A mechanical arm vibration suppression method and system based on PSO optimized integral sliding mode control and disturbance observation

Abstract

The application discloses a mechanical arm vibration suppression method and system based on PSO optimized integral sliding mode control and disturbance observation, relates to the technical field of robot motion control, and comprises the following steps: generating a quintic polynomial joint space trajectory according to initial joint angles, target joint angles and trajectory time of the mechanical arm; calculating a mass matrix, a Coriolis / centrifugal force vector and a gravity vector according to a six-degree-of-freedom mechanical arm dynamics model; constructing a disturbance observer according to a dynamics residual to obtain a disturbance torque estimation value; constructing an integral sliding mode control law according to an expected joint state, an actual joint state, an error integral and the disturbance torque estimation value, and reducing the chattering of the sliding mode control by using a saturation function; and determining control gain parameters by using a PSO optimization algorithm.The application can improve the trajectory tracking accuracy of the mechanical arm, reduce joint vibration and control torque fluctuation under the action of external disturbance.

Description

Technical Field

[0001] This invention relates to the field of robot motion control technology, specifically to a method and system for suppressing robot arm vibration based on PSO optimized integral sliding mode control and disturbance observation. Background Technology

[0002] Robotic arms need to meet both rapid response and high-precision positioning requirements in scenarios such as high-speed material handling, precision assembly, welding, grinding, and medical assistance. Due to the multi-joint coupling, inertial parameter variations, gravity effects, and external disturbances, robotic arms are prone to tracking errors, control torque fluctuations, and end-effector vibrations when joint speeds or accelerations change significantly, which can affect work quality and equipment lifespan.

[0003] Existing methods for suppressing vibration in robotic arms typically employ PID control, traditional sliding mode control, trajectory smoothing, or separate disturbance compensation methods. PID control parameter tuning relies on experience and lacks robustness in the face of strong coupling and nonlinear dynamics; while traditional sliding mode control has disturbance rejection capabilities, the sign function is prone to chattering, resulting in unsmooth control torque; and reducing vibration solely through trajectory planning struggles to handle unmodeled disturbances and dynamic errors during operation.

[0004] Therefore, a method for suppressing the vibration of a robotic arm that can take into account trajectory smoothness, dynamic compensation, disturbance estimation and control parameter optimization is needed to improve the trajectory tracking accuracy of a six-degree-of-freedom robotic arm and reduce error peaks and control torque fluctuations without increasing the complexity of the hardware. Summary of the Invention

[0005] In view of the above-mentioned problems, the present invention is proposed.

[0006] Therefore, the technical problem solved by the present invention is that existing robotic arm control methods have problems such as large trajectory tracking errors, obvious control torque jitter, insufficient disturbance compensation, and difficulty in tuning control parameters.

[0007] To address the aforementioned technical problems, this invention provides the following technical solution: a method for suppressing robotic arm vibration based on PSO-optimized integral sliding mode control and disturbance observation, comprising: generating a fifth-order polynomial trajectory based on initial joint angles and target joint angles; calculating the mass matrix, Coriolis / centrifugal force vector, and gravity vector based on a six-degree-of-freedom robotic arm dynamics model; estimating the external disturbance torque using a disturbance observer; generating control torque using an integral sliding mode control law; and optimizing the control gain using PSO to suppress robotic arm vibration.

[0008] As a preferred embodiment of the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation described in this invention, the fifth-order polynomial trajectory is constructed by normalizing the time τ, so that the velocity and acceleration of the trajectory are continuous at the start and end times, thereby reducing the impact introduced by the target trajectory itself.

[0009] As a preferred embodiment of the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation described in this invention, the dynamic model obtains the mass matrix through the kinetic energy method and calculates the partial derivative of the mass matrix with respect to the joint angle through numerical differentiation, thereby obtaining the Coriolis / centrifugal force vector.

[0010] As a preferred embodiment of the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation described in this invention, the disturbance observer updates the disturbance estimate based on the dynamic residual, so that the control law can counteract the time-varying external disturbance torque in real time.

[0011] As a preferred embodiment of the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation described in this invention, the integral sliding mode control law introduces an error integral term into the sliding surface to reduce steady-state error; at the same time, it uses a saturation function to replace the sign function to reduce chattering in sliding mode control.

[0012] As a preferred embodiment of the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation described in this invention, the PSO optimization algorithm uses comprehensive tracking error, control torque fluctuation and steady-state error as fitness evaluation indicators to optimize gain_c, gain_k, gain_epsilon and gain_zeta.

[0013] Another objective of this invention is to provide a robotic arm vibration suppression system based on PSO-optimized integral sliding mode control and disturbance observation, which can complete trajectory generation, dynamic modeling, disturbance observation, control torque calculation, and parameter optimization through a modular structure.

[0014] As a preferred embodiment of the robotic arm vibration suppression system based on PSO optimized integral sliding mode control and disturbance observation described in this invention, it includes a trajectory generation module, a dynamic modeling module, a disturbance observation module, an integral sliding mode control module, a PSO parameter optimization module, and a robotic arm execution module.

[0015] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of a robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation.

[0016] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a method for suppressing robot vibration based on PSO-optimized integral sliding mode control and disturbance observation.

[0017] The beneficial effects of this invention are as follows: The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation provided by this invention ensures the continuous and smooth motion of the desired joint through a fifth-order polynomial trajectory, improves control accuracy through inverse dynamic compensation, cancels external disturbances through a disturbance observer, reduces chattering through saturated function integral sliding mode control, and optimizes the gain parameters through PSO, so that the robotic arm can still maintain a small tracking error and a smooth control torque when subjected to external disturbances. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 The first embodiment of the present invention provides an overall flowchart of a robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation.

[0020] Figure 2 This is a schematic diagram of a robotic arm vibration suppression system based on PSO optimized integral sliding mode control and disturbance observation, provided for the first embodiment of the present invention.

[0021] Figure 3 The image shows the PSO-ISMC six-joint trajectory tracking results provided in the second embodiment of the present invention.

[0022] Figure 4 The image shows the tracking error results of the PSO-ISMC six joints provided in the second embodiment of the present invention.

[0023] Figure 5 The diagram shows the control torque results of the PSO-ISMC six joints provided in the second embodiment of the present invention.

[0024] Figure 6 The diagram shows the PSO-ISMC perturbation estimation results provided in the second embodiment of the present invention.

[0025] Figure 7 The image shows the ISMC six-joint trajectory tracking results provided for the second embodiment of the present invention.

[0026] Figure 8The diagram shows the SMC six-joint trajectory tracking results provided in the second embodiment of the present invention.

[0027] Figure 9 The PSO optimization convergence curve is provided for the second embodiment of the present invention. Detailed Implementation

[0028] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0029] Example 1, referring to Figures 1-2 As an embodiment of the present invention, a method for suppressing the vibration of a robotic arm based on PSO-optimized integral sliding mode control and disturbance observation is provided, comprising:

[0030] S1: Generate a fifth-order polynomial joint space trajectory based on the robot arm's initial joint angle q0, target joint angle qf, and trajectory time T.

[0031] Furthermore, the initial angle q0 of the six joints can be set to [0.0, 0.2, -0.1, 0.0, 0.1, -0.2]. T The target angle qf of the six joints can be set to [0.6, 0.8, 0.4, -0.3, 0.5, 0.2]. T The unit is rad.

[0032] It should also be noted that, in order to avoid the time variable from exceeding the trajectory planning range, if t≤0, let τ=0; if t≥T, let τ=1; otherwise, let τ=t / T.

[0033] The basis functions of a fifth-degree polynomial are expressed as:

[0034] s = 10τ 3- 15τ 4 +6τ 5

[0035]

[0036]

[0037] The trajectory output is represented as:

[0038] qd = q0 + (qf - q0)s

[0039]

[0040]

[0041] Where qd represents the desired joint angle, dqd represents the desired joint velocity, and ddqd represents the desired joint acceleration.

[0042] S2: Establish a dynamic model of a six-degree-of-freedom robotic arm and calculate the mass matrix, Coriolis / centrifugal force vector, gravity vector, and external disturbance torque of the robotic arm in the current joint state.

[0043] It should be noted that the dynamic model of the robotic arm is represented as follows:

[0044] M(q)qdd+C(q,dq)+G(q)=T+d(t)

[0045] Where M(q) represents the mass matrix, C(q, dq) represents the Coriolis / centrifugal force vector, G(q) represents the gravity vector, τ represents the control torque, and d(t) represents the external disturbance torque.

[0046] It should also be noted that the mass matrix is ​​obtained through the kinetic energy method. A unit velocity vector ei is set for the i-th joint, and the kinetic energy Tb(i) is calculated. Let M(i, i) = 2Tb(i). A unit velocity is simultaneously set for the i-th and j-th joints, and the kinetic energy Tij is calculated. Let M(i, j) = Tij - Tb(i) - Tb(j) to obtain the symmetric positive definite mass matrix.

[0047] The Coriolis / centrifugal force vector is calculated by the central difference of the joint angle using the mass matrix, and the central difference step size h can be taken as 1.0 × 10⁻⁶. -6 The i-th Coriolis / centrifugal force vector is represented as:

[0048]

[0049] The gravity vector is calculated from the link mass, link length, joint angle trigonometric functions, and gravitational acceleration. The external disturbance torque is set as follows:

[0050] d(t)=3sin(t) / (1+t)·l6

[0051] The joint acceleration of the robotic arm is expressed as:

[0052] qdd=M(q) -1 (τ+dCG)

[0053] S3: Construct a disturbance observer based on dynamic residuals to estimate the external disturbance torque during the operation of the robotic arm in real time.

[0054] Furthermore, the disturbance observer calculates the residual based on the actual joint acceleration qdd, control torque τ, and the output of the dynamic model, which is expressed as:

[0055] residual=M(q)qdd+C(q,dq)+G(q)-τ

[0056] The update law for the perturbation estimate is expressed as:

[0057] dhat_dot=gain_L(residual-dhat)

[0058] Where gain_L represents the observer gain, and dhat represents the estimated disturbance torque. This observer allows the controller to obtain the disturbance compensation amount without directly measuring the external disturbance.

[0059] S4: Construct an integral sliding mode control law and reduce chattering in sliding mode control by using a saturation function.

[0060] Furthermore, calculate the position error and velocity error:

[0061] e = qd - q

[0062] ed = dqd - dq

[0063] Constructing the integral sliding surface:

[0064] s = gain_c·e + ed + gain_k·ei

[0065] Where ei represents the integral error, and gain_c and gain_k represent the position error gain and integral error gain, respectively.

[0066] To reduce chattering caused by traditional sign functions, a boundary layer parameter (boundary) is introduced, and a saturation function is used:

[0067] sat_s=min(max(s / boundary,-1),1)

[0068] In one specific embodiment, the boundary can be 0.05.

[0069] The target acceleration is expressed as:

[0070] v=ddqd+gain_c·ed+gain_k·e+gain_epsilon.s+gain_zeta·sat_s

[0071] The control torque is expressed as:

[0072] τ=M(q)v+C(q,dq)+G(q)-dhat

[0073] Here, gain_epsilon and gain_zeta represent the sliding surface feedback gain and saturation term gain, respectively. By introducing inverse dynamic compensation and disturbance estimation compensation into the control torque, the impact of model coupling and external disturbances on tracking accuracy can be reduced.

[0074] S5: Determine the integral sliding mode control gain parameters using the PSO optimization algorithm.

[0075] It should be noted that the PSO optimization algorithm can use gain_c, gain_k, gain_epsilon, and gain_zeta as optimization variables, and construct a fitness function using the overall tracking error, the magnitude of the control torque change, and the steady-state error. The fitness function can be expressed as:

[0076] J=α∫||e(t)|| 2 dt+β∫||τ(t)|| 2 dt+γ||e(T)|| 2

[0077] Where α, β, and γ are weighting coefficients. The PSO optimization algorithm finds the gain combination that minimizes J by updating particle velocity and position, thereby obtaining control parameters that balance tracking accuracy and control smoothness.

[0078] Example 2, refer to Figures 3-9 As an embodiment of the present invention, a simulation experiment is provided for a method for suppressing the vibration of a robotic arm based on PSO optimized integral sliding mode control and disturbance observation.

[0079] First, to verify the effectiveness of the method of this invention, a six-degree-of-freedom manipulator trajectory, controller, disturbance observer, and dynamic model were established in the MATLAB / Simulink environment. The manipulator link parameters include m2 = 1.0, m3 = 1.0, m4 = 1.2, m5 = 1.0, m6 = 0.5, rotational inertia I1 = 0.015, I2 = 0.025, I3 = 0.032, I4 = 0.015, I5 = 0.043, I6 = 0.015, link length I2 = I3 = I5 = 0.2, and gravitational acceleration g = 9.8.

[0080] Under the same trajectory, the same external disturbance, and the same robotic arm dynamic parameters, the PSO-ISMC method of this invention is compared with the ISMC method without PSO optimization and the traditional SMC method. Figures 3-6 The trajectory tracking, tracking error, control torque, and disturbance estimation results of PSO-ISMC are shown respectively. Figure 7 and Figure 8 The trajectory tracking results of ISMC and SMC are shown; Figure 9 The PSO convergence process is shown.

[0081] Depend on Figure 3 and Figure 4 It can be seen that the method of the present invention can track the fifth-order polynomial trajectory on all six joints, and the tracking error decays rapidly after a brief transition; from Figure 5 It can be seen that the control torque is continuous and there is no large-amplitude high-frequency chattering common in traditional sliding mode control; Figure 6 It can be seen that the disturbance observer can follow the actual disturbance changes and output the disturbance estimate.

[0082] Experimental results show that the present invention can effectively suppress joint vibration of the robotic arm, improve trajectory tracking accuracy, and reduce control torque fluctuation through the synergistic effect of fifth-order polynomial trajectory, disturbance observation, integral sliding mode control, and PSO parameter optimization.

[0083] Example 3, referring to Figure 2 As an embodiment of the present invention, a robotic arm vibration suppression system based on PSO optimized integral sliding mode control and disturbance observation is provided, including a trajectory generation module, a dynamic modeling module, a disturbance observation module, an integral sliding mode control module, a PSO parameter optimization module, and a robotic arm execution module.

[0084] The trajectory generation module generates qd, dqd, and ddqd based on q0, qf, and T; the dynamic modeling module calculates M(q), C(q, dq), and G(q) based on q and dq; the disturbance observation module outputs dhat based on qdd, τ, and the dynamic residual; the integral sliding mode control module outputs τ based on the error, error integral, disturbance estimate, and control gain; the PSO parameter optimization module optimizes the control gain; and the robotic arm execution module drives the robotic arm based on τ and feeds back q, dq, and qdd.

[0085] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device to execute all or part of the steps of the methods of the various embodiments of the present invention.

[0086] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device.

[0087] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system.

[0088] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for suppressing the vibration of a robotic arm based on PSO-optimized integral sliding mode control and disturbance observation, characterized in that, include: Based on the initial joint angle, target joint angle and preset trajectory time of the robotic arm, a fifth-order polynomial joint space trajectory is constructed, and the desired joint angle, desired joint velocity and desired joint acceleration are output. A six-degree-of-freedom robotic arm dynamic model is established based on the joint position and joint velocity of the robotic arm, and the mass matrix, Coriolis / centrifugal force vector, gravity vector and external disturbance torque decaying with time are calculated. A disturbance observer is constructed based on the dynamic model of the robotic arm, the actual joint acceleration, and the control torque to obtain the estimated value of the external disturbance torque. The integral sliding mode control law is constructed based on the expected joint state, the actual joint state, the integral of the error, and the estimated value of the disturbance torque. The control torque is generated by replacing the sign function with the saturation function. The gain parameters in the integral sliding mode control law are determined by the PSO optimization algorithm, which enables the robotic arm to suppress joint vibration and control torque fluctuation when tracking the fifth-order polynomial trajectory.

2. The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in claim 1, characterized in that: The fifth-order polynomial joint space trajectory includes restricting the normalized time τ to [0, 1], and according to s = 10τ 3 -15τ 4 +6τ 5 , Calculate the trajectory basis functions, velocity basis functions, and acceleration basis functions.

3. The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in claim 2, characterized in that: The desired joint angle, desired joint velocity, and desired joint acceleration are respectively qd=q0+(qf-q0)s, Where q0 is the initial angle of the six joints and qf is the target angle of the six joints.

4. The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in claim 1, characterized in that: The dynamic model of the six-degree-of-freedom robotic arm constructs a mass matrix M(q) using the kinetic energy method, calculates the Coriolis / centrifugal force vector C(q, dq) by numerically differentiating the mass matrix with respect to the joint angle, and calculates the gravity vector G(q) based on the mass, moment of inertia, link length, and gravitational acceleration of the robotic arm link.

5. The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in claim 4, characterized in that: The external perturbation torque is d(t) = 3sin(t) / (1+t)·16, which causes each joint to be subjected to the same type of time-decreasing perturbation. The joint acceleration of the robotic arm is given by qdd = M(q). -1 (τ+dCG) is obtained.

6. The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in claim 1, characterized in that: The disturbance observer calculates the dynamic residual based on residual = M(q)qdd + C(q, dq) + G(q) - τ, and updates the disturbance torque estimate dhat based on dhat_dot = gainL(residual - dhat).

7. The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in claim 1, characterized in that: The integral sliding mode control law includes calculating the position error e = qd - q and the velocity error ed = dqd - dq, constructing the sliding surface s = gain_c·e + ed + gain_k·ei, and s is saturated using the boundary layer parameter boundary.

8. The robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in claim 7, characterized in that: The target acceleration in the control law is v = ddqd + gain_c·ed + gain_k·e + gainepsilon·s + gainzeta·sat(s / boundary), and the control torque is τ = M(q)v + C(q, dq) + G(q) - dhat.

9. A system employing the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in any one of claims 1 to 8, characterized in that: The system includes a trajectory generation module, a dynamics modeling module, a disturbance observation module, an integral sliding mode control module, a PSO parameter optimization module, and a robotic arm execution module. The trajectory generation module outputs qd, dqd, and ddqd; the dynamics modeling module outputs M(q), C(q, dq), and G(q); the disturbance observation module outputs dhat; the integral sliding mode control module outputs the control torque τ; the PSO parameter optimization module optimizes the control gain; and the robotic arm execution module drives the robotic arm to move according to the control torque and provides feedback on the joint state.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in any one of claims 1 to 8.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the robotic arm vibration suppression method based on PSO optimized integral sliding mode control and disturbance observation as described in any one of claims 1 to 8.

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