A dual adaptive high robustness control method for parallel robots

Abstract

The present invention discloses a dual-adaptive high-robustness control method for a parallel robot. For the parallel robot, a dynamic model containing lumped interference terms such as modeling error, mechanism joint friction and external interference is established; secondly, a parallel robot dynamic sliding mode controller with adaptive switching gain is designed, and the adaptive law of the constraint function is designed for its switching gain to break through the limitation of obtaining the upper limit information of the interference, so that the system can quickly overcome the interference effect and weaken the sliding mode control chattering; then, an extended state observer with adaptive bandwidth gain is designed to break through the conditional limitation that the interference term change rate is zero, reduce the initial observation error peak, and realize real-time estimation and compensation of interference, thereby reducing the burden of the sliding mode controller, further improving the system robustness and weakening the sliding mode control chattering. The present invention can improve the anti-disturbance performance of the parallel robot system, significantly reduce the sliding mode control chattering, and realize high-robustness motion control of the parallel robot.

Description

Technical Field

[0001] This invention relates to the field of industrial robot technology for electrophoretic coating conveying, and in particular to a dual adaptive high robustness control method for parallel robots. Background Technology

[0002] As a crucial link in the electrophoretic coating production line, the performance of the conveying mechanism and its control system for transporting automotive body-in-white directly affects the quality and production efficiency of automotive electrophoretic coating. A parallel robot for conveying automotive electrophoretic coating has been developed, possessing advantages such as simple structure, high flexibility, and strong load-bearing capacity. However, from a control perspective, parallel robots exhibit highly nonlinear and strongly coupled characteristics. Furthermore, the dynamic parameters are difficult to determine, leading to modeling errors in the established dynamic model. In addition, the actual operating environment presents interferences such as joint friction and external disturbances, which will affect the motion control performance of the parallel robot during operation. To improve the anti-disturbance performance of the parallel robot system and achieve highly robust motion control of the parallel robot control system, it is necessary to design its control technology.

[0003] The literature "Sliding Mode Control of Planar Five-Bar Parallel Robots" (Liu Xinle et al., Manufacturing Automation. 2017, 39(8): 35-38.) proposes a reaching law sliding mode control strategy for five-bar parallel robots. This method has the following shortcomings: (1) The dynamic model established by this method does not consider the modeling error of the parallel robot, the friction of the mechanism joints and external disturbances, etc.; (2) Since the reaching law sliding mode control law contains discontinuous sign functions, it will lead to chattering in the sliding mode control.

[0004] The literature "Adaptive Sliding Mode Control of Projectile Transfer Manipulator Based on Disturbance Observer" (Chen Longmiao et al., Journal of Nanjing University of Science and Technology (Natural Science Edition). 2015, (5): 531-537.) proposes a sliding mode control method based on disturbance observer for projectile transfer manipulators to improve the robustness of the control system. At the same time, a gain adaptive method is used to ensure that the gain of the switching term is not overestimated. The method has the following shortcomings: (1) The disturbance observer designed by this method must satisfy the condition that the rate of change of the disturbance is zero. (2) The adaptive law designed by this method can ensure that the sliding mode converges to the neighborhood of zero in a finite time, but the size of the neighborhood and the convergence time still depend on the upper bound information of the disturbance. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and, considering the characteristics of parallel robots and the requirements of actual production processes, propose a dual-adaptive, highly robust control method for parallel robots. This control method can improve the disturbance rejection performance of the parallel robot system and significantly reduce chattering in sliding mode control, thereby achieving highly robust motion control of the parallel robot control system.

[0006] The technical solution of this invention is: a dual adaptive high robustness control method for parallel robots, comprising the following steps:

[0007] 1) For parallel robots, perform kinematic analysis and establish a dynamic model that includes lumped disturbance terms such as parallel robot modeling error, mechanism joint friction and external disturbance;

[0008] 2) Determine the desired motion trajectory of the parallel robot's end effector based on actual production process requirements;

[0009] 3) Based on the parallel robot dynamics model established in step 1), a parallel robot dynamics sliding mode controller with adaptive switching gain is designed. By designing an adaptive law of constraint function for its switching gain, the limitation of needing to obtain upper bound information of interference is overcome, so that the parallel robot system can quickly overcome the interference effect and reduce the chattering of sliding mode control.

[0010] 4) Based on step 3), design an extended state observer with adaptive bandwidth gain to overcome the limitation that the change rate of the disturbance term is zero, reduce the peak value of the initial observation error of the observation value, realize the real-time estimation and compensation of the disturbance of the parallel robot system, thereby reducing the burden of the sliding mode controller to overcome the system disturbance, further improving the system robustness, and further weakening the chattering of the sliding mode control.

[0011] 5) Construct a dual-adaptive, highly robust control system for parallel robots based on a distributed structure of "upper computer (computer) + lower computer (multi-axis motion controller)";

[0012] 6) Send the calculated control quantities of each active joint of the parallel robot to each motor driver so that the parallel robot moves along the desired trajectory.

[0013] Furthermore, the specific process of step 3) is as follows:

[0014] The dynamic model, which incorporates lumped disturbance terms such as parallel robot modeling errors, joint friction, and external disturbances, is established using the Lagrange method as follows:

[0015]

[0016] In the formula, These are the pose, velocity, and acceleration of each active joint of the parallel robot; This includes lumped disturbance terms such as modeling errors of parallel robots, joint friction of mechanisms, and external disturbances. These represent the nominal inertia matrix, the nominal Coriolis force and centrifugal force terms, and the nominal gravity term, respectively; ΔM(x)∈R n×n , ΔG(x)∈R nThe model error is F(t) ∈ R. n For friction, τ d It is an external disturbance term, where τ is the active joint driving force / torque;

[0017] make

[0018]

[0019] In the formula, e, These represent the pose error and velocity error of the parallel robot's end effector, respectively; x d , These represent the desired pose and velocity of the end effector of the parallel robot, respectively.

[0020] Design the sliding surface using equation (2):

[0021]

[0022] In the formula, η=diag(eta1, eta2,..., eta n ), η1, η2, ..., η n All parameters are adjustable and satisfy the Hurwitz stability criterion.

[0023] Differentiating equation (3) with respect to time at both ends of the sliding surface, we get:

[0024]

[0025] In the formula, These represent the actual acceleration and the expected acceleration of the end effector of the parallel robot, respectively.

[0026] The approach law is chosen as follows:

[0027]

[0028] In the formula, λ=diag(λ1, λ2,…,λ n );

[0029] For equation (5), an adaptive law for the constraint function of adjusting the switching gain λ of the sliding mode control of parallel robot dynamics is designed as follows:

[0030]

[0031] In the formula, λ a (t) and λ b(S(t)) represent the values ​​at... and The value of the gain λ is switched at constant intervals. ε are all adjustable parameters. To satisfy the inequality The minimum solution is obtained, where ε is an adjustable parameter related to the neighborhood of convergence of the dynamic sliding mode variable. The finite convergence time of the sliding mode variable can be obtained through Lyapunov stability analysis.

[0032] Combining equations (1), (3), (5), and (6), the sliding mode control law for parallel robot dynamics with adaptive switching gain is obtained as follows:

[0033]

[0034] Furthermore, the specific process of step 4) is as follows:

[0035] definition

[0036]

[0037] In the formula, τ is the end-effector pose and velocity of the parallel robot; τ is the active joint driving force / torque; D is the lumped disturbance term of the parallel robot; τ a α1 and α2 are defined auxiliary variables; G is the gravity term; C is the Coriolis force and centrifugal force term;

[0038] Based on equation (1), an extended state observer for a parallel robot that can overcome the constraint that the rate of change of the disturbance term is zero is designed as follows:

[0039]

[0040] In the formula, e a ζ1 = diag(2ω0, 2ω0, ..., 2ω0), ζ2 = diag(ω0) 2 , ω0 2 , …, ω0 2 ); ω0 is an adjustable constant related to the observer gain; Let a1 and a2 be the observed values, respectively, and have

[0041] Based on the tracking error e, the bandwidth-gain adaptive law of the extended state observer is designed as follows:

[0042]

[0043] In the formula, These are adjustable parameters within the acceptable error range of the system. These are the lower and upper limits of the observer gain, respectively, where parameter ω0 ranges from... arrive The transition process can be represented as

[0044]

[0045] In the formula, tt is the adjustable transition time, and t1 is the time required to satisfy the error condition. At that time, the corresponding point in time for the system;

[0046] By designing the above-mentioned adaptive bandwidth gain law and making a reasonable selection of tt, the observation accuracy of the adaptive bandwidth gain expansion state observer for the lumped disturbance term can be guaranteed and the peak value of the initial observation error of the observation value can be reduced.

[0047] The estimated value of the lumped disturbance term in the parallel robot dynamics model in equation (9) is... Substituting into equation (7), we can obtain the dual adaptive high robustness control law for the parallel robot as follows:

[0048] τ=τ1+τ2 (13)

[0049] In the formula, τ1 is the control quantity of the adaptive switching gain dynamic sliding mode controller of the parallel robot, and τ2 is the compensation quantity of the adaptive bandwidth gain expansion state observer for the lumped disturbance term.

[0050] Furthermore, the specific process of step 5) is as follows:

[0051] Using Taidao's multi-axis motion controller (UMAC) as the core control unit, a dual adaptive high robustness control system for parallel robots is constructed based on a distributed structure of "upper computer (computer) + lower computer (multi-axis motion controller)".

[0052] The lower-level UMAC axis channel expansion card ACC-24E2A communicates with the servo driver to realize encoder information acquisition and drive control signal output functions, completing the motion control of the parallel robot. The development steps of the lower-level application program for the parallel robot dual adaptive high robustness control system are as follows:

[0053] First, in UMAC, set the preset parameters to achieve dual adaptive high robustness control of parallel robots. Set Ixx02 to define the servo motor command output address, set Ixx03 to define the servo motor position loop feedback address, set Ixx59 to select whether to use the built-in servo algorithm or an external custom algorithm, set Ixx69 to define the pulses that the servo motor can output, and set I7mn0 to define the encoder / timer decoding mode of the nth channel of the mth servo chip.

[0054] Secondly, write a program for the desired motion trajectory that meets the requirements of the dual adaptive high robustness control objective of the parallel robot;

[0055] Then, write a custom algorithm program for dual adaptive high robustness control of parallel robots;

[0056] The host computer (PC) mainly performs functions such as system initialization, data processing, code compilation, and real-time monitoring of the parallel robot's operating status. The development steps for the host computer application of the parallel robot's dual adaptive high robustness control system are as follows:

[0057] First, the communication function between the upper and lower computers is implemented based on the PComm32W dynamic link library;

[0058] Secondly, download the desired motion trajectory program that meets the requirements of the dual adaptive high robustness control objective of the parallel robot;

[0059] Then, the pre-written custom algorithm PMC file for dual adaptive high robustness control of parallel robots is downloaded to the UMAC buffer to realize dual adaptive high robustness motion control of parallel robots.

[0060] This invention proposes for the first time a dual-adaptive high-robustness control method for parallel robots to improve the disturbance rejection performance of parallel robot systems and significantly reduce chattering in sliding mode control, thereby achieving high-robustness motion control of the parallel robot control system. Its features and beneficial effects are as follows:

[0061] 1) A parallel robot dynamics sliding mode controller with adaptive switching gain can overcome the limitation of needing to obtain upper bound information of disturbance by designing an adaptive law of constraint function for its switching gain, so that the parallel robot system can quickly overcome the disturbance effect and reduce the chattering of sliding mode control.

[0062] 2) An extended state observer with adaptive bandwidth gain can overcome the limitation that the change rate of the disturbance term is zero, reduce the peak value of the initial observation error of the observation value, realize the real-time estimation and compensation of the disturbance of the parallel robot system, thereby reducing the burden of the sliding mode controller to overcome the system disturbance, further improving the system robustness, and further weakening the chattering of the sliding mode control. Attached Figure Description

[0063] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] Figure 1 This is a diagram of a single-sided structure of a parallel robot.

[0065] Figure 2 This is a schematic diagram of a dual adaptive high robustness control method for parallel robots.

[0066] Figure 3 This is a simplified diagram of the lifting and tilting mechanism.

[0067] Figure 4 It is a prototype of a parallel robot and a hardware platform for its control system.

[0068] Figure 5 This is a structural diagram of a computer control system for a parallel robot.

[0069] Figure 6 It is the estimated curve of the lumped disturbance term in the first slider of the parallel robot.

[0070] Figure 7 These are the driving force / torque curves of each active joint of the parallel robot; (a) driving force of the first slider; (b) driving force of the second slider; (c) driving torque of the first active wheel;

[0071] Figure 8 These are the trajectory tracking curves of each component of the end effector pose of the parallel robot; (a) the tracking curve in the z direction; (b) the tracking curve in the β direction;

[0072] In the diagram, 1. guide rail; 2. base; 3. travel drive motor; 4. reducer; 5. moving slider; 6. lifting drive motor; 7. connecting rod; 8. driven wheel; 9. driving wheel; 10. connecting rod; 11. vehicle body; 12. tilting drive motor; 13. electric lead screw. Detailed Implementation

[0073] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0074] First, an inverse kinematics analysis of the parallel robot is performed using analytical methods to obtain the forward kinematics and Jacobian matrix J. Then, a dynamic model incorporating lumped disturbance terms such as modeling errors, joint friction, and external disturbances is established using the Lagrange method. Second, the desired motion trajectory of the parallel robot's end effector is determined based on actual production process requirements. Next, based on the established parallel robot dynamic model, a sliding mode controller with adaptive switching gain is designed. Furthermore, an extended state observer with adaptive bandwidth gain is designed, resulting in a dual-adaptive robust controller for the parallel robot. Finally, a distributed structure is used to construct the dual-adaptive robust control system for the parallel robot. Finally, the calculated drive control quantities of each active joint of the parallel robot are sent to each motor driver, enabling the parallel robot to move along the desired trajectory. The specific method is as follows:

[0075] 1. An analytical method is used to perform inverse kinematics analysis on the parallel robot, and the forward kinematics and Jacobian matrix J of the parallel robot are further obtained.

[0076] Choosing the end-effector pose q of the parallel robot as the system's generalized coordinates, we use analytical methods to perform inverse kinematics analysis on the parallel robot to obtain its inverse position equation. Differentiating this equation, the inverse coefficient matrix is ​​the Jacobian matrix, expressed as:

[0077]

[0078] In the formula, It is the end-effector pose velocity vector; is the active joint velocity vector; J is the Jacobian matrix.

[0079] Furthermore, a dynamic model in Cartesian space containing lumped disturbance terms such as parallel robot modeling errors, mechanism joint friction, and external disturbances is established using the Lagrange method:

[0080]

[0081] In the formula, These are the end-effector pose, velocity, and acceleration of the parallel robot, respectively. These represent the nominal inertia matrix, the nominal Coriolis force and centrifugal force terms, and the nominal gravity term, respectively; ΔM(q)∈R n×n , ΔG(q)∈R n The model error is F(t) ∈ R. n For friction, τ d It represents external disturbances, and Q represents the generalized driving force.

[0082] To achieve actual control of parallel robots, the generalized driving force needs to be converted into the driving force / torque of the corresponding drive motors of each active joint. For this purpose, the Cartesian space dynamics model is transformed into joint space. The transformation relationship between the two is as follows:

[0083]

[0084] The dynamic model in joint space can be obtained through the above transformation relationship:

[0085]

[0086] In the formula, D(t) is the lumped disturbance term including modeling errors of parallel robots, joint friction of mechanisms, and external disturbances. J(q) represents the velocity vector and acceleration vector of the corresponding active joint of the drive motor. + Let M(x) ∈ R be the pseudo-inverse of the Jacobian matrix J. n×n , G(x)∈R n These represent the inertia matrix, Coriolis force and centrifugal force terms, and gravity term, respectively; ΔM(x)∈R n×n , ΔG(x)∈R n The model error is F(t) ∈ R. n For friction, τ d It is an external disturbance term, and τ is the active joint driving force / torque.

[0087] 2. Determine the desired motion trajectory of the parallel robot's end effector based on the actual application process requirements.

[0088] The desired motion trajectory q of the end effector is determined based on the actual application process requirements of the parallel robot.

[0089] 3. Based on the parallel robot dynamics model established in step 1), a parallel robot dynamics sliding mode controller with adaptive switching gain is designed. By designing an adaptive law of constraint function for its switching gain, the limitation of needing to obtain upper bound information of disturbance is overcome, enabling the parallel robot system to quickly overcome the disturbance effect and reduce the chattering of sliding mode control.

[0090] make

[0091]

[0092] In the formula, e, These represent the tracking error and velocity error of the end effector of the parallel robot, respectively; x d , These are the desired pose vector and velocity vector of the parallel robot, respectively.

[0093] Design the sliding surface using equation (5):

[0094]

[0095] In the formula, η=diag(eta1, eta2,..., eta n ), where, eta1, eta2,..., eta n All parameters are adjustable and satisfy the Hurwitz stability criterion.

[0096] Differentiating both ends of equation (6) with respect to time, we get:

[0097]

[0098] In the formula, These represent the actual acceleration and the expected acceleration of the end effector of the parallel robot, respectively.

[0099] The approach law is chosen as follows:

[0100]

[0101] In the formula, λ=diag(λ1, λ2,…,λ n ).

[0102] For equation (8), an adaptive law for the constraint function of adjusting the switching gain λ of the sliding mode control of the parallel robot dynamics is designed as follows:

[0103]

[0104] In the formula, λ a (t) and λ b (S(t)) represent the values ​​at... and The value of the gain λ is switched at constant intervals. ε are all adjustable parameters; To satisfy the inequality The minimum solution.

[0105] Combining equations (4), (6), (8), and (9), the sliding mode control law for parallel robot dynamics with adaptive switching gain is obtained as follows:

[0106]

[0107] 4. Design an extended state observer with adaptive bandwidth gain to overcome the constraint that the rate of change of the disturbance term must be zero, reduce the peak value of the initial observation error of the observation, and realize real-time estimation and compensation of disturbances in the parallel robot system. This reduces the burden on the sliding mode controller to overcome system disturbances, further improves the system robustness, and further weakens the chattering of the sliding mode control.

[0108] definition

[0109]

[0110] In the formula, τ is the end-effector pose and velocity of the parallel robot; τ is the active joint driving force / torque; D is the lumped disturbance term of the parallel robot; τ a α1 and α2 are defined auxiliary variables; G is the gravity term; C is the Coriolis force and centrifugal force term.

[0111] Based on equation (4), an extended state observer for a parallel robot that can overcome the constraint that the rate of change of the disturbance term is zero is designed as follows:

[0112]

[0113] In the formula, e a ζ1 = diag(2ω0, 2ω0, ..., 2ω0), ζ2 = diag(ω0) 2 , ω0 2 , …, ω0 2 ); ω0 is an adjustable constant related to the observer gain; Let a1 and a2 be the observed values, respectively, and have

[0114] Based on the tracking error e, the bandwidth gain adaptive law is designed as follows:

[0115]

[0116] In the formula, These are adjustable parameters within the acceptable error range of the system. These represent the lower and upper limits of the observer gain, respectively, where parameter ω0 ranges from... arrive The transition process can be represented as

[0117]

[0118] In the formula, tt is the transition time, and t1 is the time required to satisfy the error condition. The time point corresponding to the system.

[0119] The estimated value of the disturbance term in the dynamic model in equation (12) Substituting into equation (10), the dual adaptive high robustness control of the parallel robot can be obtained as follows:

[0120] τ=τ1+τ2 (15)

[0121] In the formula, τ1 is the control quantity of the adaptive switching gain dynamic sliding mode controller for the parallel robot, and we have τ2 is the compensation amount for the lumped disturbance term by the adaptive bandwidth gain expansion state observer, and we have

[0122] 5. Constructing a dual-adaptive, highly robust control system for parallel robots based on a distributed structure of "host computer (computer) + slave computer (multi-axis motion controller)".

[0123] Figure 4 As a prototype and control system hardware platform for parallel robots, a dual adaptive high robustness control system for parallel robots is constructed based on this. The system uses the multi-axis motion controller (UMAC) of Taidao Company as the core control unit and is based on a distributed structure of "upper computer (computer) + lower computer (multi-axis motion controller)" to build a dual adaptive high robustness control system for parallel robots.

[0124] The lower-level UMAC axis channel expansion card ACC-24E2A communicates with the servo driver to realize encoder information acquisition and drive control signal output functions, completing the motion control of the parallel robot. The development steps of the lower-level application program for the parallel robot dual adaptive high robustness control system are as follows:

[0125] First, in UMAC, preset parameters are set to enable dual adaptive high robustness control of parallel robots. Ixx02 is set to define the servo motor command output address, Ixx03 is set to define the servo motor position loop feedback address, Ixx59 is set to select whether to use the built-in servo algorithm or an external custom algorithm, Ixx69 is set to define the pulses that the servo motor can output, and I7mn0 is set to define the encoder / timer decoding mode of the nth channel of the mth servo chip.

[0126] Secondly, write a program for the desired motion trajectory that meets the requirements of the dual adaptive high robustness control objective of the parallel robot.

[0127] Then, a custom algorithm program for dual adaptive high robustness control of parallel robots was written.

[0128] The host computer (PC) mainly performs functions such as system initialization, data processing, code compilation, and real-time monitoring of the parallel robot's operating status. The development steps for the host computer application of the parallel robot's dual adaptive high robustness control system are as follows:

[0129] First, the communication function between the upper and lower computers is implemented based on the PComm32W dynamic link library;

[0130] Secondly, download the desired motion trajectory program that meets the requirements of the dual adaptive high robustness control objective of the parallel robot;

[0131] Then, the pre-written custom algorithm (PMC) file for dual adaptive high robustness control of the parallel robot is downloaded to the UMAC buffer to realize dual adaptive high robustness motion control of the parallel robot.

[0132] 6. Send the calculated control values ​​for each active joint of the parallel robot to each motor driver, so that the parallel robot moves along the desired trajectory.

[0133] The drive control quantities of each active joint of the parallel robot, calculated according to equation (15), are then programmed into a host computer and transmitted via... Figure 5 The control system shown sends signals to the motor drivers of each active joint of the parallel robot to drive the parallel robot to move along the desired trajectory.

[0134] The following is an embodiment of the present invention:

[0135] Example 1

[0136] The control method of this invention focuses on achieving highly robust motion control of parallel robots using a dual-adaptive, highly robust control technology. Taking a parallel robot used in automotive electrophoretic coating as an example, the specific implementation of this control method is as follows:

[0137] 1. An analytical method is used to perform inverse kinematics analysis on a parallel robot used for automotive electrophoretic coating conveying, and the forward kinematics and Jacobian matrix of the parallel robot are further obtained.

[0138] exist Figure 3 In this process, the rod length constraint equation is used, and the mechanism position equation can be obtained by reorganizing the structure of the lifting and tilting mechanism.

[0139]

[0140] In the formula, L1 is the length of the connecting rod (in meters); z i (i = 1, 2), β i (i = 1, 2) are respectively Figure 1 The z-axis positions of both ends of the connecting rod 16 in the static coordinate system and the counterclockwise rotation angle around the y-axis (units: m and rad, respectively); x i (i = 1, 2, 3, 4) are respectively Figure 1 The positions of the four sliders along the x-axis (in meters); They are respectively Figure 1 The angle of counterclockwise rotation of the two driving wheels around the y-axis (in rad); r2 and r1 are the radii of the driving wheel and the driven wheel, respectively (in m).

[0141] From equation (16) and the motion characteristics of the mechanism, the unique solution to the inverse kinematics of the lifting and tilting mechanism is:

[0142]

[0143] By inverting equation (17), we can obtain the kinematic solution.

[0144] The Jacobian matrix of the lifting and tilting mechanism can be solved by the differential transformation method, that is, by differentiating both sides of equation (17) with respect to time and simplifying, we can obtain:

[0145]

[0146] Equation (18) is abbreviated as The Jacobian matrix of the lifting and tilting mechanism is:

[0147]

[0148] In the formula, J is the Jacobian matrix.

[0149] Furthermore, using the Lagrange method and through the transformation relationship between Cartesian space and joint space, the dynamic model of the parallel robot for automotive electrophoretic coating conveying in joint space can be obtained:

[0150]

[0151] In the formula, M(x) is a symmetric positive definite inertia matrix; G(x) represents the Coriolis force and centrifugal force terms; G(x) represents the gravity term. These are the velocity vector and acceleration vector of the active joint corresponding to the drive motor, respectively; D(t) is the dynamic model of the parallel robot including lumped disturbance terms such as modeling error, joint friction and external disturbance; τ is the driving force / torque of the active joint.

[0152] 2. Based on the requirements of automotive electrophoretic coating process, determine the desired motion trajectory of the end effector of the parallel robot used for automotive electrophoretic coating conveying.

[0153] Based on the requirements of automotive electrophoretic coating process, determine the desired motion trajectory q=(z,β) of the end position of the lifting and tilting mechanism. T for:

[0154]

[0155] 3. Based on the dynamic model of the parallel robot used for automotive electrophoretic coating established in step 1, a sliding mode controller with adaptive switching gain is designed. By designing an adaptive law of constraint function for its switching gain, the limitation of needing to obtain the upper bound information of interference is overcome, enabling the parallel robot system to quickly overcome the interference effect and reduce the chattering of sliding mode control.

[0156] A dynamic model of a parallel robot for automotive electrophoretic coating conveying is established based on Lagrange, and a sliding mode control law with adaptive switching gain for the parallel robot dynamics is designed:

[0157]

[0158] 4. Design an extended state observer with adaptive bandwidth gain to overcome the constraint that the rate of change of the disturbance term must be zero, reduce the peak value of the initial observation error of the observation, and realize real-time estimation and compensation of disturbances in the parallel robot system. This reduces the burden on the sliding mode controller to overcome system disturbances, further improves the system robustness, and further weakens the chattering of the sliding mode control.

[0159] The following is an extended state observer designed for a parallel robot used in automotive electrophoretic coating conveying that can overcome the constraint that the rate of change of the disturbance term must be zero:

[0160]

[0161] In the formula, ζ1=diag(2ω0, 2ω0, 2ω0, 2ω0, 2ω0, 2ω0), ζ2=diag(ω0 2 , ω0 2 , ω0 2 , ω0 2, ω0 2 , ω0 2 );e a ω represents the error between the actual and observed values ​​of the end-effector pose and velocity of the parallel robot; ω0 is an adjustable constant related to the observer gain. The observed values ​​are α1 and α2, respectively, and have

[0162] Design an adaptive law that adjusts the observer bandwidth gain in real time based on system error, and then obtain a dual adaptive high robustness control law for a parallel robot used in automotive electrophoretic coating conveying:

[0163] τ=τ1+τ2 (24)

[0164] In the formula, τ1 is the control quantity of the adaptive switching gain dynamic sliding mode controller for the parallel robot, and we have τ2 is the compensation amount for the lumped disturbance term by the adaptive bandwidth gain expansion state observer, and we have

[0165] 5. Constructing a dual-adaptive, highly robust control system for a parallel robot used in automotive electrophoretic coating conveying based on a distributed architecture of "upper computer (computer) + lower computer (multi-axis motion controller)".

[0166] The control system of the parallel robot used for automotive electrophoretic coating conveying adopts a distributed structure of "upper computer IPC + lower computer UMAC multi-axis motion controller", and its system is as follows: Figure 5 As shown in the diagram, this control system is based on the UMAC multi-axis motion controller. The UMAC CPU board, TURBO PMAC2 CPU module, communicates with the host computer (IPC) via an Ethernet RJ45 port for human-machine interface interaction. The host PC is equipped with an Intel Core i7-4790 3.60GHz processor and primarily performs system initialization, data processing, code compilation, and real-time monitoring of the robot's operating status. The UMAC multi-axis motion controller's axis channel expansion card ACC-24E2A communicates with the servo drivers to acquire encoder information and output drive control signals. The UMAC multi-axis motion controller's digital I / O expansion board ACC-65E transmits information with each servo driver and the parallel robot, primarily handling robot motion control, acquiring commands from the host computer, and outputting control signals to each axis servo driver, acquiring encoded information, and providing feedback on the robot's real-time operating status. In addition, the control system uses a high-precision absolute position detection device to detect the absolute position of the servo driver. The host computer uses an RS232 / RS422 interface converter to communicate with the servo driver via serial port to read the absolute position information.

[0167] 6. The calculated control values ​​for each active joint of the parallel robot used for automotive electrophoretic coating are sent to each motor driver, so that the parallel robot moves along the desired trajectory.

[0168] The drive control quantities of each active joint of the parallel robot for automotive electrophoretic coating conveying, calculated according to formula (24), are then programmed into a host computer and transmitted via... Figure 5 The control system shown sends signals to the motor drivers of each active joint of the parallel robot to drive the parallel robot to move along the desired trajectory.

[0169] A dynamic model and designed control law for a parallel robot used in automotive electrophoretic coating conveying were developed using S-functions in MATLAB / Simulink. Simulation analysis was performed, and experiments were conducted on a prototype platform. The control performance of the proposed parallel robot dual adaptive robust control method (TESO-FTDSMC) was compared with that of an adaptive dynamic sliding mode controller combining a fixed-gain extended state observer (FESO-FTDSMC) and a reaching law sliding mode controller combining an adaptive bandwidth gain extended state observer (TESO-SMC). Results were obtained for each method. Figure 6 The curve shown is the estimation curve of the lumped disturbance term in the first slider of the parallel robot used for automotive electrophoretic coating conveying. Figure 7 The diagram shows the driving force / torque curves of each active joint of the parallel robot used for automotive electrophoretic coating conveying. Figure 8 The image shows the trajectory tracking curves of the end effector of the parallel robot used for automotive electrophoretic coating conveying in the z-direction and β-angle components.

[0170] Figure 6 This indicates that the proposed dual adaptive high robustness controller for the parallel robot used in automotive electrophoretic coating conveying is designed with an adaptive law for the observer gain, while also considering the transition time during the gain change process. This allows the observer gain to be adaptively adjusted with a suitable time pattern under the rule of "small gain for large error, large gain for small error", thus effectively suppressing the phenomenon of observation error peak. Figure 7 This demonstrates that the proposed controller overcomes the limitation of needing to acquire upper bound information on disturbances by designing an adaptive law of constraint function for the switching gain of dynamic sliding mode control, enabling the parallel robot system to quickly overcome disturbances and reduce chattering in sliding mode control. Figure 8 This demonstrates that, under the action of the dual adaptive high robustness controller of the parallel robot used for automotive electrophoretic coating conveying, the control system has high trajectory tracking accuracy. Therefore, this invention can improve the anti-disturbance performance of the parallel robot system and realize high robustness motion control of the parallel robot control system.

Claims

1. A dual adaptive high robustness control method for a parallel robot, characterized in that: The steps include: 1) For the parallel robot, kinematic analysis is performed and a dynamic model containing the lumped interference terms of the parallel robot modeling error, mechanism joint friction and external interference is established; 2) Determine the expected motion trajectory of the parallel robot end position according to the actual production process requirements; 3) Based on the parallel robot dynamics model established in step 1), a parallel robot dynamics sliding mode controller with adaptive switching gain is designed. By designing an adaptive law of the constraint function for its switching gain, the limitation of obtaining the upper bound information of the interference is broken through, so that the parallel robot system can quickly overcome the interference effect and weaken the chattering of the sliding mode control; 4) Based on step 3), an extended state observer with adaptive bandwidth gain is designed to break through the zero condition restriction of the change rate of the interference term, reduce the initial observation error peak of the observation value, and realize real-time estimation and compensation of the parallel robot system interference, thereby reducing the burden of the sliding mode controller to overcome the system interference, further improving the system robustness, and further weakening the sliding mode control chattering; 5) Based on the distributed structure of "host computer + slave computer", a dual adaptive high robustness control system of parallel robots is constructed, where the host computer is a computer and the slave computer is a multi-axis motion controller; 6) Sending the calculated control amount of each active joint of the parallel robot to each motor driver to make the parallel robot move along the desired trajectory; The specific process of step 3) is as follows: The Lagrange method is used to establish the dynamic model of the lumped disturbance term including the parallel robot modeling error, mechanism joint friction and external disturbance: In the formula, are the position, velocity and acceleration of each active joint of the parallel robot respectively; is the lumped disturbance term including the parallel robot modeling error, mechanism joint friction and external disturbance. They are the nominal inertia matrix, the nominal Coriolis force and centrifugal force terms, and the nominal gravity term; ΔM(x)∈R n×n , ΔG(x)∈R n is the model error; and F(t)∈R n is the friction term, τ d is the external disturbance term, τ is the active joint driving force / torque; make In the formula, They are the posture error and velocity error of the terminal posture of the parallel robot respectively; are the expected position and velocity of the end position of the parallel robot respectively; The sliding surface is designed by formula (2): In the formula, η=diag(η1,η 2, …,η n ),η1,η 2, …,η n All are adjustable parameters, satisfying the Hurwitz stability criterion; Derivative the two ends of the sliding surface of equation (3) with respect to time to obtain: In the formula, are the actual acceleration and expected acceleration of the end position of the parallel robot respectively; Select the reaching law as: In the formula, λ=diag(λ1,λ2,…,λ n ); According to equation (5), a constraint function adaptive law for adjusting the switching gain λ of the parallel robot dynamic sliding mode control is designed as follows: In the formula, λ a (t) and λ b (S(t)) are respectively and Switch the value of gain λ at any time, are all adjustable parameters, and t satisfies the inequality The minimum solution of , where ε is an adjustable parameter related to the neighborhood where the dynamic sliding mode variable converges. The limited convergence time of the sliding mode variable can be obtained through Lyapunov stability analysis; Combining equations (1), (3), (5), and (6), the dynamic sliding mode control law of the parallel robot with adaptive switching gain is obtained as follows: The specific process of step 4) is as follows: definition In the formula, is the end position velocity of the parallel robot; τ is the active joint driving force / torque; D is the lumped interference term of the parallel robot; τ a , α1 and α2 are defined auxiliary variables; G is the gravity term; C is the Coriolis force and centrifugal force term; According to formula (1), an extended state observer of a parallel robot that can break through the condition that the change rate of the interference term is zero is designed as follows: In the formula, e a is the error between the actual value and the observed value of the end position velocity of the parallel robot; M is the inertia matrix; ζ1=diag(2ω0,2ω 0, …,2ω0),ζ2=diag(ω0 2 ,ω0 2 ,…,ω0 2 );ω0 is an adjustable constant related to the observer gain; are the observed values ​​of α1 and α2 respectively, and there is According to the tracking error e, the extended state observer bandwidth gain adaptive law is designed as follows: In the formula, is an adjustable parameter within the acceptable error range of the system; are the lower and upper limits of the observer gain, respectively, where the parameter ω0 is arrive The transition process can be expressed as In the formula, tt is the adjustable transition time, t1 is the time required to meet the error condition When is the time point corresponding to the system; By designing the above bandwidth gain adaptive law and reasonably selecting tt, the observation accuracy of the adaptive bandwidth gain extended state observer on the lumped interference term can be guaranteed and the initial observation error peak value of the observation value can be reduced; The estimated value of the lumped disturbance term in the parallel robot dynamics model in formula (9) is Substituting into equation (7), we can obtain the dual adaptive high robustness control law of the parallel robot: τ=τ1+τ2 (13) Where τ1 is the control quantity of the parallel robot adaptive switching gain dynamic sliding mode controller, τ2 is the compensation quantity of the adaptive bandwidth gain extended state observer for the lumped disturbance term, and 2. The dual adaptive high robustness control method for parallel robots according to claim 1, characterized in that: The specific process of step 5) is as follows: Taking Taidao's multi-axis motion controller (UMAC) as the core control unit, a parallel robot dual adaptive high robustness control system is constructed based on the distributed structure of "host computer + slave computer". The host computer is a computer and the slave computer is a multi-axis motion controller. The UMAC axis channel expansion card ACC-24E2A of the lower computer communicates with the servo drive to realize the encoder information collection and the output function of the drive control signal, and completes the motion control of the parallel robot. The lower computer application development steps of the parallel robot dual adaptive high robustness control system are as follows: First, set the parameter presets that can realize the dual adaptive high robustness control of the parallel robot in UMAC, set Ixx02 to define the servo motor command output address, set Ixx03 to define the servo motor position loop feedback address, set Ixx59 to choose to use the built-in servo algorithm or use an external custom algorithm, set Ixx69 to define the servo motor output pulses, and set I7mn0 to define the nth channel encoder / timer decoding method of the mth servo chip; Secondly, write the desired motion trajectory program that can meet the dual adaptive high robustness control target requirements of the parallel robot; Then, write a custom algorithm program for the dual adaptive high robustness control of the parallel robot; The host PC implements functions including system initialization, data processing, code compilation and real-time monitoring of the parallel robot's operating status. The steps for developing the host computer application for the parallel robot's dual adaptive high robustness control system are as follows: Firstly, the communication function between the upper and lower computers is realized based on the PComm32W dynamic link library; Secondly, download the desired motion trajectory program that can meet the dual adaptive high robustness control target requirements of the parallel robot; Then, the pre-written PMC file of the parallel robot dual adaptive high robustness control custom algorithm is downloaded to the UMAC buffer to realize the dual adaptive high robustness motion control of the parallel robot.

Images