A parallel platform control method based on ADRC and consistency algorithm

Abstract

The present application relates to a parallel platform control method based on ADRC and a consistency algorithm, comprising the following steps: designing an ADRC controller for each electric cylinder; the ADRC controller includes an extended state observer (ESO) and a state error feedback controller; designing a consistency control algorithm with displacement and velocity coordination for coordinated control, and inputting the output of the coordinated control into the state error feedback controller to achieve high-precision control of the Stewart platform; the coordination factor and tracking factor in the consistency control algorithm are determined based on a cooperative Markov game. The present invention improves the problems of first-order ADRC control of a single electric cylinder, such as inability to adapt to system dynamics, low control accuracy, weak anti-interference capability, and poor robustness, by using third-order ADRC and a second-order consistency algorithm. It also improves the problems of limited accuracy, poor stability, and insufficient anti-interference capability that occur when using velocity coordinated control of multiple cylinders.

Description

Technical Field

[0001] The present application relates to the field of parallel robot control, and specifically to a parallel platform control method based on ADRC and consistency algorithm. Background Art

[0002] As a parallel robot structure, the Stewart platform typically consists of a fixed base and a movable upper platform. N independently driven electric cylinders connect the fixed base and the upper platform via 2N universal joints, enabling the upper platform to move with N degrees of freedom. Due to its high degrees of freedom, high precision, high rigidity, and high load capacity, the Stewart platform is widely used in aircraft simulators, aerospace device testing, medical surgical robots, motion simulation platforms, vibration table experiments, and simulated driving training.

[0003] The current mainstream control strategy for Stewart platforms is as follows: after receiving the dynamic platform's pose information, the pose controller on the lower platform uses an inverse kinematics algorithm to determine the position of the connection between the dynamic platform and each electric cylinder, thereby determining the extension of each cylinder rod. The dynamic platform's pose control is then achieved by varying the extension of each of the N electric cylinders. This transforms the original multi-input, multi-output system into N mutually coupled single-input, single-output systems. While this approach reduces the complexity of Stewart platform pose control, it also has drawbacks. First, while theoretically the parameters of the six electric cylinders are consistent, in practice there are still some differences. Furthermore, after a period of use, the degree of running-in and circuit aging of each cylinder make it difficult to maintain consistency. Second, the N parallel electric cylinders are strongly coupled through the upper platform, resulting in mutual interference. Third, the Stewart platform itself exhibits a certain amount of interference. Due to these three factors, mainstream control strategies struggle to achieve high-precision pose control.

[0004] Patent publication CN112847303B proposes a coordinated control method for a Stewart platform. This collaborative control algorithm mitigates the problems of position mismatch and overfitting among the six electric cylinders in the Stewart platform, as well as mutual disturbances among the six cylinders, caused by objective internal differences and varying external operating conditions. Furthermore, an ADRC (Active Disturbance Rejection Control) controller is employed to control the motion of individual electric cylinders, improving both precision and robustness. However, this method still has two shortcomings: on the one hand, this method only uses first-order anti-disturbance control for a single cylinder, and can only observe one state, which may not be able to capture more complex system dynamic characteristics, resulting in low control accuracy; it may not be able to effectively suppress the impact of large-scale and frequently changing external disturbances on the system; it lacks sufficient robustness in the face of changes in internal system parameters and external environment changes, and has weak precise control capabilities for higher-order systems; on the other hand, this method uses a single speed consistency control for the coordinated control of multiple cylinders, only considering the speed response of the electric cylinder, ignoring the defects of position error, which may lead to insufficient accuracy of the extension and retraction of the electric cylinder and inability to achieve precise control; it ignores the impact of position error on the stability of the electric cylinder system, and oscillation may occur during the operation of the electric cylinder, reducing stability; it lacks the ability to correct position error and has weak resistance to external interference. Summary of the Invention

[0005] The purpose of the present invention is to propose a parallel platform control method based on ADRC and consistency algorithm. Through third-order ADRC and second-order consistency algorithms, the problems of first-order ADRC control of a single electric cylinder, such as not adapting to system dynamic changes, low control accuracy, weak anti-interference ability and poor robustness, are improved. The problems of limited accuracy, poor stability and insufficient anti-interference ability of speed coordinated control of multiple cylinders are also improved.

[0006] The technical solution adopted by the present invention is: a parallel platform control method based on ADRC and consistency algorithm, which is used to perform high-precision control of the Stewart platform, specifically comprising the following steps:

[0007] S1: Consider each electric cylinder in the Stewart platform as a system, establish a control model for the control motor of each electric cylinder, and design an active disturbance rejection controller, namely ADRC controller. The ADRC controller includes an extended state observer (ESO) and a state error feedback controller. The ESO is used to observe the system input and output, estimate the system's unmodeled dynamics and external disturbances, and thus adjust the system output to offset the impact of the disturbance. The state error feedback controller is used to use the error between the estimated value and the actual value of the system output as a feedback signal based on the output of the ESO to adjust the system input to achieve system control.

[0008] S2: Design a consistent control algorithm with displacement and speed coordination based on the displacement tracking error, speed tracking error, displacement coordination error, and speed coordination error of each electric cylinder;

[0009] S3: Input the current target posture signal of each electric cylinder and the extension and contraction amount signal of the electric cylinder into the Stewart platform for kinematic inverse solution to obtain the expected extension and contraction displacement and expected extension and contraction velocity of each electric cylinder, and input them into the ADRC controller of each electric cylinder to perform ADRC control on each electric cylinder and output the extension and contraction displacement and extension and contraction velocity of each electric cylinder;

[0010] S4: Calculate the displacement tracking error, velocity tracking error, displacement coordination error and velocity coordination error of each electric cylinder based on the expected telescopic displacement, expected telescopic velocity, telescopic displacement and telescopic velocity of each electric cylinder, input them into the consistency control algorithm for coordinated control, and input the output of the coordinated control into the state error feedback controller in each ADRC controller, and perform ADRC control on each electric cylinder again to achieve high-precision control of the Stewart platform.

[0011] Furthermore, the specific expression of the extended state observer ESO is:

[0012]

[0013] Where k = 1, 2, ..., N, N is the total number of electric cylinders in the Stewart platform; is the derivative of the state estimation vector, A is the state transfer matrix; The state quantity x of the kth electric cylinder by the extended state observer ESO is k The estimated value of represents an estimate of the displacement, represents the derivative of the displacement estimator, represents an estimate of the velocity, represents the derivative of the velocity estimator, represents the estimate of acceleration, represents the derivative of the acceleration estimate, represents the extended state, which is used to estimate the unmodeled dynamics and external disturbances of the system, represents the derivative of the extended state; B is the input vector, representing the impact of external input on the system state; u k is the system input of the kth electric cylinder; L is the coefficient matrix of the difference between the actual value and the estimated value of the system output; y k is the kth electric cylinder system output, is the estimated value of the k-th electric cylinder system output by the extended state observer ESO; E is the total disturbance f of the k-th electric cylinder k The derivative of The coefficient vector of , C is the output vector.

[0014] Furthermore, the specific expression of the state error feedback controller is:

[0015]

[0016] in, represents the output of the state error feedback controller of the kth electric cylinder, K is the controller state transfer matrix, is the input matrix of the state error feedback controller.

[0017] Furthermore, the specific expression of the consistency control algorithm is:

[0018]

[0019] Among them, u kc is the coordinated input of the kth electric cylinder, c1 is the displacement coordination factor, E xk is the displacement coordination error of the kth electric cylinder, c2 is the displacement tracking factor, is the displacement tracking error of the kth electric cylinder, c3 is the speed coordination factor, is the speed coordination error of the kth electric cylinder, c4 is the speed tracking factor, is the speed tracking error of the kth electric cylinder;

[0020] The displacement tracking error Speed tracking error Displacement coordination error and speed coordination error The specific expression is:

[0021]

[0022] Among them, x k,2 is the extension and contraction speed of the kth electric cylinder, is the expected telescopic displacement of the kth electric cylinder, are the expected extension and contraction speeds of the kth electric cylinder, is the displacement tracking error of the j-th electric cylinder, is the speed tracking error of the j-th electric cylinder.

[0023] Furthermore, the displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 are determined according to a cooperative Markov game, specifically by:

[0024] The displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 are regarded as four players. For the i-th player, i = 1, 2, 3, 4, the players are discretized in the corresponding value range, and the discretized values are used as actions to form the corresponding action space A. i , A i ={a i1 ,a i2 ,…,a im ,…,a iM}, where M represents the total number of actions, a im represents the mth action of the i-th player;

[0025] The design state transfer function is: P m (s ′ |s,a 1m ,a 2m ,a 3m ,a 4m ), indicating that in state s, each player takes action a im After that, the system goes to state s ′ probability;

[0026] The reward function is designed for the action space. The smaller the difference between the Stewart platform output posture and the target posture, the larger the reward function value. The reward function form is: R im (s,a im ,a ln ,a on ,a pn ), represents the immediate rewards obtained when the i-th player takes the m-th action and the three players take the n-th action in state s, where l, o, and p represent the numbers of the other three players, i, l, o, and p ∈ [1, 2, 3, 4], and the values of i, l, o, and p are different;

[0027] R m (s,a 1m ,a 2m ,a 3m ,a 4m )=R 1m (s,a 1m ,a 2n ,a 3n ,a 4n )+R 2m (s,a 1n ,a 2m ,a 3n ,a 4n )+

[0028] R 3m (s,a 1n,a 2n ,a 3m ,a 4n )+R 4m (s,a 1n ,a 2n ,a 3n ,a 4m );

[0029] Among them, R m (s,a 1m ,a 2m ,a 3m ,a 4m ) represents the total reward function;

[0030] Take the total reward function R m (s,a 1m ,a 2m ,a 3m ,a 4m ) is the largest corresponding action combination (a 1m ,a 2m ,a 3m ,a 4m ) are used as the values of displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 respectively.

[0031] Furthermore, after the output of the coordinated control is input into the state error feedback controller in each ADRC controller, the specific expression of the state error feedback controller is:

[0032]

[0033] The beneficial effects of the present invention are:

[0034] (1) The present invention adopts third-order ADRC control for a single electric cylinder, and the extended state observer (ESO) estimates and suppresses the displacement, velocity, and acceleration disturbances of the system, which can capture more dynamic characteristics and external disturbances of the system, effectively suppress the influence of internal and external, known and unknown disturbances on the system, improve the robustness and anti-interference performance of the system, and have better control capabilities for higher-order systems; the state error feedback controller can adjust the control input in real time according to the system state error, so that the system can respond to control requirements more quickly, and improve the dynamic performance of the system;

[0035] (2) The present invention adopts a consistency algorithm to control N electric cylinders, and performs coordinated control on the displacement and speed of the extension and retraction of the N electric cylinders, thereby improving the influence of position deviation on the control accuracy and system stability, increasing the position error correction capability, and effectively improving the overall incoordination problem caused by the differences between the multiple electric cylinders themselves and the different working conditions of each electric cylinder; the most appropriate coordination factor and tracking factor can be obtained by using cooperative Markov game, thereby improving the method of selecting factor values. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0037] Figure 1 This is a control flow chart of an embodiment of the present invention;

[0038] Figure 2 is the yaw angle change curve of the Stewart platform without cooperative control when it is disturbed in the initial state;

[0039] Figure 3 The yaw angle change curve of the Stewart platform with only speed cooperative control when it is disturbed in the initial state;

[0040] Figure 4 This is a curve showing the change of the yaw angle when the embodiment of the present invention is disturbed in the initial state. DETAILED DESCRIPTION

[0041] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0042] like Figure 1 As shown, an embodiment of the present invention provides a parallel platform control method based on ADRC and a consistency algorithm for high-precision control of a Stewart platform, specifically comprising the following steps:

[0043] S1: Each electric cylinder in the Stewart platform is regarded as a system, a control model is established for the control motor of each electric cylinder, and an active disturbance rejection controller, namely ADRC controller, is designed; the ADRC controller includes an extended state observer ESO and a state error feedback controller. The extended state observer ESO is used to observe the input and output of the system, estimate the unmodeled dynamics and external disturbances of the system, and thus adjust the output of the system to offset the influence of the disturbance; the state error feedback controller is used to use the error between the estimated value and the actual value of the system output as a feedback signal according to the output of the extended state observer ESO, and is used to adjust the input of the system to achieve control of the system. Therefore, the ADRC controller has the ability to resist internal disturbances, external disturbances and unknown factors of the system itself.

[0044] The specific expression of the extended state observer ESO is:

[0045]

[0046] Where k = 1, 2, ..., N, N is the total number of electric cylinders in the Stewart platform; is the derivative of the state estimation vector, A is the state transfer matrix; The state quantity x of the kth electric cylinder by the extended state observer ESO is k The estimated value of represents an estimate of the displacement, represents the derivative of the displacement estimator, represents an estimate of the velocity, represents the derivative of the velocity estimator, represents the estimate of acceleration, represents the derivative of the acceleration estimate, represents the extended state, which is used to estimate the unmodeled dynamics and external disturbances of the system, represents the derivative of the extended state; B is the input vector, representing the impact of external input on the system state; u k is the system input of the kth electric cylinder; L is the coefficient matrix of the difference between the actual value and the estimated value of the system output; y k is the kth electric cylinder system output, is the estimated value of the k-th electric cylinder system output by the extended state observer ESO; E is the total disturbance f of the k-th electric cylinder k The derivative of The coefficient vector of , C is the output vector.

[0047] The specific expression of the state error feedback controller is:

[0048]

[0049] in, represents the output of the state error feedback controller of the kth electric cylinder, K is the controller state transfer matrix, is the input matrix of the state error feedback controller.

[0050] S2: Because each electric cylinder in the Stewart platform communicates through the posture controller on the lower platform, and the communication between the cylinders does not interfere with each other, a corresponding consistency algorithm can be designed. Each electric cylinder is treated as an independent intelligent agent. The posture controller receives the input posture signal and uses the inverse kinematic solution to calculate the desired displacement and velocity of the electric cylinder as the leader. The displacement and velocity of the six electric cylinders are followers. Based on the displacement tracking error, velocity tracking error, displacement coordination error, and velocity coordination error of each electric cylinder, a consistency control algorithm with displacement and velocity coordination is designed.

[0051] The specific expression of the consistency control algorithm is:

[0052]

[0053] Among them, u kc is the coordinated input of the kth electric cylinder, c1 is the displacement coordination factor, E xk is the displacement coordination error of the kth electric cylinder, c2 is the displacement tracking factor, is the displacement tracking error of the kth electric cylinder, c3 is the speed coordination factor, is the speed coordination error of the kth electric cylinder, c4 is the speed tracking factor, is the velocity tracking error of the kth electric cylinder.

[0054] S3: Input the current target posture signal of each electric cylinder and the extension and contraction amount signal of the electric cylinder into the Stewart platform for kinematic inverse solution to obtain the expected extension and contraction displacement and expected extension and contraction speed of each electric cylinder, and input them into the ADRC controller of each electric cylinder. ADRC control is performed on each electric cylinder, and the extension and contraction displacement and extension and contraction speed of each electric cylinder are output.

[0055] S4: Calculate the displacement tracking error, velocity tracking error, displacement coordination error and velocity coordination error of each electric cylinder based on the expected telescopic displacement, expected telescopic velocity, telescopic displacement and telescopic velocity of each electric cylinder, input them into the consistency control algorithm for coordinated control, and input the output of the coordinated control into the state error feedback controller in each ADRC controller, and perform ADRC control on each electric cylinder again to achieve high-precision control of the Stewart platform.

[0056] The displacement tracking error Speed tracking error Displacement coordination error and speed coordination error The specific expression is:

[0057]

[0058] Among them, x k,2 is the extension and contraction speed of the kth electric cylinder, is the expected telescopic displacement of the kth electric cylinder, are the expected extension and contraction speeds of the kth electric cylinder, is the displacement tracking error of the j-th electric cylinder, is the speed tracking error of the j-th electric cylinder.

[0059] In an embodiment of the present invention, the displacement coordination factor c1, the displacement tracking factor c2, the speed coordination factor c3, and the speed tracking factor c4 are determined according to a cooperative Markov game. The specific method is:

[0060] The displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 are regarded as four players. For the i-th player, i = 1, 2, 3, 4, the players are discretized in the corresponding value range, and the discretized values are used as actions to form the corresponding action space A. i , A i ={a i1 ,a i2 ,…,a im ,…,a iM}, where M represents the total number of actions, a im represents the mth action of the i-th player;

[0061] The design state transfer function is: P m (s ′ |s,a 1m ,a 2m ,a 3m ,a 4m ), indicating that in state s, each player takes action a im After that, the system goes to state s ′ probability;

[0062] The reward function is designed for the action space. The smaller the difference between the Stewart platform output posture and the target posture, the larger the reward function value. The reward function form is: R im (s,a im ,a ln ,a on ,a pn), represents the immediate rewards obtained when the i-th player takes the m-th action and the three players take the n-th action in state s, where l, o, and p represent the numbers of the other three players, i, l, o, and p ∈ [1, 2, 3, 4], and the values of i, l, o, and p are different;

[0063] R m (s,a 1m ,a 2m ,a 3m ,a 4m )=R 1m (s,a 1m ,a 2n ,a 3n ,a 4n )+R 2m (s,a 1n ,a 2m ,a 3n ,a 4n )+

[0064] R 3m (s,a 1n ,a 2n ,a 3m ,a 4n )+R 4m (s,a 1n ,a 2n ,a 3n ,a 4m );

[0065] Among them, R m (s,a 1m ,a 2m ,a 3m ,a 4m ) represents the total reward function;

[0066] Take the total reward function R m (s,a 1m ,a 2m ,a 3m ,a 4m ) is the largest corresponding action combination (a 1m ,a 2m ,a 3m ,a 4m ) are used as the values of displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 respectively.

[0067] After the output of the coordinated control is input to the state error feedback controller in each ADRC controller, the specific expression of the state error feedback controller is:

[0068]

[0069] Figures 2 to 4 The yaw angle change curves of the Stewart platform without coordinated control, the Stewart platform with only speed coordinated control in CN112847303B, and the Stewart platform with speed and position coordinated control in the embodiment of the present invention are shown in the figure below when the platform is disturbed at 0.02-0.04 seconds, 0.06 seconds, and 0.08 seconds. Figure 3 It can be seen from Figure 1 that the Stewart platform with only speed coordinated control has a certain resistance to disturbances, but at the end of the disturbance, the trajectory has obvious oscillations. Figure 4 It can be seen from the figure that the Stewart platform with coordinated speed and position control not only has enhanced disturbance resistance, but also has no oscillation after the disturbance ends.

[0070] In an embodiment of the present invention, a third-order active disturbance rejection controller (ADRC) is used on a single electric cylinder to compensate for internal and external deterministic and uncertain disturbances, achieving high-precision and interference-resistant control of the telescopic displacement, velocity, and acceleration of the single electric cylinder. Multi-agent collaborative control is employed among N electric cylinders, whereby collaborative control of the displacement and velocity of the N electric cylinders is achieved through a consensus algorithm. Each electric cylinder on the Stewart platform is treated as an agent, and the N electric cylinders form a multi-agent system. The input displacement and velocity serve as the leader displacement and velocity, and the displacement and velocity output by each of the N electric cylinders serve as the follower displacement and velocity. The telescopic displacement and velocity of each motor are then collaboratively controlled. Since different channels have differences at different times, the two synergy factors, displacement and speed, need to be adaptively adjusted. In this embodiment of the present invention, the overall posture of the platform is used as the state space of the Markov game, and the synergy factor is used as the action space to establish a Markov game model and a reward function for the synergy factor. According to the characteristics of the Markov game and the strategy selection of the intelligent agent, the Nash equilibrium solution is found by solving the optimal corresponding function of each synergy factor, thereby determining the value of the synergy factor and ultimately achieving high-precision control of the Stewart platform.

[0071] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A parallel platform control method based on ADRC and consistency algorithm, characterized in that: It is used to perform high-precision control of the Stewart platform, including the following steps: S1: Consider each electric cylinder in the Stewart platform as a system, establish a control model for the control motor of each electric cylinder, and design an active disturbance rejection controller, namely ADRC controller. The ADRC controller includes an extended state observer (ESO) and a state error feedback controller. The ESO is used to observe the system input and output, estimate the system's unmodeled dynamics and external disturbances, and thus adjust the system output to offset the impact of the disturbance. The state error feedback controller is used to use the error between the estimated value and the actual value of the system output as a feedback signal based on the output of the ESO to adjust the system input to achieve system control. S2: Design a consistent control algorithm with displacement and speed coordination based on the displacement tracking error, speed tracking error, displacement coordination error, and speed coordination error of each electric cylinder; S3: Input the current target posture signal of each electric cylinder and the extension and contraction amount signal of the electric cylinder into the Stewart platform for kinematic inverse solution to obtain the expected extension and contraction displacement and expected extension and contraction velocity of each electric cylinder, and input them into the ADRC controller of each electric cylinder to perform ADRC control on each electric cylinder and output the extension and contraction displacement and extension and contraction velocity of each electric cylinder; S4: Calculate the displacement tracking error, velocity tracking error, displacement coordination error and velocity coordination error of each electric cylinder based on the expected telescopic displacement, expected telescopic velocity, telescopic displacement and telescopic velocity of each electric cylinder, input them into the consistency control algorithm for coordinated control, and input the output of the coordinated control into the state error feedback controller in each ADRC controller, and perform ADRC control on each electric cylinder again to achieve high-precision control of the Stewart platform.

2. A parallel platform control method based on ADRC and consistency algorithm according to claim 1, characterized in that: The specific expression of the extended state observer ESO is: Where k = 1, 2, ..., N, N is the total number of electric cylinders in the Stewart platform; is the derivative of the state estimation vector, A is the state transfer matrix; The state quantity x of the kth electric cylinder by the extended state observer ESO is k The estimated value of represents an estimate of the displacement, represents the derivative of the displacement estimator, represents an estimate of the velocity, represents the derivative of the velocity estimator, represents the estimated acceleration, represents the derivative of the acceleration estimate, represents the extended state, which is used to estimate the unmodeled dynamics and external disturbances of the system, represents the derivative of the extended state; B is the input vector, representing the impact of external input on the system state; u k is the system input of the kth electric cylinder; L is the coefficient matrix of the difference between the actual value and the estimated value of the system output; y k is the kth electric cylinder system output, is the estimated value of the k-th electric cylinder system output by the extended state observer ESO; E is the total disturbance f of the k-th electric cylinder k The derivative of The coefficient vector of , C is the output vector.

3. The parallel platform control method based on ADRC and consistency algorithm according to claim 2, characterized in that: The specific expression of the state error feedback controller is: in, represents the output of the state error feedback controller of the kth electric cylinder, K is the controller state transfer matrix, is the input matrix of the state error feedback controller.

4. The parallel platform control method based on ADRC and consistency algorithm according to claim 3, characterized in that: The specific expression of the consistency control algorithm is: Among them, u kc is the coordinated input of the kth electric cylinder, c1 is the displacement coordination factor, E xk is the displacement coordination error of the kth electric cylinder, c2 is the displacement tracking factor, is the displacement tracking error of the kth electric cylinder, c3 is the speed coordination factor, is the speed coordination error of the kth electric cylinder, c4 is the speed tracking factor, is the speed tracking error of the kth electric cylinder; The displacement tracking error Speed tracking error Displacement coordination error and speed coordination error The specific expression is: Among them, x k,2 is the extension and contraction speed of the kth electric cylinder, is the expected telescopic displacement of the kth electric cylinder, are the expected extension and contraction speeds of the kth electric cylinder, is the displacement tracking error of the j-th electric cylinder, is the speed tracking error of the j-th electric cylinder.

5. The parallel platform control method based on ADRC and consistency algorithm according to claim 4, characterized in that: The displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 are determined according to a cooperative Markov game, specifically: The displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 are regarded as four players. For the i-th player, i = 1, 2, 3, 4, the players are discretized in the corresponding value range, and the discretized values are used as actions to form the corresponding action space A. i , A i ={a i1 ,a i2 ,…,a im ,…,a iM }, where M represents the total number of actions, a im represents the mth action of the i-th player; The designed state transfer function is: P m (s ′ |s,a 1m ,a 2m ,a 3m ,a 4m ), indicating that in state s, each player takes action a im After that, the system goes to state s ′ probability; The reward function is designed for the action space. The smaller the difference between the Stewart platform output posture and the target posture, the larger the reward function value. The reward function form is: R im (s,a im ,a ln ,a on ,a pn ), represents the immediate rewards obtained when the i-th player takes the m-th action and the three players take the n-th action in state s, where l, o, and p represent the numbers of the other three players, i, l, o, and p ∈ [1, 2, 3, 4], and the values of i, l, o, and p are different; R m (s,a 1m ,a 2m ,a 3m ,a 4m )=R 1m (s,a 1m ,a 2n ,a 3n ,a 4n )+R 2m (s,a 1n ,a 2m ,a 3n ,a 4n )+ R 3m (s,a 1n ,a 2n ,a 3m ,a 4n )+R 4m (s,a 1n ,a 2n ,a 3n ,a 4m ); Among them, R m (s,a 1m ,a 2m ,a 3m ,a 4m ) represents the total reward function; Take the total reward function R m (s,a 1m ,a 2m ,a 3m ,a 4m ) is the largest corresponding action combination (a 1m ,a 2m ,a 3m ,a 4m ) are used as the values of displacement coordination factor c1, displacement tracking factor c2, speed coordination factor c3 and speed tracking factor c4 respectively.

6. The parallel platform control method based on ADRC and consistency algorithm according to claim 5, characterized in that: After the output of the coordinated control is input to the state error feedback controller in each ADRC controller, the specific expression of the state error feedback controller is:

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