Mechanical arm trajectory tracking control system and method based on adaptive fuzzy PID
By using an adaptive fuzzy PID control system, which combines fuzzy inference and adaptive parameter adjustment, the problem of insufficient accuracy and real-time performance of traditional PID control in robotic arm systems is solved, and high-precision, fast-response robotic arm trajectory tracking control is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- MCC SHENKAN ENG TECH CO LTD
- Filing Date
- 2025-12-18
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies struggle to balance control accuracy with the real-time performance and engineering applicability of algorithms. Traditional PID controllers perform poorly in nonlinear, strongly coupled robotic arm systems, fuzzy control relies on expert experience and lacks precision, model predictive control is computationally complex and costly, and adaptive control is complex to design and difficult to analyze for stability.
An adaptive fuzzy PID control system is adopted, which combines a trajectory planning module, an adaptive fuzzy PID controller, a robotic arm dynamics compensator, and an anti-saturation protection module. The PID parameters are optimized online through fuzzy inference and adaptive parameter adjustment. Combined with robotic arm dynamics feedforward compensation and anti-saturation processing, torque limiting and integral anti-saturation are achieved.
It improves the trajectory tracking accuracy of the robotic arm, with a steady-state tracking error of less than 0.02m and a settling time of less than 3 seconds. Compared with traditional PID control, the accuracy is improved by 50-80%, the response speed is improved by 68%, and it has high precision, fast response and strong robustness.
Smart Images
Figure CN121552364B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of industrial robot control technology, specifically to a robotic arm trajectory tracking control system and method based on adaptive fuzzy PID. Background Technology
[0002] Industrial robots play a vital role in modern manufacturing, and their trajectory tracking accuracy directly impacts production quality and efficiency. Traditional robotic arm control methods can be broadly categorized as follows: (1) Traditional PID control: It has the advantages of simple structure and easy implementation, but when faced with complex systems such as robotic arms that are nonlinear and strongly coupled, the fixed-parameter PID controller is difficult to maintain excellent performance under different operating conditions. Its control law can be expressed as: ;in, To control the torque, To track errors, , , These are fixed parameters.
[0003] (2) Fuzzy control: It can handle system nonlinearity and uncertainty, but control methods that do not rely on precise mathematical models often have insufficient accuracy and rely heavily on expert experience.
[0004] (3) Model predictive control: Although the control accuracy is high, the calculation is complex, the processor performance requirements are high, and the cost is high in actual industrial applications.
[0005] (4) Adaptive control: It can adjust parameters online, but the design is complex and the stability analysis is difficult.
[0006] In summary, existing technologies struggle to balance control precision with the real-time performance and engineering applicability of the algorithm. Summary of the Invention
[0007] To address the aforementioned problems, the present invention aims to provide a robotic arm trajectory tracking control system and method based on adaptive fuzzy PID.
[0008] To achieve the above objectives, the technical solution adopted by the present invention is: a robotic arm trajectory tracking control system based on adaptive fuzzy PID, including a trajectory planning module, an adaptive fuzzy PID controller, a robotic arm dynamics compensator, and an anti-saturation protection module; The trajectory planning module is used to generate the desired trajectory according to task requirements; The adaptive fuzzy PID controller is used to adjust the PID control parameters online. The robotic arm dynamics compensator is used to provide feedforward compensation; The anti-saturation protection module is used to implement torque limiting and integral anti-saturation processing.
[0009] Furthermore, the adaptive fuzzy PID controller includes a fuzzy inference unit and a parameter adaptation unit.
[0010] This invention also provides a control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID, specifically including the following steps: Step 1, System Initialization: Set the robotic arm parameters, controller initial parameters, and sampling time; Step 2: The trajectory planning module generates the desired trajectory based on task requirements. , , ;in, For the desired trajectory position, For the desired trajectory velocity, Acceleration for the desired trajectory; Step 3, Status Detection: Obtain the actual position of the robotic arm through sensors. and actual speed ; Step 4: Calculate the trajectory tracking error and error change rate ; Step 5: The fuzzy inference unit performs fuzzy inference: based on the error... and error change rate PID parameter adjustment amount is calculated through fuzzy inference. , , Specifically: ΔK p ,ΔK i ,ΔK d =F(e, ); Where F is the fuzzy inference function; based on the input e and Output three parameter adjustment amounts , , ; ΔK p The proportional gain adjustment amount obtained through fuzzy inference; ΔK i : The integral gain adjustment amount obtained through fuzzy inference; ΔK d : Differential gain adjustment amount obtained through fuzzy reasoning; Step 6: The parameter adaptive unit performs parameter adaptive adjustment: updates the adaptive parameters according to the system performance indicators. , and Specifically: ; ; ; in, , , For adaptive parameters, , , The initial values for the adaptive parameters are... , , For adaptive gain coefficients; Step 7, Calculate the control torque: Calculate the adaptive fuzzy PID control torque. Specifically: ; Step 8: Perform feedforward compensation using the robotic arm dynamics compensator: Calculate the robotic arm dynamics feedforward compensation torque. Specifically: ; Where M(q) is the inertia matrix, Here are the Coriolis force and centrifugal force matrices, and G(q) is the gravity term. , Let the desired trajectory acceleration and the desired trajectory velocity be denoted as . Step 9: Calculation of total control torque τ: ; Step 10: The anti-saturation protection module undergoes anti-saturation treatment; Step 11: Output control signal: Output the processed control torque to the actuator; Step 12: Repeat the process until the task is completed.
[0011] Furthermore, in step 4, the trajectory tracking error and error change rate Specifically: ; ; Where e is the trajectory tracking error, which is the difference between the expected trajectory position and the actual position; This is the rate of change of error, i.e., the time derivative of the error.
[0012] Furthermore, in step 7, the adaptive PID parameters... , , The calculation is as follows: ; ; ; in, , , These are the initial values for the PID parameters.
[0013] Furthermore, in step 8, taking a two-degree-of-freedom robotic arm as an example, the inertia matrix M(q) is specifically as follows: ; ; ; ; in, m 1 and m 2 is the mass of the connecting rod. l 1 and l 2 is the length of the connecting rod. q 2 is the angle of joint 2; M 11 This represents the equivalent inertia of joint 1 itself; M 12 M 21 It is the inertial coupling between joint 1 and joint 2, representing the effect of the acceleration of one joint on the torque of the other joint; M 22 It is the equivalent inertia of joint 2 itself.
[0014] Furthermore, in step 8, taking a two-degree-of-freedom robotic arm as an example, the Coriolis force and centrifugal force matrix... Specifically: ; ; ; ; Among them, C 11 C 12 It reflects the coupled inertial force generated by the movement of joint 2 on joint 1; C 21 It reflects the Coriolis force effect generated by the movement of joint 1 on joint 2; C 22 =0 indicates that the centrifugal force of joint 2 itself is zero; , These represent the angular velocities of joint 1 and joint 2, respectively. Furthermore, in step 8, taking a two-degree-of-freedom robotic arm as an example, the gravity term G(q) is specifically: ; ; g It is the acceleration due to gravity. q 1 indicates the position of joint 1; q 2 indicates the position of joint 2.
[0015] Furthermore, the anti-saturation treatment in step 10 includes torque limiting and integral anti-saturation treatment, specifically as follows: ; ; ; Where sat(·) is the saturation function. K aw (·) represents the anti-saturation gain; τ max The maximum torque output by the actuator; τ min The minimum torque output by the actuator; τ actual This refers to the actual control torque output to the actuator. τ structual For structural moments; τ computed To calculate the torque; u integral This is an integral term.
[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention achieves online self-tuning of PID parameters by integrating fuzzy logic reasoning and adaptive control technology; it improves trajectory tracking accuracy by combining robotic arm dynamics feedforward compensation; and it designs an anti-saturation protection mechanism to ensure safe system operation. This invention can achieve a steady-state tracking error of less than 0.02m and a settling time of less than 3 seconds, improving accuracy by 50-80% and response speed by 68% compared to traditional PID control. It possesses advantages such as high precision, fast response, strong robustness, and strong engineering applicability, making it suitable for precision control tasks of various industrial robots. Attached Figure Description
[0017] Figure 1This is a structural block diagram of the robotic arm trajectory tracking control system based on adaptive fuzzy PID of the present invention; Figure 2 This is a block diagram of the adaptive fuzzy PID controller of the present invention; Figure 3 This is a comparison chart of the trajectory tracking effects of the robotic arm according to the present invention; Figure 4 This is a convergence curve of the tracking error of the present invention; Figure 5 This is a diagram showing the control torque output curve of the present invention; Figure 6 This is a diagram showing the joint angle tracking curve of the present invention; Figure 7 This is the adaptive parameter adjustment curve of the present invention; Figure 8 This is a real-time demonstration diagram of the adaptive fuzzy PID control of the present invention; Figure 9 This is a system stability analysis diagram for the present invention. Detailed Implementation
[0018] The following examples are used to illustrate the present invention, but are not intended to limit the scope of the invention.
[0019] Example 1: Reference Figure 1 A robotic arm trajectory tracking control system based on adaptive fuzzy PID includes a trajectory planning module, an adaptive fuzzy PID controller, a robotic arm dynamics compensator, and an anti-saturation protection module. The trajectory planning module is used to generate the desired trajectory according to task requirements; The adaptive fuzzy PID controller is used to adjust PID control parameters online; the adaptive fuzzy PID controller includes a fuzzy inference unit and a parameter adaptation unit. The robotic arm dynamics compensator is used to provide feedforward compensation; The anti-saturation protection module is used to implement torque limiting and integral anti-saturation processing.
[0020] Example 2: This embodiment uses a two-degree-of-freedom robotic arm as an example, with the following specific parameters: Linkage mass: , Link length: , ; Sampling time: ; Controller parameter settings: Initial PID parameters: , , T stands for transpose; Adaptive gain: , , ; The trajectory tracking task aims to achieve a circular trajectory. ; ; X d The desired position of the robotic arm's end effector in the X-axis direction, in meters; y d The desired position of the robotic arm's end effector in the Y-axis direction, in meters; t represents time.
[0021] Reference Figures 2-9 This embodiment provides a control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID, which is implemented using the robotic arm trajectory tracking control system based on adaptive fuzzy PID described in Embodiment 1, and specifically includes the following steps: Step 1, System Initialization: Set the robotic arm parameters, controller initial parameters, and sampling time; Step 2: The trajectory planning module generates the desired trajectory based on task requirements. , , ;in, For the desired trajectory position, For the desired trajectory velocity, Acceleration for the desired trajectory; Step 3, Status Detection: Obtain the actual position of the robotic arm through sensors. and actual speed ; Step 4: Calculate the trajectory tracking error and error change rate Specifically: ; ; Where e is the trajectory tracking error, which is the difference between the expected trajectory position and the actual position; This is the rate of change of the error, i.e., the time derivative of the error; Reference Figure 2 Step 5: The fuzzy inference unit performs fuzzy inference: based on the error... and error change rate PID parameter adjustment amount is calculated through fuzzy inference. , , Specifically: ΔK p ,ΔK i ,ΔK d =F(e, ); Where F is the fuzzy inference function; based on the input e and Output three parameter adjustment amounts , , ; ΔK p The proportional gain adjustment amount obtained through fuzzy inference; ΔK i : The integral gain adjustment amount obtained through fuzzy inference; ΔK d : Differential gain adjustment amount obtained through fuzzy reasoning; Step 6: The parameter adaptive unit performs parameter adaptive adjustment: updates the adaptive parameters according to the system performance indicators. , and Specifically: ; ; ; in, , , For adaptive parameters, , , The initial values for the adaptive parameters are... , , For adaptive gain coefficients; Step 7, Calculate the control torque: Calculate the adaptive fuzzy PID control torque. Specifically: ; Among them, adaptive PID parameters , , The calculation is as follows: ; ; ; in, , , These are the initial values for the PID parameters; Step 8: Perform feedforward compensation using the robotic arm dynamics compensator: Calculate the robotic arm dynamics feedforward compensation torque. Specifically: ; Where M(q) is the inertia matrix, Here are the Coriolis force and centrifugal force matrices, and G(q) is the gravity term. , Let the desired trajectory acceleration and the desired trajectory velocity be denoted as . In step 8, the inertia matrix M(q) is specifically: ; ; ; ; in, m 1 and m 2 is the mass of the connecting rod. l 1 and l 2 is the length of the connecting rod. q 2 is the angle of joint 2; M 11 This represents the equivalent inertia of joint 1 itself; M 12 M 21 It is the inertial coupling between joint 1 and joint 2, representing the effect of the acceleration of one joint on the torque of the other joint; M 22 It is the equivalent inertia of joint 2 itself; Coriolis force and centrifugal force matrix Specifically: ; ; ; ; Among them, C 11 C 12 It reflects the coupled inertial force generated by the movement of joint 2 on joint 1; C 21 It reflects the Coriolis force effect generated by the movement of joint 1 on joint 2; C 22 =0 indicates that the centrifugal force of joint 2 itself is zero; , These represent the angular velocities of joint 1 and joint 2, respectively. The gravity term G(q) is specifically: ; ; g It is the acceleration due to gravity. q 1 indicates the position of joint 1; q 2 indicates the position of joint 2; Step 9: Calculation of total control torque τ: ; Step 10: The anti-saturation protection module undergoes anti-saturation treatment; The anti-saturation treatment in step 10 includes torque limiting and integral anti-saturation treatment, specifically: ; ; ; Where sat(·) is the saturation function. K aw (·) represents the anti-saturation gain; τ max The maximum torque output by the actuator; τ min The minimum torque output by the actuator; τ actual This refers to the actual control torque output to the actuator. τ structual For structural moments; τ computed To calculate the torque; u integral It is an integral term; Step 11: Output control signal: Output the processed control torque to the actuator; Step 12: Repeat the process until the task is completed.
[0022] Stability Analysis: The global stability of the system is proved using Lyapunov stability theory. The Lyapunov function is as follows: ; in, It is a Lyapunov function; For parameter estimation error, , For the true parameter vector, For parameter estimation vectors; This is the adaptive gain matrix; s is the sliding mode variable, usually defined as a combination of the tracking error and its time derivative, for example... ,in , It is a positive definite diagonal matrix; s T This is the transpose of the sliding mode variable; T For parameter estimation error transpose; K is the control gain matrix (positive definite symmetric); The time derivative of the Lyapunov function is: ; in, This is the time derivative of the Lyapunov function; This is the rate of change of the error, i.e., the time derivative of the error; The time derivative of M(q); For parameter estimation error The time derivative; e T This is the transpose of the trajectory tracking error e; By designing a suitable adaptive law, it can be guaranteed that This proves the global asymptotic stability of the system.
[0023] like Figure 9 As shown, the implementation results of the two-degree-of-freedom robotic arm in Embodiment 2 of the present invention are as follows: Maximum tracking error: 0.3506m; Steady-state tracking error: 0.0172m; Track tracking RMSE: 0.0819m; Settling time: 2.38s; Overshoot: 40.2%; The control torque is smooth and without drastic fluctuations.
[0024] Example 3: The present invention is applied to a six-degree-of-freedom industrial robot. The adaptive fuzzy PID-based robotic arm trajectory tracking control method of the present invention is used for trajectory tracking control in a welding task. Implementation results: Track tracking accuracy: ±0.015mm; Repeat positioning accuracy: ±0.008mm.
[0025] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.
Claims
1. A control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID, characterized in that, The robotic arm trajectory tracking control system based on adaptive fuzzy PID includes a trajectory planning module, an adaptive fuzzy PID controller, a robotic arm dynamics compensator, and an anti-saturation protection module. The trajectory planning module is used to generate the desired trajectory according to task requirements; The adaptive fuzzy PID controller is used to adjust the PID control parameters online. The robotic arm dynamics compensator is used to provide feedforward compensation; The anti-saturation protection module is used to implement torque limiting and integral anti-saturation processing; The adaptive fuzzy PID controller includes a fuzzy inference unit and a parameter adaptation unit; The control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID specifically includes the following steps: Step 1, System Initialization: Set the robotic arm parameters, controller initial parameters, and sampling time; Step 2: The trajectory planning module generates the desired trajectory based on task requirements. q d , , ;in, q d For the desired trajectory position, For the desired trajectory velocity, Acceleration for the desired trajectory; Step 3, Status Detection: Obtain the actual position of the robotic arm through sensors. q and actual speed ; Step 4: Calculate the trajectory tracking error e and error change rate ; Step 5: The fuzzy inference unit performs fuzzy inference: based on the error... e and error change rate PID parameter adjustment amount is calculated through fuzzy inference. , , Specifically: ； Where F is the fuzzy inference function; based on the input e and Output three parameter adjustment amounts , , ; The proportional gain adjustment amount obtained through fuzzy inference; : The integral gain adjustment amount obtained through fuzzy inference; : Differential gain adjustment amount obtained through fuzzy reasoning; Step 6: The parameter adaptive unit performs parameter adaptive adjustment: updates the adaptive parameters according to the system performance indicators. a , β and γ Specifically: ； ； ； in, a , β , γ For adaptive parameters, a 0、 β 0、 γ 0 is the initial value of the adaptive parameter. η , ζ , ξ For adaptive gain coefficients; Step 7, Calculate the control torque: Calculate the adaptive fuzzy PID control torque. Specifically: ； Step 8: Perform feedforward compensation using the robotic arm dynamics compensator: Calculate the robotic arm dynamics feedforward compensation torque. Specifically: ； Where M(q) is the inertia matrix, Here are the Coriolis force and centrifugal force matrices, and G(q) is the gravity term. , Let the desired trajectory acceleration and the desired trajectory velocity be denoted as . Step 9: Calculation of total control torque τ: ； Step 10: The anti-saturation protection module undergoes anti-saturation treatment; Step 11: Output control signal: Output the processed control torque to the actuator; Step 12: Repeat the process until the task is completed.
2. The control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID as described in claim 1, characterized in that, In step 4, the trajectory tracking error e and error change rate Specifically: e=q d -q ； ； in, e This refers to the trajectory tracking error, which is the difference between the expected trajectory position and the actual position. This is the rate of change of error, i.e., the time derivative of the error.
3. The control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID as described in claim 1, characterized in that, In step 7, the adaptive PID parameters K p , K i , K d The calculation is as follows: ； ； ； in, K p0 , K i0 , K d0 These are the initial values for the PID parameters.
4. The control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID as described in claim 1, characterized in that, In step 8, taking a two-degree-of-freedom robotic arm as an example, the inertia matrix M(q) is specifically: ； ； M 21 = M 12 ； ； in, m 1 and m 2 is the mass of the connecting rod. l 1 and l 2 is the length of the connecting rod. q 2 is the angle of joint 2; M 11 This represents the equivalent inertia of joint 1 itself; M 12 M 21 It is the inertial coupling between joint 1 and joint 2, representing the effect of the acceleration of one joint on the torque of the other joint; M 22 It is the equivalent inertia of joint 2 itself.
5. The control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID as described in claim 4, characterized in that, In step 8, taking a two-degree-of-freedom robotic arm as an example, the Coriolis force and centrifugal force matrix... Specifically: ； ； ； C 22 =0； Among them, C 11 C 12 It reflects the coupled inertial force generated by the movement of joint 2 on joint 1; C 21 It reflects the Coriolis force effect generated by the movement of joint 1 on joint 2; C 22 =0 indicates that the centrifugal force of joint 2 itself is zero; , These represent the angular velocities of joint 1 and joint 2, respectively.
6. The control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID as described in claim 4, characterized in that, In step 8, taking a two-degree-of-freedom robotic arm as an example, the gravity term G(q) is specifically: ； ； g It is the acceleration due to gravity. q 1 indicates the position of joint 1; q 2 indicates the position of joint 2.
7. The control method for a robotic arm trajectory tracking control system based on adaptive fuzzy PID as described in claim 1, characterized in that, The anti-saturation treatment in step 10 includes torque limiting and integral anti-saturation treatment, specifically: τ max =sat( τ , τ max , τ min ); τ actual= sat( τ computed ,- τ max , τ max ); u integral= u integral -K aw ( τ actual - τ computed )； Where sat(·) is the saturation function. K aw (·) represents the anti-saturation gain; τ max The maximum torque output by the actuator; τ min The minimum torque output by the actuator; τ actual This refers to the actual control torque output to the actuator. τ computed To calculate the torque; u integral This is an integral term.