A method of input shaping for vibration suppression in articulated robots

Abstract

The present invention discloses an input shaping method for vibration suppression of an articulated robot. The algorithm of the present invention introduces a negative pulse, which significantly improves the response speed of the system compared with an algorithm with only a positive pulse. There is no need to find an analytical solution for the pulse sequence parameters, and a numerical optimal solution can be quickly obtained by a computer, so the amount of manual calculation is small. The system output oscillation can be suppressed in any parameter variation range, and the system may not be symmetrical around the nominal parameter. Constraints can be flexibly set according to the variation range of system variables, and vibration suppression can be performed for any variable.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration suppression of a load end of a robot arm, and in particular to an input shaping method for vibration suppression of an articulated robot. Background Art

[0002] Vibration suppression at the load end of the robot arm is a technical problem in the robot manufacturing industry, which greatly hinders the accuracy and efficiency of the robot in production applications. The control methods for vibration suppression widely used in the industry can be mainly divided into two categories: feedback control and input shaping. In the design of feedback control, on the one hand, most of them need to install sensors at the end of the robot arm to receive acceleration or displacement signals, and the robot arm with a load at the end structurally limits the installation of sensors, which requires the design of observers to estimate the vibration at the load end. In this case, Kalman filters and L observers can be used to estimate the system state. On the other hand, since most robots are required to adapt to variable load conditions, it is usually necessary to design more complex controllers such as adaptive control and disturbance observers to meet the accuracy requirements. Even if the design requirements can be met, the above two engineering requirements will significantly increase the complexity of the control system and the difficulty of controller design. At the same time, due to the poor portability of the feedback control algorithm, changes in the controlled object often require the controller to be redesigned, and even the structure of the control system needs to be adjusted.

[0003] Compared with feedback control, the input shaping method greatly reduces the requirements for calculation, programming and hardware, shortening the design cycle and cost. Input shaping only requires estimating the model parameters of the system, and does not require any online parameter estimation, sensors, or any feedback or feedforward signals. Moreover, input shaping itself will not cause system instability, and it has good robustness to parameter uncertainties. Input shaping is highly portable and can be applied to vibration suppression in various systems. Different systems only need to adjust the shaping curve parameters.

[0004] Most of the published engineering applications of input shaping algorithms use methods such as ZV and ZVD. Such methods have the following disadvantages. First, such methods cannot arbitrarily set the parameter variation range of vibration suppression for variable parameter systems, nor can they set the vibration suppression effect requirements for the corresponding intervals, thus limiting the robustness of the system, the flexibility of design, and the breadth of application. Most of the published methods only include shaping positive pulse sequence excitation, and the pulse delay must increase in multiples of the system vibration half-cycle, not continuously. This affects the response speed of the system. Even if some methods include negative pulses, the algorithm fixes the positive pulse amplitude, resulting in an increase in the actuator design cost, and it is easy to excite high-frequency modes, which in turn causes the robot arm to oscillate. At the same time, the published shaping algorithms all obtain the shaping pulse sequence by solving the analytical solution method, which increases the amount of manual calculation.

[0005] In view of this, it is necessary to provide a new input shaping method for vibration suppression of articulated robots to overcome the above-mentioned defects. Summary of the invention

[0006] The purpose of the present invention is to provide a method for input shaping of vibration suppression of articulated robots, which significantly improves the response speed of the system, does not require analytical solutions to pulse sequence parameters, can quickly obtain numerical optimal solutions using computers, and requires little manual calculation.

[0007] In order to achieve the above object, the present invention provides a method for input shaping of vibration suppression of an articulated robot, comprising the following steps:

[0008] S1: Build a model for the control system of a single-joint robot;

[0009] S2: Obtain the dynamic characteristics of the oscillation mode of the single-joint robot control system;

[0010] S3: List the constraint equations for solving the shaping curve optimization problem and minimize the objective function min(t n );

[0011] S4: Calculate the corresponding system natural frequency and damping ratio range according to the range of the robot single joint load time-varying system parameters;

[0012] S5: Calculate the shaped pulse train by solving the optimal value problem;

[0013] S6: Shaping curve.

[0014] Preferably, the expressions in the motor, reducer and load modules of the single-joint robot are modeled according to the transfer functions of the corresponding parts; the input U(s) is the input torque, the output Y(s) is the actual load end angular displacement, Jm is the motor moment of inertia; Bm is the motor damping ratio coefficient; Bml is the coupling damping ratio coefficient; Kml is the coupling stiffness; Jl is the load moment of inertia; Bl is the load damping ratio coefficient;

[0015] Applying the Mason gain formula, the transfer function from U to Y is:

[0016]

[0017] Where Kt is the torque coefficient, s represents the Laplace transform operator, a 0 =0; a 1 =Bl*Kml+Bm*Kml; a 2 =Bl*Bm+Bl*Bml+Bm*Bml+Jl*Kml+Jm*Kml; a 3=Bl*Jm+Bm*Jl+Bml*Jl+Bml*Jm;a 4 =Jl*Jm,b 0 =Kml,b 1 =Bml;

[0018] Outer loop controller transfer function G o and the inner loop controller transfer function G i They are:

[0019] G o =K po (1b)

[0020]

[0021] Among them, K po is the outer loop proportional controller coefficient, K pi is the proportional coefficient of the inner loop controller, K ii is the integral coefficient, and the transfer function of the frequency domain response of the closed-loop control system is obtained by the Mason gain formula:

[0022]

[0023] Obtain the corresponding transfer coefficient value a 1 、a 2 、a 3 、a 4 、a 5 、b 0 、b 1 、b 2 ;

[0024] Among them, b 2 =Bml*K po *Kt*K pi , b 1 =Bml*K po *Kt*K ii +Kml*K po *Kt*K pi , b 0 =Kml*K po *Kt*K ii , a 5 =Jl*Jm,a 4 =Bl*Jm+Bm*Jl+Bml*Jl+Bml*Jm+Jl*Kt*K pi , a 3 =Bl*Bm+Bl*Bml+Bm*Bml+Jl*Kml+Jm*Kml+Bl*Kt*K pi +Bml*Kt*K pi +Jl*Kt*K ii+Jl*K po *Kt*K pi , a 2 =Bl*Kml+Bm*Kml+Bl*Kt*K ii +Bml*Kt*K ii +Kml*Kt*K pi +Bl*K po *Kt*K pi +Bml*K po *Kt*K pi +Jl*K po *Kt*K ii ;

[0025] a 1 =Kml*Kt*Kv ii +Bl*K po *Kt*K ii +Bml*K po *Kt*K ii +Kml*K po *Kt*K pi ;

[0026] a 0 =Kml*K po *Kt*K ii ; Input R(s) is the target load end angular displacement, and output Y(s) is the actual load end angular displacement.

[0027] Preferably, the corresponding transfer function coefficient value is obtained according to the transfer function of the frequency domain response of the control system of the single-joint robot to obtain the dynamic characteristics of the oscillation mode, and the transfer function (2) of the frequency domain response of the control system of the single-joint robot has 5 roots, and the 5 roots include 1 pair of conjugate complex roots and 3 real negative roots;

[0028] The oscillation of the load end of the control system of the single-joint robot is only generated by the conjugate complex root. Decompose into a standard second-order oscillation system part G1 containing conjugate complex roots and a part G2 not containing conjugate complex roots.

[0029] Right now:

[0030] ω is the natural frequency of the control system of the single-joint robot, and ζ is the damping ratio.

[0031] Preferably, step S3 includes step S31: listing the vibration suppression ratio constraint in the constraint equation; the vibration suppression ratio is the amplitude of the response curve generated by the shaped pulse sequence excitation system divided by the amplitude of the response curve generated by the unit amplitude pulse excitation system at time zero,

[0032] The vibration suppression ratio corresponding to the closed-loop control system characteristic (ω, ζ) is:

[0033]

[0034] In the above formula (4),

[0035]

[0036]

[0037] Among them, A i and t i is the amplitude and time of the ith pulse, and the residual vibration of the closed-loop control system under the system characteristics (ω, ζ) is less than the given value, that is,

[0038]

[0039] S32: Perform a single constraint on the pulse amplitude; use a mixed superposition of positive and negative pulses, specifically:

[0040] 0<A i ≤1, i is an odd number (8)

[0041] A i =-A max , i is an even number (9);

[0042] S33: collectively constrain the amplitude of the pulse sequence; the sum of the amplitudes of the shaped pulse sequence is equal to the reference pulse amplitude 1, i.e. A 1 +A 2 +…+A n =1, the cumulative constraint is:

[0043]

[0044] In the above formula (10), A i is the amplitude of the ith pulse; k represents the current pulse; n is the total number of pulses in the sequence, where n = 5. The five pulse sequence amplitude collective constraints are obtained by equation (10), which are:

[0045]

[0046] S34: List the minimization objective function min(t n );

[0047] Preferably, a closed-loop control system corresponding to five points near the nominal value of the load moment of inertia J1 is selected as a vibration suppression object, and the five points are 0.6*J1, 0.7*J1, 0.8*J1, 0.9*J1 and J1 respectively;

[0048] According to step S2, the values ​​of the system characteristic parameters (ω, ζ) corresponding to each point are obtained; the (ω, ζ) of the five points are substituted into the above formula (7) to obtain five constraint equations.

[0049] Preferably, by solving the minimization objective function min(t n ) to obtain the amplitude and time of the shaped pulse train (A i ,t i ), the amplitude and time (A i ,t i ) is convolved and superimposed with the reference S-curve to obtain the final shaping curve.

[0050] Compared with the prior art, the beneficial effects are: 1) The algorithm in the present invention introduces negative pulses, which significantly improves the response speed of the system compared to the algorithm with only positive pulses. There is no need to find an analytical solution for the pulse sequence parameters, and the numerical optimal solution can be quickly obtained by computer, so the amount of manual calculation is small.

[0051] 2) It is possible to suppress system output oscillation within any parameter variation range, and it is not necessary to be symmetrical around the nominal parameters. Constraints can be flexibly set according to the system variable variation range, and vibration suppression can be performed for any variable. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0053] Figure 1 A flow chart of the method for input shaping for vibration suppression of an articulated robot provided by the present invention.

[0054] Figure 2 It is a structural diagram of the closed-loop control system.

[0055] Figure 3 This is a schematic diagram of the structure of the motor, reducer and load of the closed-loop control system.

[0056] Figure 4 This is a response curve diagram of the angular displacement of the load end of the single-joint robot arm of an embodiment of the present invention to the input of the shaping curve. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solution and beneficial technical effect of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. It should be understood that the specific implementation methods described in this specification are only for explaining the present invention, not for limiting the present invention.

[0058] See also Figure 1 The present invention provides a method for input shaping for vibration suppression of an articulated robot, comprising the following steps:

[0059] S1: Build a model for the control system of a single-joint robot;

[0060] like Figure 2 and 3 As shown, specifically, the expressions in the motor, reducer and load modules of the single-joint robot correspond to the transfer functions of the corresponding parts to establish a model; the input U(s) is the input torque, the output Y(s) is the actual load end angular displacement, Jm is the motor moment of inertia; Bm is the motor damping ratio coefficient; Bml is the coupling damping ratio coefficient; Kml is the coupling stiffness; Jl is the load moment of inertia; Bl is the load damping ratio coefficient;

[0061] Applying the Mason gain formula, the transfer function from U to Y is:

[0062]

[0063] Where Kt is the torque coefficient, s represents the Laplace transform operator, a 0 =0; a 1 =Bl*Kml+Bm*Kml; a 2 =Bl*Bm+Bl*Bml+Bm*Bml+Jl*Kml+Jm*Kml; a 3 =Bl*Jm+Bm*Jl+Bml*Jl+Bml*Jm;a 4 =Jl*Jm,b 0 =Kml,b 1 =Bml.

[0064] by Figure 2 The closed-loop control system of a single-joint robot is used as an example to illustrate. Figure 2 The outer loop controller transfer function G in o and the inner loop controller transfer function G i They are:

[0065] G o =K po (1b)

[0066]

[0067] Among them, K po is the outer loop proportional controller coefficient, K pi is the proportional coefficient of the inner loop controller, K ii is the integral coefficient, and the transfer function of the frequency domain response of the closed-loop control system is obtained by the Mason gain formula:

[0068]

[0069] Obtain the corresponding transfer coefficient value a 1 、a 2 、a 3 、a 4 、a 5 、b 0 、b 1 、b 2 ; Among them, b 2 =Bml*K po *Kt*K pi , b 1 =Bml*K po *Kt*K ii +Kml*K po *Kt*K pi , b 0 =Kml*K po *Kt*K ii , a 5 =Jl*Jm,

[0070] a 4 =Bl*Jm+Bm*Jl+Bml*Jl+Bml*Jm+Jl*Kt*K pi ,

[0071] a 3 =Bl*Bm+Bl*Bml+Bm*Bml+Jl*Kml+Jm*Kml+Bl*Kt*K pi +Bml*Kt*K pi +Jl*Kt*K ii +Jl*K po *Kt*K pi ,

[0072] a 2 =Bl*Kml+Bm*Kml+Bl*Kt*K ii +Bml*Kt*K ii +Kml*Kt*K pi +Bl*K po *Kt*K pi +Bml*K po *Kt*K pi +Jl*K po *Kt*K ii;

[0073] a 1 =Kml*Kt*Kv ii +Bl*K po *Kt*K ii +Bml*K po *Kt*K ii +Kml*K po *Kt*K pi ; a 0 =Kml*K po *Kt*K ii ; Input R(s) is the target load end angular displacement, and output Y(s) is the actual load end angular displacement.

[0074] S2: Obtain the dynamic characteristics of the oscillation mode of the single-joint robot control system.

[0075] Specifically, firstly, the transfer function of the frequency domain response of the closed-loop control system is calculated to obtain the corresponding transfer function coefficient value, and the dynamic characteristics of the oscillation mode are obtained.

[0076] There are five roots (also called modes) in the transfer function of the frequency domain response of the closed-loop control system, including one pair of conjugate complex roots and three real negative roots.

[0077] The oscillation of the load end of the control system of the single-joint robot is only caused by the conjugate complex roots, so it is only necessary to eliminate the oscillation caused by the conjugate complex roots. Decompose into a standard second-order oscillation system part G1 containing conjugate complex roots and a part G2 not containing conjugate complex roots, that is:

[0078]

[0079] ω is the natural frequency of the system, ζ is the damping ratio, and equations (2) and (3) above are different expressions of the transfer function of the same closed-loop control system.

[0080] It should be noted that according to different model parameter values, the coefficient values ​​ai and bi of the transfer function of the frequency domain response of the closed-loop control system, that is, the numerical solution of G(s), can be obtained, and then the natural frequency and damping ratio (ω, ζ) corresponding to a pair of conjugate complex roots of G(s) can be obtained.

[0081] S3: List the constraint equations for solving the shaping curve optimization problem and minimize the objective function min(t n ).

[0082] Specifically, S31: lists the vibration suppression ratio (also called residual vibration) constraint in the constraint equation; the vibration suppression ratio is the amplitude of the response curve generated by the shaped pulse sequence excitation system divided by the amplitude of the response curve generated by the unit amplitude pulse excitation system at time zero.

[0083] Furthermore, the vibration suppression ratio corresponding to the system characteristic (ω, ζ) of the closed-loop control system is:

[0084]

[0085] In the above formula (4),

[0086]

[0087]

[0088] Among them, A i and t i is the amplitude and time of the ith pulse, and the residual vibration of the closed-loop control system under the system characteristics (ω, ζ) is less than the given value, that is,

[0089]

[0090] S32: Perform a single constraint on the pulse amplitude; use a mixed superposition of positive and negative pulses to significantly shorten the control time of the single-joint robot to enter a steady state, specifically:

[0091] 0<A i ≤1, i is an odd number (8)

[0092] A i =-A max , i is an even number (9);

[0093] This constraint can ensure that the pulse amplitude A i There will not be an infinite optimal solution that has no actual physical meaning. The value of Amax depends on the maximum current that the actuator can withstand.

[0094] S33: collectively constrain the amplitude of the pulse sequence; usually the sum of the amplitudes of the shaped pulse sequence needs to be equal to the reference pulse amplitude 1, that is, A 1 +A 2 +…+A n =1, which can ensure that the amplitude of the final shaping curve is equal to the amplitude of the reference shaping curve. Corresponding to the mixed shaping of positive and negative pulses in the present invention, the cumulative constraint condition needs to be met:

[0095]

[0096] In the above formula (10), A i is the amplitude of the ith pulse; k represents the current pulse; n is the total number of pulses in the sequence. In the embodiment of the present invention, n=5 is set as an example, so the five pulse sequence amplitude collective constraints are obtained through the above formula (10), which are:

[0097]

[0098] S34: List the minimization objective function min(t n );

[0099] S4: Calculate the corresponding system natural frequency and damping ratio range according to the closed-loop control system parameter variation range.

[0100] Specifically, the closed-loop control systems corresponding to five points near the nominal value of the load moment of inertia J1 are selected as vibration suppression objects, and the five points are 0.6*J1, 0.7*J1, 0.8*J1, 0.9*J1 and J1 respectively;

[0101] According to step S2, the values ​​of the system characteristic parameters (ω, ζ) corresponding to each point are obtained; the (ω, ζ) of the five points are substituted into the above formula (7) to obtain five constraint equations.

[0102] It should be noted that in this patent application, the vibration suppression ratio V tol =5%. Compared with the published patents, this patent application selects a range of Jl (0.6*Jl~Jl) for vibration suppression instead of just corresponding to the nominal value Jl, because all system models have errors, and selecting a range can enhance the robustness of a shaping curve corresponding to changes in system parameters.

[0103] S5: Calculate the shaped pulse sequence by solving the optimal value problem.

[0104] Specifically, the solution of the present patent application needs to solve the nonlinear conditions (i.e., equations 7, 8, 9, 10) and minimize the objective function min(t n ) to obtain the amplitude and time of the shaped pulse train (A i ,t i ), the number of pulses i can be selected according to the target performance requirements of the system. In the embodiment of the present invention, i=5 is selected, so 2 negative pulses are included, and the fmincon function of Matlab is applied to find the optimal solution.

[0105] The optimal solution of nonlinear constraints with non-single peaks and single valleys depends on the selection of initial values. The Gradient / Jacobian and Hessian (Lagrangian second-order derivative) of the objective function and constraints are added to the constraints to help Matlab find the optimal solution more quickly and easily.

[0106] S6: Shaping curve.

[0107] The embodiment of the present invention uses the S-shaped membership function as the reference curve to adjust a and b to adjust the slope of the curve. The amplitude and time (A) of each shaped pulse obtained in S5 are i ,t i ) is convolved and superimposed with the reference S-curve to obtain the final shaping curve as the system input.

[0108] The embodiment of the present invention uses an S-shaped membership function as a reference curve, which can reduce the system's requirements for peak current compared to a step function. At the same time, the curve obtained by this function can adjust the rising slope, thereby ensuring that the system responds fastest within the allowable current range.

[0109] The S-shaped membership function expression used in the embodiment of the present invention is:

[0110]

[0111] The following is a further example to illustrate the parameters of the established model.

[0112] The main nominal parameters of the model are as follows: The outer loop proportional controller coefficient K po =30; Inner loop controller proportional coefficient K pi =0.25, integral coefficient K ii =0.1; motor moment of inertia Jm = 2.0 × 10 -5 Kg m 2 ; Motor damping ratio coefficient Bm = 2 × 10 -4 (N s) / m; coupling damping ratio coefficient Bml=2×10 -3 (N s) / m; coupling stiffness Kml = 0.82N / m; load moment of inertia Jl = 3×10 -4 Kg m 2 ; Load damping ratio coefficient Bl = 6.1 × 10 -4 (N s) / m, torque coefficient Kt=0.4N m / Arms.

[0113] The transfer function of the closed-loop control system from the target load end angular displacement to the actual load end angular displacement is obtained as follows:

[0114]

[0115] From the above formula (14), the nominal natural frequency of the system is calculated to be ω = 48 rad / s, and the damping ratio ζ = 0.126;

[0116] The systems corresponding to the five points near the nominal value of the load moment of inertia Jl are selected as the vibration suppression objects. These five points are 0.6*Jl, 0.7*Jl, 0.8*Jl, 0.9*Jl and Jl. The parameter values ​​of the system characteristic description (ω, ζ) corresponding to these five points are calculated to be (62.63, 0.147), (57.8, 0.141), (53.9, 0.135), (50.7, 0.130), (48, 0.126), and the obtained suppression ratio V tol =5%;

[0117] The number of shaped pulses is selected as 5, so it contains 2 negative pulses with an amplitude of A max =0.75. Substitute the above results into the constraint equations (Formula 4, Formula 7, Formula 8, Formula 9, Formula 10) for solving the shaping curve problem and the minimization objective function, and use Matlab's fmincon function to solve the optimal shaping pulse sequence amplitude [0.8383 -0.7500 0.8212-0.7500 0.8406], and the corresponding time is [0 0.0178 0.0473 0.0947 0.1009]. Under the premise of ensuring that the current reaches the maximum peak as much as possible within the saturation range, the benchmark S curve obtained through iteration is:

[0118]

[0119] In the embodiment of the present invention, the steady-state angular displacement is required to be 45 degrees, so the S curve actually used is 45f(x; 0, 0.242), and each shaped pulse is convolved with 45f(x; 0, 0.242) and superimposed to obtain the final shaped curve.

[0120] like Figure 4 As shown in the figure, the response of the closed-loop control system input with the reference curve and the shaping curve is compared. The shaping curve corresponds to the response of the closed-loop control system under the nominal parameters, that is, (ω, ζ) = (48, 0.126), and the target angular displacement is 45 degrees. Compared with the reference curve response, the shaping curve response reaches the steady state faster and no overshoot is observed by the naked eye.

[0121] The transient response of the closed-loop control system under 5 sets of parameters is as follows:

[0122]

[0123] It can be seen from the table that under the excitation of the shaping curve, the time for the actual angular displacement of all closed-loop control systems to stabilize within 0.01 degrees of the target angular displacement does not exceed 0.5 seconds, and the time to stabilize at the target value of 0.003 degrees is basically maintained within 0.6 seconds. The above results prove that the algorithm of the present invention provides the system with good transient and steady-state response speed and robustness to parameter changes.

[0124] The present invention is not limited to what is described in the specification and implementation modes, and therefore additional advantages and modifications can be easily realized by those skilled in the art. Therefore, without departing from the spirit and scope of the general concept defined by the claims and the equivalent scope, the present invention is not limited to the specific details, representative devices, and examples shown and described herein.

Claims

1. A method for input shaping for vibration suppression of an articulated robot, characterized in that: The steps include: S1: Build a model for the control system of a single-joint robot; S2: Obtain the dynamic characteristics of the oscillation mode of the single-joint robot control system; S3: List the constraint equations for solving the shaping curve optimization problem and minimize the objective function min(t n ); S4: Calculate the corresponding system natural frequency and damping ratio range according to the range of the robot single joint load time-varying system parameters; S5: Calculate the shaped pulse train by solving the optimal value problem; S6: shaping curve; The expressions in the motor, reducer and load modules of the single-joint robot are matched to the transfer functions of the corresponding parts to establish a model; the input U(s) is the input torque, the output Y(s) is the actual load end angular displacement, Jm is the motor moment of inertia; Bm is the motor damping ratio coefficient; Bml is the coupling damping ratio coefficient; Kml is the coupling stiffness; Jl is the load moment of inertia; Bl is the load damping ratio coefficient; Applying the Mason gain formula, the transfer function from U to Y is: Where Kt is the torque coefficient, s represents the Laplace transform operator, a0 = 0; a1 = Bl*Kml+ Bm*Kml; a2=Bl*Bm+Bl*Bml+Bm*Bml+Jl*Kml+Jm*Kml; a3=Bl*Jm+ Bm*Jl+Bml*Jl+Bml*Jm; a4=Jl*Jm, b0=Kml, b1=Bml; Outer loop controller transfer function G o and the inner loop controller transfer function G i They are: G o =K po , (1b); Among them, K po is the outer loop proportional controller coefficient, K pi is the proportional coefficient of the inner loop controller, K ii is the integral coefficient, and the transfer function of the frequency domain response of the closed-loop control system is obtained by the Mason gain formula: Obtain the corresponding transfer coefficients a1, a2, a3, a4, a5, b0, b1, b2; where b2 = Bml * K po * Kt * K pi and b1 = Bml * K po * Kt * K ii + Kml * K po * Kt * K pi and b0 = Kml * K po * Kt * K ii and a5 = Jl * Jm, a4 = Bl * Jm + Bm * Jl + Bml * Jl + Bml * Jm + Jl * Kt * K pi and a3 = Bl * Bm + Bl * Bml + Bm * Bml + Jl * Kml + Jm * Kml + Bl * Kt * K pi + Bml * Kt * K pi + Jl * Kt * K ii + Jl * K po * Kt * K pi and a2 = Bl * Kml + Bm * Kml + Bl * Kt * K ii + Bml * Kt * K ii + Kml * Kt * K pi + Bl * K po * Kt * K pi + Bml * K po * Kt * K pi + Jl * K po * Kt * K ii ; a1=Kml*Kt*Kv ii +Bl*K po *Kt*K ii +Bml*K po *Kt*K ii +Kml*K po *Kt*K pi ; a0=Kml*K po *Kt*K ii ; Input R(s) is the target load end angular displacement, and output Y(s) is the actual load end angular displacement; According to the transfer function of the frequency domain response of the control system of the single-joint robot, the corresponding transfer function coefficient value is obtained to obtain the dynamic characteristics of the oscillation mode. The transfer function (2) of the frequency domain response of the control system of the single-joint robot has 5 roots, including 1 pair of conjugate complex roots and 3 real negative roots. The oscillation of the load end of the control system of the single-joint robot is only generated by the conjugate complex root. Decompose into a standard second-order oscillation system part G1 containing conjugate complex roots and a part G2 not containing conjugate complex roots. Right now: ω is the natural frequency of the control system of the single-joint robot, ζ is the damping ratio; Step S3 includes step S31: listing the vibration suppression ratio constraint in the constraint equation; the vibration suppression ratio is the amplitude of the response curve generated by the shaping pulse sequence excitation system divided by the amplitude of the response curve generated by the unit amplitude pulse excitation system at time zero, The vibration suppression ratio corresponding to the closed-loop control system characteristic (ω, ζ) is: In the above formula (4), Among them, A i and t i is the amplitude and time of the ith pulse, and the residual vibration of the closed-loop control system under the system characteristics (ω, ζ) is less than the given value, that is, S32: Perform a single constraint on the pulse amplitude; use a mixed superposition of positive and negative pulses, specifically: 0<A i ≤1, i is an odd number (8) A i = -A max ,i even number (9); S33: collectively constrain the amplitude of the pulse sequence; the sum of the amplitudes of the shaped pulse sequence is equal to the reference pulse amplitude 1, that is, A1+A2+…+A n =1, the cumulative constraint is: In the above formula (10), A i is the amplitude of the ith pulse; k represents the current pulse; n is the total number of pulses in the sequence, where n = 5. The five pulse sequence amplitude collective constraints are obtained by equation (10), which are: S34: List the minimization objective function min(t n ).

2. The input shaping method for vibration suppression of an articulated robot according to claim 1, characterized in that: The closed-loop control systems corresponding to five points near the nominal value of the load moment of inertia Jl are selected as vibration suppression objects. The five points are 0.6*Jl, 0.7*Jl, 0.8*Jl, 0.9*Jl and Jl respectively. According to step S2, the values ​​of the system characteristic parameters (ω, ζ) corresponding to each point are obtained; the (ω, ζ) of the five points are substituted into the above formula (7) to obtain five constraint equations.

3. The input shaping method for vibration suppression of an articulated robot according to claim 1, characterized in that: By solving the minimization objective function min(t n ) to obtain the amplitude and time of the shaped pulse train (A i ,t i ), the amplitude and time (A i ,t i ) is convolved and superimposed with the reference S-curve to obtain the final shaping curve.

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