure 6 It can be seen that the control output curve of the combined control is smoother, while the traditional active disturbance rejection control has chattering. Compared with the traditional active disturbance rejection control, the combined control produces less elastic vibration and can suppress vibration more quickly.

[0196] Secondly, referring to Figure 7As shown, this application provides a flexible robotic arm control system based on fractional-order complementary sliding mode. The system includes: a data acquisition module 100, a model construction module 200, a first calculation module 300, and a second calculation module 400.

[0197] The data acquisition module 100 is configured to acquire relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-load mass, robotic arm rotation angle, and robotic arm end-vibration.

[0198] The model building module 200 is configured to: construct a dynamic model of the flexible manipulator based on the relevant parameters of the manipulator, the assumed modal method, and the Lagrange method; and decouple the dynamic model of the flexible manipulator based on the singular perturbation method to generate a slow-varying subsystem model and a fast-varying subsystem model.

[0199] The first calculation module 300 is configured to: establish a superspiral expansion state observer based on the slow-varying subsystem model and generate observed disturbance values; generate a fractional-order complementary sliding mode surface based on the position tracking error of the flexible robotic arm; differentiate the fractional-order complementary sliding mode surface to generate a fractional-order complementary sliding mode control law; and generate a trajectory tracking control law based on the tracking differentiator, the observed disturbance values, and the fractional-order complementary sliding mode control law.

[0200] The second calculation module 400 is configured to: generate a vibration suppression control law based on the fast-change subsystem model, the super-helical algorithm, and the vibration amount at the end of the robotic arm; and combine the trajectory tracking control law and the vibration suppression control law to generate a total control law.

[0201] The effects of applying the aforementioned method in the above system can be found in the description of the aforementioned method embodiments, and will not be repeated here.

[0202] A third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method described in the first aspect or any possible implementation thereof.

[0203] A fourth aspect of the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect or any possible implementation thereof.

[0204] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0205] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0206] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0207] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0208] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A control method for a flexible robotic arm based on fractional-order complementary sliding mode, characterized in that, The method includes: Obtain relevant parameters of the robotic arm; the relevant parameters of the robotic arm include: robotic arm length, robotic arm end-effector load mass, robotic arm rotation angle, and robotic arm end-effector vibration. A dynamic model of the flexible robotic arm is constructed based on the relevant parameters of the robotic arm, the hypothetical modal method, and the Lagrange method. The dynamic model of the flexible robotic arm is decoupled according to the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model. A superspiral expansion state observer is established based on the slow-varying subsystem model, and observation perturbation values ​​are generated. A fractional-order complementary sliding surface is generated based on the position tracking error of the flexible robotic arm; Differentiating the fractional-order complementary sliding surface generates the fractional-order complementary sliding mode control law; A trajectory tracking control law is generated based on the tracking differentiator, the observed disturbance value, and the fractional-order complementary sliding mode control law. A vibration suppression control law is generated based on the fast-change subsystem model, the super-helical algorithm, and the vibration amount at the end of the robotic arm. The trajectory tracking control law and the vibration suppression control law are combined to generate the overall control law; The formula for the vibration suppression control law is as follows: in, , For parameter matrices, For state variables, , For parameters, For sliding modulus; The formula for the superspiral expansion state observer is as follows: in, , and They are respectively , and The estimated value, To assist in the amount of feedback, , , .

2. The flexible robotic arm control method based on fractional-order complementary sliding mode according to claim 1, characterized in that, The formula for the slowly varying subsystem model is as follows: in, ,in for matrix elements, for The estimated value, For the control quantity of the slow-varying subsystem, External disturbances .

3. The flexible robotic arm control method based on fractional-order complementary sliding mode according to claim 1, characterized in that, The formula for the rapidly changing subsystem model is as follows: in, It is a positive real number. , , For the new state variables, For the control quantity of the fast variable subsystem, is a coefficient.

4. The flexible robotic arm control method based on fractional-order complementary sliding mode according to claim 1, characterized in that, The formula for the fractional-order complementary sliding mode control law is as follows: in, This is an equivalent control law. To switch control laws.

5. The flexible robotic arm control method based on fractional-order complementary sliding mode according to claim 1, characterized in that, The formula for the trajectory tracking control law is as follows: in, For fractional-order complementary sliding mode control, For observation purposes, , for Matrix elements.

6. A flexible robotic arm control system based on fractional-order complementary sliding mode, characterized in that, The flexible robotic arm control method based on fractional-order complementary sliding mode, as described in any one of claims 1 to 5, comprises: a data acquisition module, a model construction module, a first calculation module, and a second calculation module; The data acquisition module is configured to acquire relevant parameters of the robotic arm, including: robotic arm length, end-effector load mass, robotic arm rotation angle, and end-effector vibration. The model building module is configured to: construct a dynamic model of the flexible manipulator based on the relevant parameters of the manipulator, the assumed modal method, and the Lagrange method; and decouple the dynamic model of the flexible manipulator based on the singular perturbation method to generate a slow-variable subsystem model and a fast-variable subsystem model. The first calculation module is configured to: establish a superspiral expansion state observer based on the slow-varying subsystem model and generate observed disturbance values; generate a fractional-order complementary sliding mode surface based on the position tracking error of the flexible robotic arm; differentiate the fractional-order complementary sliding mode surface to generate a fractional-order complementary sliding mode control law; and generate a trajectory tracking control law based on the tracking differentiator, the observed disturbance values, and the fractional-order complementary sliding mode control law. The second calculation module is configured to: generate a vibration suppression control law based on the fast-change subsystem model, the super-helical algorithm, and the vibration amount at the end of the robotic arm; and combine the trajectory tracking control law and the vibration suppression control law to generate a total control law.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements a flexible robotic arm control method based on fractional-order complementary sliding mode as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a flexible robotic arm control method based on fractional-order complementary sliding mode as described in any one of claims 1 to 5.

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