Multi-parallel platform self-adaptive vibration reduction control method based on RBFNN dynamic surface

Abstract

The invention relates to a multi-parallel platform self-adaptive vibration reduction control method based on an RBFNN (Radial Basis Function Neural Network) dynamic surface. The multi-parallel platform self-adaptive vibration reduction control method comprises the following steps of establishing a kinematics inverse solution model for a multi-channel parallel platform and performing kinematics inverse solution; establishing an environment contact force model to obtain a force error obtained by subtracting the expected force from the environment contact force; respectively inputting the force error into a dynamic surface self-adaptive module based on an RBF network and an impedance control module based on mass-damping-spring to obtain a position correction amount and a position compensation amount, and adjusting a movable platform expected position of the multi-channel parallel platform to enable the environment contact force to approach the expected force, so as to achieve the purpose of improving the stability of the multi-channel parallel platform. And the vibration reduction control of the multi-channel parallel platform is realized. According to the method, high-frequency vibration is suppressed through the dynamic surface technology, nonlinear disturbance is compensated through the RBFNN, namely the radial basis function neural network, the force error amplitude is reduced, platform vibration is effectively suppressed, and the adaptability of a system to a dynamic change environment is improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of parallel robot control, in particular to a multi-parallel platform adaptive vibration suppression control method based on an RBFNN dynamic surface. BACKGROUND

[0002] A multi-channel parallel platform, such as a six-degree-of-freedom Stewart platform, is usually composed of a static platform, i.e., a lower platform, and a dynamic platform, i.e., an upper platform, and is driven to realize multi-degree-of-freedom motion by controlling the extension and retraction of each electric cylinder. Such a platform is prone to vibration in actual application due to external interference and internal parameter uncertainty, which further affects its positioning accuracy and stability. Traditional vibration suppression control methods, such as PID control, fuzzy control, and traditional adaptive impedance control, can suppress platform vibration to some extent, but they are difficult to cope with complex situations such as system nonlinearity, strong coupling, and parameter uncertainty. In recent years, adaptive control methods based on neural networks have shown great potential in the field of vibration suppression control due to their strong self-learning ability and nonlinear approximation ability. Among them, the radial basis function (RBF) neural network has become a research hotspot due to its simple structure, fast convergence speed, and high approximation accuracy.

[0003] However, existing RBF network-based vibration suppression control methods still have some shortcomings: 1. Traditional RBF networks rely on analytical derivatives or numerical differentiation, which can introduce noise and errors and increase computational burden; 2. Traditional methods have poor robustness to unmodeled dynamics and external disturbances of the system, making it difficult to ensure the stability and control accuracy of the system. SUMMARY

[0004] The purpose of the present application is to provide a multi-parallel platform adaptive vibration suppression control method based on an RBFNN dynamic surface, which suppresses high-frequency vibration through dynamic surface technology and compensates for nonlinear disturbances through an RBFNN, i.e., a radial basis neural network, to reduce the amplitude of force error and effectively suppress platform vibration, thereby improving the system's ability to adapt to dynamic changes in the environment.

[0005] The technical solution adopted by the present application is as follows: a multi-parallel platform adaptive vibration suppression control method based on an RBFNN dynamic surface, comprising the following steps: S1: Establishing a kinematic inverse model for a multi-channel parallel platform, performing kinematic inverse solution on the expected position of the dynamic platform of the multi-channel parallel platform, and inversely solving the motion of the dynamic platform of the multi-channel parallel platform to obtain the motion of each single channel; and controlling the motion of each single channel to realize overall motion control of the dynamic platform of the multi-channel parallel platform. ​​S2: According to the actual position of the moving platform of the multi-channel parallel platform, the environmental position, the environmental damping coefficient and the environmental stiffness coefficient, an environmental contact force model is established, and the environmental contact force is obtained ; The expected force set in advance is subtracted ; ; S3: The force error e is input into the dynamic surface adaptive module based on the RBF network and the impedance control module based on the mass-damping-spring, respectively, to obtain the position correction amount from the impedance control module and the position compensation amount u from the dynamic surface adaptive module, so as to obtain the total position adjustment amount ; The expected position of the moving platform of the multi-channel parallel platform is adjusted , and the reference position of the moving platform of the multi-channel parallel platform is obtained ; through cyclic adjustment, an adaptive vibration reduction control system is established, so that the environmental contact force approaches the expected force , vibration control of the multi-channel parallel platform is realized, and vibration suppression of the multi-channel parallel platform is achieved.

[0006] Further, the environmental contact force model is a spring-damping model, and the specific expression is: ; wherein, represents the environmental contact force, X e represents the environmental position, i.e. the actual position of the environmental surface, X represents the actual position of the moving platform of the multi-channel parallel platform, b e represents the damping coefficient of the environmental contact force model, and k e represents the stiffness coefficient of the environmental contact force model, represents the first derivative of the environmental position.

[0007] Further, the specific expression of the position correction amount output by the impedance control module based on the mass-damping-spring is:

[0008] wherein, m z represents the mass coefficient of the impedance control module, b z represents the damping coefficient of the impedance control module, k z represents the stiffness coefficient of the impedance control module, and s represents a complex frequency domain variable.

[0009] Furthermore, the dynamic surface adaptive control module based on RBF network includes an input layer, an RBF hidden layer, and an output layer; The input to the input layer is the force error e and the first derivative of the force error e. The output is a dynamic surface. ,in, Indicates the gain coefficient. ;RBF hidden layer is ,in, This is a vector composed of the output values ​​of the radial basis functions. Let n be the nth radial basis function output value in the vector formed by the radial basis function output values, where n is a positive integer; The portion of the adaptive vibration reduction control system excluding the dynamic adaptive module based on the RBF network is considered as a single system. This system is a nonlinear system, and its specific expression is as follows: ; in, Let W represent the ideal weight vector, which is a nonlinear system. This represents the transpose of the ideal weight vector. Indicates the approximation error; Let the output of the dynamic adaptive module based on the RBF network be... Approximating nonlinear systems The output of the dynamic adaptive module based on the RBF network can be obtained. The specific expression is: ; in, This represents the estimated vector of the ideal weight vector W. This represents the transpose of the estimated vector of the ideal weight vector; Estimated vector of the ideal weight vector of the RBF network To perform an update, the specific expression is: ; in, The update rate represents the estimated vector of the ideal weight vector W. Let S denote the positive definite gain matrix; The specific formula for updating the estimated ideal weight vector is as follows: ; in, This represents the estimated vector of the ideal weight vector after the (N+1)th update. This represents the estimated vector of the ideal weight vector after the Nth update. N represents the time interval for each update, where N is an integer greater than 0; The specific expression of the output layer output position compensation amount u is: ; Wherein, represents the transpose of the estimated vector of the ideal weight vector, represents a vector composed of radial basis function output values, and K represents a feedback gain coefficient.

[0010] Further, the adjusting formula of the moving platform reference position X f of the multi-channel parallel platform is: ; Wherein, X f represents a reference position, U represents a position total adjusting amount, represents a position correction amount, and u represents a position compensation amount. The process of the cyclic adjustment is as follows: the moving platform reference position X of the multi-channel parallel platform obtained after adjustment is subjected to inverse kinematics to obtain expected motion amounts of each channel , the expected motion amounts of each channel are subjected to closed-loop control to obtain actual motion amounts of each channel ; the actual motion amounts of each channel act on the multi-channel parallel platform to obtain the actual position X of the moving platform of the multi-channel parallel platform; the difference between the actual position X of the moving platform of the multi-channel parallel platform and the environmental position is input to the environmental contact force model again, and the whole process is repeatedly cycled, so that the difference between the actual position X of the moving platform of the multi-channel parallel platform and the environmental position is continuously reduced, thereby realizing the effect of reducing the environmental contact force .

[0011] The present application has the following beneficial effects: (1) The present application adopts dynamic surface control technology, combines tracking error and its derivative, and converts complex system dynamics into a simplified first-order model , which greatly reduces the design complexity of the control module; compared with the traditional method, the present application does not need to derive high-order error equations step by step, significantly reduces the parameter adjustment dimension, and makes the control module more easily realized in engineering; the dynamic surface technology can also quickly capture the transient characteristics of the system, automatically suppresses external disturbances and model uncertainties in the convergence process, and is especially suitable for precision machining, robot high-frequency motion and other scenes that require fast stability and vibration suppression; (2) The RBF network is used to globally and highly accurately approximate unknown nonlinear dynamics in the system, such as friction, unmodeled dynamics and external disturbances, solve the performance bottleneck of the traditional linear control module in the strong nonlinear scene, and dynamically generate compensation signals based on the real-time collected force error information to offset the influence of vibration sources and disturbances; (3) The dynamic surface adaptive control module of the RBF network can guarantee the accurate control of the contact force and trajectory through nonlinear dynamic compensation and fast error convergence, and the universality under complex working conditions is significantly better than that of the traditional method. Even if the load inertia is unknown or sudden external force disturbance occurs, the compliant motion can still be maintained to avoid damage to the workpiece. BRIEF DESCRIPTION OF DRAWINGS

[0012] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0013] Figure 1 The control flowchart of the embodiment of the present application is shown in the figure. Figure 2 The network structure diagram of the dynamic surface adaptive control module based on the RBF network in the embodiment of the present application is shown in the figure. Figure 3 The algorithm flowchart of the dynamic surface adaptive control module based on the RBF network in the embodiment of the present application is shown in the figure. Figure 4 The force error comparison diagrams of the traditional adaptive impedance control method and the method described in the embodiment of the present application under step disturbance and sinusoidal disturbance are shown in the figure. (a) is the force error comparison diagram under step disturbance, and (b) is the force error comparison diagram under sinusoidal disturbance. Figure 5 The structure diagram of the multi-channel parallel platform and the reference coordinate system diagram in the embodiment of the present application are shown in the figure. Figure 6 The diagram of the i th channel in the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0014] In order to more clearly illustrate the above-mentioned purposes, features and advantages of the present application, the present application will be further described in detail below in combination with the drawings and specific embodiments. In the following description, a large number of specific details are set forth in order to fully understand the present application, but the present application can also be implemented in other ways different from those described herein, and therefore, the present application is not limited to the specific embodiments disclosed below.

[0015] As shown in the figure, the adaptive vibration reduction control method of the multi-parallel platform based on the RBFNN dynamic surface includes the following steps: Figure 1 S1: A kinematic inverse model is established for the multi-channel parallel platform, and the expected position of the moving platform of the multi-channel parallel platform is calculated. S2: The expected velocity of the moving platform is calculated according to the expected position of the moving platform. kinematic inverse solution of the motion, the desired position of the moving platform of the multi-channel parallel platform is solved by the inverse solution of the motion of each single channel; by controlling the motion of each single channel, the overall motion control of the moving platform of the multi-channel parallel platform is realized. Wherein, the desired position of the moving platform refers to the target spatial position or trajectory that the end effector of the multi-channel parallel platform is expected to reach or track; in the embodiments of the present application, the desired position of the moving platform represents the ideal position that the moving platform of the multi-channel parallel platform should reach under no environmental disturbance.

[0016] The kinematic inverse solution process is as follows: As shown in Figure 5 , a structural diagram of the multi-channel parallel platform is established and a reference coordinate system is established, and the center point O B of the lower platform is established as the origin of the global coordinate system {B}, and the center point O p of the upper platform is established as the origin of the local coordinate system {P}, and the coordinates of each point in the global coordinate system {B} and the local coordinate system {P} are obtained: ; Wherein, represents the coordinates of the i-th upper platform point, represents the coordinates of the i-th lower platform point, represents the angle between the connecting line of the i-th upper platform point and the upper platform center point O p and the x-axis of the local coordinate system {P}, represents the angle between the connecting line of the i-th lower platform point and the lower platform center point O B and the x-axis of the global coordinate system {B}, R P represents the radius of the upper platform, R B represents the radius of the lower platform.

[0017] The schematic diagram of the i-th channel is shown in Figure 6 , and the local coordinate system B i -x-y-z and the local coordinate system P i -x-y-z are established with the i-th lower platform point B i and the i-th upper platform point P i as the origin, respectively. The z-axis of the local coordinate system B i -x-y-z and the local coordinate system P i -x-y-z is along the axis of the actuator, and the vector from the lower platform center point O B to the lower platform point B i is defined as b i , and the vector from the upper platform center point O P to the upper platform point P i is defined as p iFrom the center point O of the lower platform B Go to the central point O of the platform P Let the vector be t, and the lower platform point be B. i Go to the platform point P i The vector is l i That is, the position and elongation of the actuator in a certain pose are represented by the vector l. i express.

[0018] The rotation matrix R of the upper platform about the z-axis z for: ; The final rotation matrix R of the upper platform is: ; in, This represents the angle by which the local coordinate system {P} rotates counterclockwise around the x-axis of the global coordinate system {B}. This represents the angle by which the local coordinate system {P} rotates counterclockwise around the y-axis of the global coordinate system {B}. This represents the angle by which the local coordinate system {P} rotates counterclockwise around the z-axis of the global coordinate system {B}.

[0019] The relationship between the angular velocity of the platform in the global coordinate system {B} and its rotation angle about the ZYX axes in the local coordinate system {P} for: ; The relationship between the acceleration of the platform in the global coordinate system {B} and its rotation angle about the ZYX axes in the local coordinate system {P} for: ; in, express The first derivative, express The first derivative, express The first derivative, express The second derivative, express The second derivative, express The second derivative is defined as follows: .

[0020] Finally, the inverse kinematics formulas for the motion vector of a single channel and the positions of the upper and lower platform points can be obtained as follows: ; in, The length of the module is denoted as .

[0021] The single-channel expected motion signal is input into the single-channel feedback-controlled output single-channel actual motion amount , and the single-channel actual motion amount is input into the multi-channel parallel platform to obtain the end actual position X of the multi-channel parallel platform.

[0022] S2: According to the moving platform actual position of the multi-channel parallel platform, the environment position, the environment damping coefficient and the environment stiffness coefficient, an environment contact force model is established, and the environment contact force F is obtained , the environment contact force F is subtracted by the pre-set expected force F , and the force error e of the environment contact force minus the expected force is obtained: .

[0023] The environment contact force model is a spring-damping model, and the specific expression is: ; Wherein, represents the environment contact force, X e represents the environment position, i.e. the actual position of the environment surface, X represents the actual position of the moving platform of the multi-channel parallel platform, b e represents the damping coefficient of the environment contact force model, and k e represents the stiffness coefficient of the environment contact force model, represents the first derivative of the environment position.

[0024] S3: The force error e is input into the dynamic surface adaptive control module based on RBF network and the impedance control module based on mass-damping-spring respectively, and the position correction amount u from the impedance control module and the position compensation amount u from the dynamic adaptive module are obtained respectively, so as to obtain the total position adjustment amount u , which is used to adjust the expected position of the moving platform of the multi-channel parallel platform , and further obtain the reference position of the moving platform of the multi-channel parallel platform ; through cyclic adjustment, an adaptive vibration reduction control system is established, so that the environment contact force F approaches the expected force F , the vibration reduction control of the multi-channel parallel platform is realized, and the vibration suppression of the multi-channel parallel platform is realized.

[0025] The specific expression of the position correction amount u output by the impedance control module based on mass-damping-spring is: ; ​wherein, m z represents the mass coefficient of the impedance control module, b z represents the damping coefficient of the impedance control module, k z represents the stiffness coefficient of the impedance control module, s represents a complex frequency domain variable.

[0026] As shown in Figure 2 , the dynamic surface adaptive control module based on the RBF network comprises an input layer, an RBF hidden layer and an output layer; The input of the input layer is the force error e and the first derivative of the force error e , and the output is the dynamic surface , wherein, represents a gain coefficient, ; the RBF hidden layer is , wherein, is a vector composed of radial basis function output values, is the nth radial basis function output value in the vector composed of radial basis function output values, and n is a positive integer; The part of the adaptive vibration suppression control system except the dynamic surface adaptive control module based on the RBF network is regarded as a system, the input of which is the force error e and the output of which is the position compensation amount u. Since the multi-channel parallel platform itself has high nonlinearity, the system containing the multi-channel parallel is also nonlinear. The specific expression of the system is: ; wherein, represents a nonlinear system, W represents an ideal weight vector, represents the transpose of the ideal weight vector, represents an approximation error.

[0027] Let the output of the dynamic surface adaptive control module based on the RBF network approximate the nonlinear system , and the specific expression of the output of the dynamic surface adaptive control module based on the RBF network is: ; wherein, represents an estimated vector of the ideal weight vector W, represents the transpose of the estimated vector of the ideal weight vector.

[0028] The estimated vector of the ideal weight vector of the RBF network is updated, and the specific expression is: ; wherein, The update rate represents the estimated vector of the ideal weight vector W. Let S denote the positive definite gain matrix, and let S denote the dynamic surface.

[0029] The specific formula for updating the estimated ideal weight vector is as follows: ; in, This represents the estimated vector of the ideal weight vector after the (N+1)th update. This represents the estimated vector of the ideal weight vector after the Nth update. N represents the time interval for each update, where N is an integer greater than 0.

[0030] The specific expression for the output position compensation amount u of the output layer is: ; in, This represents the transpose of the estimated vector of the ideal weight vector. This represents the vector formed by the output values ​​of the radial basis functions, and K represents the feedback gain coefficient.

[0031] Reference position X of the moving platform of the multi-channel parallel platform f The adjustment formula is: ; Among them, X f Indicates the reference position, and U represents the total position adjustment. represents the position correction amount, and u represents the position compensation amount.

[0032] The cyclic adjustment process is as follows: the reference position of the moving platform of the multi-channel parallel platform obtained after adjustment. The expected motion quantities of each channel are obtained through inverse kinematics. Expected motion volume of each channel The actual motion volume of each channel is controlled through a closed loop. The actual amount of movement in each channel Applying this to a multi-channel parallel platform, we obtain the actual position X of the moving platform; the actual position X of the moving platform of the multi-channel parallel platform is compared with the environmental position. The difference is then input into the environmental contact force model, continuously cycling the entire process, so that the actual position X of the moving platform of the multi-channel parallel platform is different from the environmental position. The difference continuously decreases, thereby reducing the environmental contact force. Its function.

[0033] like Figure 3As shown, the algorithm flow of the dynamic surface adaptive control module based on RBF network is as follows: Step 1: Set the initial weights and parameters; Step 2: Measure and read the force error and its derivative; Step 3: Calculate the dynamic surface; Step 4: Update and estimate the ideal network vector; Step 5: Calculate and update the control input; Step 6: Output the control signal and return to Step 2 for looping.

[0034] like Figure 4 As shown in (a), a vertical step disturbance is applied to the multi-channel parallel platform, and control is performed using both the traditional adaptive impedance control method and the method described in this embodiment of the invention. Figure 4 As can be seen from (a) in the figure, the method of the present invention has a significantly better effect on suppressing force error than the traditional adaptive impedance control method. Figure 4 As shown in (b), a sinusoidal disturbance in the vertical direction is applied to the multi-channel parallel platform, and control is performed using both the traditional adaptive impedance control method and the method described in this embodiment of the invention. Figure 4 As can be seen from (b) in the figure, the method described in the embodiments of the present invention has a significantly better effect on suppressing force errors than the traditional adaptive impedance control method. Therefore, it can be concluded that the vibration reduction effect of the method described in the embodiments of the present invention is better than that of the traditional adaptive impedance control method.

[0035] The RBF network structure used in this embodiment of the invention is simple and requires only a small number of hidden layer nodes to operate efficiently. Combined with the low-order design of dynamic surface technology, the overall algorithm computation is far lower than that of deep learning solutions. The adaptive mechanism reduces the dependence on manual parameter tuning. Engineers only need to set the initial network size and adaptive gain, and the system can automatically optimize through online learning, which greatly reduces the debugging cycle and maintenance costs, providing a cost-effective solution for industrial implementation.

[0036] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-parallel platform adaptive vibration control method based on the dynamic surface of the RBFNN, characterized in that, The method comprises the following steps: S1: Establish an inverse kinematics model for a multi-channel parallel platform, and determine the desired position of the moving platform of the multi-channel parallel platform. The motion is solved by inverse kinematics, and the desired position of the multi-channel parallel platform is obtained. The inverse kinematics is solved into the motion of each individual channel; by controlling the motion of each individual channel, the overall motion control of the multi-channel parallel platform is realized. S2: According to the actual position of the moving platform of the multi-channel parallel platform, the environmental position, the environmental damping coefficient and the environmental stiffness coefficient, an environmental contact force model is established, and the environmental contact force is obtained , the environmental contact force is subtracted from the pre-set expected force , and the force error e of the environmental contact force minus the expected force is obtained ； S3: force error The dynamic surface adaptive module based on RBF network and the impedance control module based on mass-damping-spring are input respectively to obtain the position correction amount from the impedance control module and the position compensation amount u from the dynamic surface adaptive module, so as to obtain the total position adjustment amount The expected position of the moving platform of the multi-channel parallel platform is adjusted, and the reference position of the moving platform of the multi-channel parallel platform is obtained The adaptive vibration reduction control system is established through cyclic adjustment, so that the environmental contact force approaches the expected force The vibration reduction control of the multi-channel parallel platform is realized, and the vibration of the multi-channel parallel platform is suppressed.​​​ 2. The adaptive vibration control method for a multi-parallel platform based on the dynamic surface of the RBFNN according to claim 1, characterized in that, The environment contact force model is a spring-damping model, and a specific expression is as follows: ； wherein, represents the environmental contact force, X e represents the environmental position, i.e. the actual position of the environmental surface, X represents the actual position of the moving platform of the multi-channel parallel platform, b e represents the damping coefficient of the environmental contact force model, k e represents the stiffness coefficient of the environmental contact force model, represents the first derivative of the environmental position.

3. The adaptive vibration control method for a multi-parallel platform based on the dynamic surface of the RBFNN according to claim 2, characterized in that, a correction amount of the position output by the mass-damper-spring-based impedance control module The specific expression is: ； where m z represents the mass coefficient of the impedance control module, b z represents the damping coefficient of the impedance control module, k z represents the stiffness coefficient of the impedance control module, s represents a complex frequency domain variable.

4. The adaptive vibration control method for a multi-parallel platform based on the dynamic surface of the RBFNN according to claim 3, characterized in that, The dynamic surface adaptive control module based on the RBF network comprises an input layer, an RBF hidden layer and an output layer. The input of the input layer is force error e and first derivative of force error e , and the output is dynamic surface , wherein, represents a gain coefficient, ; the RBF hidden layer is , wherein, is a vector composed of radial basis function output values, is the nth radial basis function output value in the vector composed of radial basis function output values, and n is a positive integer; A part of the adaptive vibration control system except the dynamic surface adaptive control module based on the RBF network is regarded as a system, and the system is a nonlinear system, and a specific expression is as follows: ； wherein, represents a nonlinear system, W represents an ideal weight vector, represents a transpose of the ideal weight vector, represents an approximation error; Let the output of the dynamic adaptive module based on RBF network approximating a nonlinear system , the output of the dynamic adaptive module based on RBF network is ； wherein denotes an estimate vector of the ideal weight vector W, denotes the transpose of the estimate vector of the ideal weight vector. An estimated vector of ideal weight vectors for a RBF network The update is performed with the expression: ； wherein, denotes the update rate of the estimate vector of the ideal weight vector W, denotes a positive definite gain matrix, S denotes a dynamic surface; A specific formula for updating the estimation vector of the ideal weight vector is as follows: ； wherein, represents an estimated vector of the ideal weight vector after the N+1th update, represents an estimated vector of the ideal weight vector after the Nth update, is a time interval for each update, N is an integer and greater than 0; A specific expression of the output layer outputting the position compensation quantity u is as follows: ； wherein denotes the transpose of the estimated vector of ideal weight vectors, denotes a vector of radial basis function output values, K denotes a feedback gain coefficient.

5. The adaptive vibration control method for a multi-parallel platform based on the dynamic surface of the RBFNN according to claim 4, characterized in that, Reference position X of moving platform of multi-channel parallel platform f The adjustment formula is: ； wherein X f represents a reference position, U represents a position total adjustment amount, represents a position correction amount, and u represents a position compensation amount; The process of the cycle regulation is to regulate the reference position of the moving platform of the multi-channel parallel platform The expected motion amount of each channel is obtained through the inverse kinematics solution The expected motion amount of each channel The actual motion amount of each channel is controlled through the closed loop control The actual motion amount of each channel The actual position X of the moving platform of the multi-channel parallel platform is obtained by acting on the multi-channel parallel platform The difference between the actual position X of the moving platform of the multi-channel parallel platform and the environmental position is input to the environmental contact force model again, and the whole process is continuously cycled, so that the difference between the actual position X of the moving platform of the multi-channel parallel platform and the environmental position is continuously reduced, thereby realizing the effect of reducing the environmental contact force ​​

Images