Redundant pneumatic parallel platform active disturbance rejection control method based on driving force decoupling optimization

Abstract

The invention provides a redundant pneumatic parallel platform active disturbance rejection control method based on driving force decoupling optimization, and the method comprises the following steps: firstly, carrying out the real-time quantification and solving a state variable and unpredictable disturbance of a pneumatic redundant parallel platform under the optimal driving force; the control accuracy and the response speed are improved through total disturbance feedforward compensation, and the influence of external interference on the system performance is effectively restrained; secondly, designing a proper sliding mode control law based on the estimated internal state of the system and the total disturbance, so as to ensure that the state of the system stably and quickly approaches a sliding mode surface; according to the invention, through estimating the total disturbance suffered by the redundant pneumatic parallel platform in the motion process and carrying out feedforward compensation, a self-adaptive gain sliding mode control law is further constructed so as to ensure that the error change between the system state and the sliding mode surface can dynamically adjust the control gain; and the control precision and stability of the complex nonlinear redundant pneumatic parallel system under the conditions of internal state uncertainty and external interference are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of parallel robot motion control. Specifically, it relates to an active disturbance rejection control method for a redundant pneumatic parallel platform considering the optimization of driving force decoupling. Background Art

[0002] At the present stage, the research on the motion planning of parallel platforms mainly focuses on single objectives such as time optimality and the shortest telescopic length of cylinders, and rarely considers the motion space constraints and external random disturbance effects suffered by parallel platforms in complex environments. As a result, in the presence of random error disturbances, the tracking control accuracy of parallel platforms and the overall robustness of parallel systems are affected. In order to plan more reasonable and effective motion trajectories, in the trajectory planning problem, multiple constraints such as the motion model, dynamic model, load capacity, and movable space of the parallel platform should be considered. Especially in application scenarios involving high dynamic responses, not only the motion paths of each actuator need to be independently optimized, but also the overall pose changes of the platform need to be synchronously planned and adjusted to ensure that the platform can exhibit excellent performance whether it is performing fine operations or rapid positioning when executing complex tasks.

[0003] Most existing control strategies are based on ideal condition assumptions and insufficiently consider the inevitable random disturbances in the actual process, resulting in a certain gap between the theoretical model and practical applications. Secondly, in order to achieve high-precision position tracking and attitude adjustment, it generally relies on complex mathematical modeling and advanced control algorithm design, but these methods often increase the computational burden of the system and reduce the real-time response performance. When it comes to multi-objective optimization problems, there is less research on how to simultaneously meet the objective requirements such as rapidity and stability and balance the contradictions between different performance indicators. Although some research has introduced intelligent learning mechanisms to enhance the adaptive ability of the system, its generalization ability and long-term stability still need to be further verified, resulting in poor intelligence of redundant parallel platforms. Summary of the Invention

[0004] In order to solve problems such as the decline in the tracking accuracy of parallel platforms and the degradation of system stability in non-predictable environments, the present invention inputs the state information and output quantities collected by the redundant parallel platform itself into the differential estimation model to estimate the current state of the platform and external non-predictable disturbances. Decouple and optimize the allocation of the redundant driving force of the platform according to the pose transformation of the parallel platform under different task requirements. At the same time, in order to ensure smooth and stable motion, based on the driving limit principle, a control law is constructed by combining the power approach and the adaptive gain strategy, and the approach rate is dynamically adjusted according to the error change between the system state and the sliding mode surface. By repeatedly executing the above steps, the tracking accuracy and anti-interference ability of the redundant parallel platform are improved.

[0005] To solve the above problems, the present invention provides an active disturbance rejection control method for a redundant pneumatic parallel platform based on driving force decoupling optimization, and the method includes the following steps:

[0006] Step 1: Quantify and solve the state variables and non-predictable disturbances under the optimal driving force of the pneumatic redundant parallel platform in real time.

[0007] Based on the Newton-Euler mechanics framework, using Newton's second law of motion, establish the dynamic equations of the system in each translational degree of freedom. When dealing with the rotational motion of the system around a fixed point or the center of mass, use Euler's equations to establish the dynamic equations about the relationship between the change rate of angular momentum and the applied torque. Further, comprehensively combine the two motion modes to obtain the dynamic equilibrium equations of all degrees of freedom of motion.

[0008] Considering the compressibility of the gas, flow friction, and the fact that the parallel platform is vulnerable to various non-predictable disturbances in the actual environment, introduce non-linear terms into the dynamic equilibrium equations to establish the dynamic mathematical model of the pneumatic redundant parallel platform. The redundant design is the redundancy of the internal driving force. Under the premise of meeting the task requirements of the redundant parallel platform, perform load distribution on the actuators.

[0009] Improper force distribution of the redundant actuators will cause internal force conflicts in the platform. Use the pseudo-inverse method to achieve the decoupling distribution of the driving force from the workspace to the joint space. By imposing constraint conditions on the driving force of the actuators, ensure that the working state of the actuators remains within the physically feasible range, while improving the anti-disturbance ability and vibration damping performance of the system. Also, consider the gas utilization rate to achieve the effective allocation of resources. Introduce appropriate weight factors to reasonably quantify the above objectives, and use advanced optimization algorithms to seek the global optimal solution to achieve the balance between high performance and low consumption.

[0010] Using the driving force equation of the actuator, calculate the position and velocity control input parameters of the actuator at each moment, and the actual position measurement value obtained by the sensor. Through the differential estimation model, calculate the accurate state estimation of the actuator and the disturbance received by the actuator. Further, based on the estimation of the actuator, calculate the accurate estimation of the driving force, and substitute it into the state parameters of the parallel platform and the total disturbance estimation equation to complete the accurate estimation of the state and non-predictable disturbance of the actuator and the redundant parallel platform at any moment.

[0011] Step 2: Design a sliding mode control law based on the system state and total disturbance estimation.

[0012] Use the current initial pose information of the redundant parallel robot and the movement to the target pose to obtain the rotation and translation transformation matrix. Through the inverse kinematics solution of the platform and coordinate system mapping, solve the length information of each branch chain in the base coordinate system of the parallel platform as the input reference signal.

[0013] A differential tracker is established based on the fast optimal comprehensive control function to process the given position signal, and the change curves of the position and its speed are analyzed. By adjusting the fast factor and filtering factor of the differentiator, the dynamic response characteristics can be changed according to the desired approaching speed and trajectory smoothness, taking into account both the speed response and trajectory smoothness.

[0014] According to the position and speed values at each sampling moment, they are substituted into the driving force equation to calculate the driving force of the actuator. The adjustable parameters of the tracking differentiator are adjusted to ensure that the driving force of the actuator is within the feasible range. Further, an error polynomial sliding mode surface containing the error and its derivative terms is designed to ensure that under external disturbances, the control strategy enables the system state to be forced to converge to the sliding mode surface and approach the desired curve trajectory along this surface.

[0015] Based on the error size of the system state trajectory reaching this sliding mode surface, through the Lyapunov inverse sliding mode surface control law, an improved adaptive control law is proposed by combining the power approach and adaptive gain strategy, which can dynamically adjust the approaching rate according to the real-time error between the system state and the sliding mode surface, accelerate the error convergence process, and ensure that the system state quickly and accurately reaches and remains on the sliding mode surface.

[0016] The beneficial effects of the active disturbance rejection control method for a redundant pneumatic parallel platform based on driving force decoupling optimization proposed by the present invention are as follows: (1) A series of constraint conditions are imposed on the driving force of the actuator, and a weight factor is introduced to comprehensively quantify and evaluate various performance indicators. According to different task requirements, the balance between the disturbance rejection ability, vibration suppression and energy consumption of the redundant parallel platform can be flexibly adjusted. For the disturbance estimation of the actuator and the parallel platform at the current moment, a differential state estimation model is designed for total disturbance feedforward compensation before the next control. (2) An error polynomial sliding mode surface of a fractional-order differential operator is proposed, and an adaptive gain sliding mode control law is constructed to ensure that the error change between the system state and the sliding mode surface can dynamically adjust the control gain, providing a new solution for the high-performance control of complex nonlinear systems. Description of the Drawings

[0017] Figure 1 It is a schematic diagram of the basic process of the embodiment of the present invention;

[0018] Figure 2 It is a schematic diagram of the coordinate system of the redundant parallel platform in the embodiment of the present invention;

[0019] Figure 3 It is a schematic diagram of the detailed process of the embodiment of the present invention;

[0020] Figure 4 It is a schematic diagram of the detailed process of quantifying and solving the state variables and unknown disturbances under the optimal driving force of the pneumatic redundant parallel platform in the embodiment of the present invention, corresponding to Figure 1 step S1 in

[0021] Figure 5 This is a detailed flow schematic diagram of the improved adaptive control law according to the embodiment of the present invention, corresponding to Figure 1 step S2 in

[0022] Figure 6 This is a schematic diagram of the control structure according to the embodiment of the present invention. Detailed implementation manners

[0023] To make the above objects, features and advantages of the present invention more obvious and understandable, the following will describe in detail the specific embodiments of the present invention with reference to the accompanying drawings.

[0024] As Figure 1 shown, the embodiment of the present invention provides a self-disturbance rejection control method for a redundant pneumatic parallel platform considering the optimization of the decoupling of the driving force, and the method includes the following steps:

[0025] Step S1, quantize and solve the state variables and non-predictable disturbances under the optimal driving force of the pneumatic redundant parallel platform in real time.

[0026] As Figure 2 shown, according to the position information of the upper and lower hinge points P i and b i of the i-th actuator of the redundant pneumatic parallel platform, the length of the position vector of the i-th actuator in its base coordinate system {B} can be solved by using inverse kinematics. Further, the telescopic speed and acceleration of the actuator are solved through the platform movement speed, and the driving force f i of the actuator is generated by the forces f i1 , f i2 in the two chambers, the damping c and the air spring stiffness k together.

[0027] Specifically, as Figure 3 and 4 shown, based on the Newton-Euler mechanics framework, considering the compressibility of the gas, the flow friction and the platform disturbance, appropriate non-linear terms are introduced to establish the dynamic mathematical model of the pneumatic redundant parallel platform as shown in Equation (1):

[0028]

[0029] Among them, is the pose of the moving platform, is the mass matrix dependent on the platform pose, is the Coriolis force and centrifugal force matrix related to the platform pose and speed, is the gravity term, is the driving force vector of the actuator, is the transpose of the Jacobian matrix that maps the driving force of the actuator to the force in the moving platform space, It covers the uncertainties of actuator model parameters, the inaccuracies of the platform structure, and the disturbances to the system caused by the external environment.

[0030] According to the rotation matrix of the moving platform, the length of the position vector of the i-th actuator in its base coordinate system is solved by inverse kinematics as shown in Equation (2):

[0031]

[0032] Where, is the length vector of the actuator in the base coordinate system, is the translation vector from the origin of the base coordinate system to the origin of the moving platform coordinate system, B R E is the rotation matrix from the moving platform coordinate system to the base coordinate system, is the position vector of the upper hinge point in the moving platform coordinate system, is the position vector of the lower hinge point in the base coordinate system.

[0033] The axial telescopic speed of the actuator is jointly determined by the translational speed and rotational speed of the moving platform. The mapping under the unit vector of the actuator's axial movement in the base coordinate system is the required telescopic speed. At this time, combined with the actuator vector length formula shown in Equation (2), the axial telescopic speed of the actuator can be solved, as shown in Equation (3):

[0034]

[0035] Where, B T E is the transformation matrix from the moving platform coordinate system to the base coordinate system, are respectively the translational speed and rotational speed of the moving platform in the base coordinate system, is the axial telescopic speed of the actuator, is the unit direction vector of the i-th actuator.

[0036] Based on the axial telescopic speed of the actuator in the base coordinate system, the calculation formulas for the telescopic speed and acceleration of the actuator in the world coordinate system are further solved through coordinate transformation and differentiation using Equation (3), as shown in Equation (4):

[0037]

[0038] Where, J is the Jacobian matrix of the moving platform attitude change rate and the length change rate of each actuator, represents the generalized speed of the moving platform coordinate system relative to the base coordinate system, W T B is the transformation matrix from the base coordinate system to the world coordinate system, including translation and rotation.

[0039] The driving force vector equation of the actuator is determined by the combined action of the internal pressure value, damping, air spring stiffness, and total disturbance parameters, as shown in Equation (5).

[0040]

[0041] Among them, P1 is the pressure parameter that provides the main driving effect for the double-chamber actuator, P2 is the pressure parameter that regulates the telescopic speed of the double-chamber actuator, A1 and A2 are the surface areas of the double-chamber action respectively, C is the damping parameter of the actuator, K is the air spring stiffness parameter of the actuator, W L is the position of the actuator in the world coordinate system, W L0 is the initial position of the actuator in the world coordinate system. The initial position of each actuator will be different due to mechanical errors, and d is the non-predictable disturbance received by the actuator.

[0042] The driving force of the redundant parallel platform in the Cartesian space is redundant and difficult to calculate directly. At this time, it is necessary to propose an optimization index for the redundant force and perform an optimized calculation of the driving force to achieve the decoupled distribution of the driving force from the workspace to the joint space. Substituting into the driving force decoupling equation shown in Equation (6), the specific driving force distribution values for each actuator are obtained.

[0043]

[0044] Among them, is the pseudo-inverse matrix, is the total required force in the workspace, N is the null space basis matrix of J T , and λ is the null space force coefficient vector, which determines the force distribution in the null space.

[0045] To comprehensively evaluate the performance of the redundant parallel platform, considering the constraint conditions of the actuator driving force as shown in Equation (7):

[0046]

[0047] Among them, m is the number of actuators, f min and f max are the lower and upper limit values of the force that the actuator can apply respectively, Γ is the overall force balance equation of the platform, Ω is the physically feasible range of the actuator driving force, Λ is the stiffness equation of each motion direction of the platform, and the platform stiffness will further affect the vibration transmission efficiency. Υ is the driving force equation affected by gas pressure, air spring force, and other disturbances that are difficult to measure and described by mathematical formulas, and is used to evaluate the energy consumption index. P i1 、P i2 are the pressure parameters that provide the main driving effect and regulate the telescopic speed of the double-chamber actuator respectively, is the actuator telescopic vector in the world coordinate system, is the initial expansion and contraction vector of the actuator in the world coordinate system.

[0048] Based on different task requirements, weight factors are introduced to comprehensively quantify and evaluate various performance indicators. The optimization algorithm is used to seek the global optimal solution of the driving force. The weight ratios of each performance indicator are flexibly adjusted according to different working conditions as shown in Equation (8):

[0049]

[0050] Among them, Q Γ is the expected driving force balance evaluation equation, σ is a positive parameter used to adjust the influence degree of the error, Q Ω is the physical feasibility evaluation equation of the actuator driving force, f i，min and f i，max are the minimum and maximum allowable output forces of the i-th actuator respectively, Q Λ is the platform vibration reduction and anti-interference evaluation equation, G r is the vibration transfer function, Q Υ is the energy consumption evaluation equation, h 1i and h 2i are the initial heights of the chambers of the i-th actuator respectively. According to the predefined rule set, the weight factors are automatically adjusted under specific conditions.

[0051] Determine the driving forces of each actuator after decoupling under the optimal comprehensive evaluation index, substitute them into the driving force equation shown in Equation (5), solve the state variables of the actuator with disturbances, and estimate the accurate state variables and disturbances of the actuator through the differential estimation model as shown in Equation (9).

[0052]

[0053] Among them, X1 is the moving core position vector of the actuator, Z1 is the estimated moving core position vector of the actuator, Z2 is the estimated expansion and contraction speed vector, Z3 is the estimated disturbance, M is the axial pressure vector of the actuator, C is the damping coefficient vector, K is the stiffness vector, Z3 is the part of the actuator modeling uncertainty and external disturbance, and δ1, δ2, δ3 are the actuator observation gains.

[0054] Substitute the accurately estimated state variables of the actuator into the platform dynamic mathematical model, and finally estimate the overall state and total disturbance of the redundant parallel platform as shown in Equation (10):

[0055]

[0056] Among them, y is the target pose of the parallel platform, l1 is the estimated pose of the parallel platform, l2 is the estimated pose of the parallel platform, l3 is the estimated total disturbance of the parallel platform, and δ4, δ5, δ6 are the observation gains of the redundant parallel platform.

[0057] Step S2: Design a sliding mode control law based on system state and total disturbance estimation.

[0058] Specifically, as Figure 3 and 5 shown, through platform inverse kinematics solution and coordinate system mapping, the length information of each branch chain in the base coordinate system of the parallel platform is solved as the input reference signal. According to the fast optimal synthesis control function, a differential tracker is established to process the given position signal, and the change curves of the position and its velocity are analyzed as shown in Equation (11):

[0059]

[0060] where, x0 is the given reference signal, x1 is the tracking signal of x0, x2 is the derivative of x1, and f han is the fast optimal synthesis function, and r0 and h0 are two adjustable parameters of the tracking differentiator, which track the given reference signal according to the desired speed and smoothness. The fast optimal synthesis function is specifically shown in Equation (12):

[0061]

[0062] Based on the position and velocity values at each sampling moment, an error polynomial sliding mode surface is designed using the error and its derivative terms as shown in Equation (13):

[0063]

[0064] where, is the sliding mode surface polynomial regarding the system position and velocity errors, φ1 is the position tracking error, φ2 is the velocity tracking error. This polynomial needs to satisfy the Hurwitz stability condition. α > 0 is the integral gain used to eliminate the steady-state error, β > 0 is the fractional-order gain to adjust the dynamic response, is the Caputo fractional-order differential operator, is the velocity error gain for fast convergence.

[0065] Based on the error magnitude of the system state trajectory reaching this sliding mode surface, through the Lyapunov inverse sliding mode surface control law, combined with the power approach and adaptive gain strategy, an improved adaptive control law is proposed as shown in Equation (14), which can dynamically adjust the approaching rate according to the real-time error between the system state and the sliding mode surface, and accelerate the error convergence process.

[0066]

[0067] where, U eq is the pressure equivalent control rate of the double-chamber actuator, U sw is the switching control rate, sat(s) is the saturation function, k2(t) is the time-varying gain parameter used to balance the dynamic response and steady-state accuracy, k20 The base gain can ensure the minimum convergence speed. γ controls the convergence speed of the nonlinear term and provides a stronger approaching force when the error is large. η(t) and ε(t) are parameter factors for adaptively adjusting the convergence speed and smoothness, and k1|s| γ sat(s) provides nonlinear rapid approach, and k2(t)s ensures the convergence speed and smooth convergence at small errors.

[0068] The adaptive gain adjustment factor is shown in Equation (15):

[0069]

[0070] Among them, η0 is the maximum gain amplitude, and θ is the smooth transition threshold, which determines the sensitivity of the gain change with the error.

[0071] The smooth adjustment factor is shown in Equation (16):

[0072]

[0073] Among them, ε min is the lower limit value to ensure that the denominator of the adaptive gain is not zero, and ε max is the upper limit value to limit the maximum smoothness, is the decay rate coefficient.

[0074] For Figure 1 After expanding the steps shown in detail, the detailed control structure diagram of the active disturbance rejection control of a redundant pneumatic parallel platform based on the decoupling optimization of the driving force described in the present invention is as shown in Figure 6 shown.

[0075] According to the above steps, the redundant parallel platform performs decoupling and optimal distribution of the driving force to achieve the optimal comprehensive performance evaluation index. When the driving force is known, the states of each actuator are estimated, and then the overall state and total disturbance of the platform are estimated. A combined fractional-order differential operator error polynomial sliding mode surface is proposed, and a control law is constructed by combining power approach and adaptive gain strategy to ensure that the error change between the system state and the sliding mode surface can dynamically adjust the control gain, providing a new solution for the high-performance control of complex nonlinear redundant pneumatic parallel systems.

Claims

1. A self-disturbance rejection control method for a redundant pneumatic parallel platform based on driving force decoupling optimization, characterized in that The method includes the following steps: Step 1: Quantify and solve the state variables and unforeseen disturbances under the optimal driving force of the pneumatic redundant parallel platform in real time: Based on the Newton-Euler method, considering the compressibility of the gas, flow friction, and platform disturbances, appropriate nonlinear terms are introduced to establish the dynamic mathematical model of the pneumatic redundant parallel platform. At the same time, considering that improper force distribution of the redundant actuators will cause internal force conflicts in the platform, the pseudo-inverse method is used to achieve the decoupling distribution of the driving force from the workspace to the joint space. On this basis, the actual position measurement value is input into the differential state estimation model to estimate the state of each actuator and the internal disturbance respectively, and further estimate the state parameters and total disturbance of the parallel platform system in real time; Step 2: Design a sliding mode control law based on the system state and total disturbance estimation: Given the target pose of the end effector of the redundant parallel platform, analyze the rotation and translation transformation relationship of the platform to calculate the actuator position quantity. To achieve the smooth approximation of the given actuator position signal and its differential signal and suppress noise, a differential tracker based on the fast optimal synthesis control function is used to process the given reference signal, and the driving force provided by the actuator at each sampling time is determined according to the reference curve. On this basis, an adaptive gain sliding mode control law is designed for the tracking error system according to the driving limit principle, so that the system position and velocity states track the set state curve, and the state tracking error converges rapidly within a finite time.

2. The self-disturbance rejection control method for a redundant pneumatic parallel platform based on driving force decoupling optimization according to claim 1, wherein The dynamic mathematical model of the pneumatic redundant parallel platform described in Step 1 is shown in Equation (1): Among them, is the pose of the moving platform, is the mass matrix dependent on the platform pose, is the Coriolis force and centrifugal force matrix related to the platform pose and velocity, is the gravity term, is the driving force vector of the actuator, is the transpose of the Jacobian matrix that maps the driving force of the actuator to the spatial force of the moving platform, covers the total disturbances caused to the system due to the uncertainty of the actuator model parameters, the inaccuracy of the platform structure, and the external environment. The method for decoupling and distributing the driving force from the workspace to the joint space is shown in Equation (2): Among them, is the pseudo-inverse matrix, is the total required force in the workspace, is J T 's null space basis matrix, is the null space force coefficient vector, which determines the force distribution in the null space. For the comprehensive performance evaluation index of the redundant parallel platform, four constraint conditions are proposed for the driving force distribution of the actuators for comprehensive optimization, as shown in Equation (3): Among them, m is the number of actuators, f min and f max are respectively the lower limit value and the upper limit value of the driving force that the actuator can apply. Γ is the force balance equation of the overall platform, Ω is the physically feasible range of the driving force of the actuator, Λ is the stiffness equation of each movement direction of the platform, Υ is the driving force equation affected by gas pressure, air spring force, and other disturbances that are difficult to measure and described by mathematical formulas, P i1 and P i2 are respectively the pressure parameters for the double-chamber actuator to provide the main driving effect and adjust the telescopic speed. A i1 and A i2 are respectively the surface areas of the double-chamber action. is the actuator telescopic vector in the world coordinate system. is the initial actuator telescopic vector in the world coordinate system. Taking the intersection of the above four constraint conditions, an optimization region is determined, enabling the driving force to freely distribute the force in the redundant space without affecting the pose of the moving platform. For a certain pose of the moving platform, J T , and N are determined. By imposing constraint conditions on the driving force of the actuator, it is ensured that the driving forces of each degree of freedom of the parallel platform are kept within the physically feasible range, while improving the anti-disturbance ability and vibration damping performance of the system. Considering the gas utilization rate to achieve the effective allocation of resources, weight factors are introduced to weight and quantify the above performance indicators, and an advanced optimization algorithm is used to seek the global optimal solution. The estimation of the state and internal disturbance of each actuator is substituted into the differential estimation model according to the position measurement value, as shown in Equation (4): wherein, is the position vector of the actuator's moving core, is the estimated position vector of the actuator's moving core, is the estimated telescopic speed vector, is the estimated disturbance, is the axial pressure vector of the actuator, is the damping coefficient vector, is the stiffness vector, is the part of the actuator modeling uncertainty and external disturbance, and δ1, δ2, δ3 are the actuator observation gains. The real-time estimation of the state parameters and total disturbance of the parallel platform system takes the accurately estimated position information and velocity of each actuator during the dynamic motion process of the platform as input, substitutes them into the driving force equation, and calculates the driving force vector of the actuator. The pose transformation of the parallel platform can be collected by the motion capture system and brought into the platform dynamic mathematical model (1), and finally the overall state and total disturbance of the redundant parallel platform are estimated, as shown in Equation (5): Among them, is the target pose of the parallel platform, is the estimated pose of the parallel platform, is the estimated pose of the parallel platform, is the total estimated disturbance of the parallel platform, and δ4, δ5, δ6 are the observation gains of the redundant parallel platform.

3. A self-disturbance rejection control method for a redundant pneumatic parallel platform based on driving force decoupling optimization, characterized in that The analysis of the rotation and translation transformation relationship of the platform described in Step 2 to calculate the actuator position quantity, obtains the rotation matrix and translation vector according to the initial pose and the target pose, and substitutes them into the inverse kinematics mathematical model of the parallel platform to uniquely determine the length of each actuator, so as to ensure that the entire parallel platform can accurately transform from its initial pose to the target pose. The differential tracker based on the fast optimal synthesis control function processes the given reference signal as shown in Equation (6): Among them, x0 is a given reference signal, x1 is the tracking signal of x0, x2 is the derivative of x1, and f han is a fast optimal synthesis function, and r0 and h0 are two adjustable parameters of the tracking differentiator, respectively, which track the given reference signal according to the desired speed and smoothness. The driving limit principle is used to limit the magnitude of the actuator driving force. Excessive target driving will lead to exceeding the actual motion ability. To improve the tracking performance and robustness of the system, an error polynomial sliding mode surface including the tracking error and its derivative is designed, as shown in Equation (7): Among them, is the sliding mode surface polynomial for the system position and velocity errors. φ1 is the position tracking error, and φ2 is the velocity tracking error. This polynomial needs to satisfy the Hurwitz stability condition. α > 0 is the integral gain used to eliminate the steady-state error, and β > 0 is the fractional-order gain to adjust the dynamic response. is the Caputo fractional-order differential operator. is the velocity error gain for fast convergence. An adaptive control law is designed for the tracking error system based on the driving overrun principle. The control law affects the tracking error, and the tracking effect is intuitively expressed by the speed of the curve tracking sliding mode surface s. Further, the Lyapunov inversion control law, power approach, and adaptive gain can be applied to the design of the control law, as shown in Equation (8): where, U eq is the pressure equivalent control rate of the double-chamber actuator, U sw is the switching control rate, sat(s) is the saturation function, k2(t) is the time-varying gain parameter used to balance the dynamic response and the steady-state accuracy, k 20 is the basic gain that can ensure the minimum convergence speed, γ is the convergence speed of the control nonlinear term, providing a stronger approaching force when the error is large, η and ε are the parameters for adaptively adjusting the convergence speed and smoothness, k1|s| γ sat(s) provides nonlinear fast approaching, and k2(t)s ensures the convergence speed and smooth convergence at small errors.

4. A self-disturbance rejection control method based on decoupling optimization of driving force of a redundant pneumatic parallel platform according to claim 1, characterized in that, During the platform pose adjustment process, the redundant driving force of the platform is decoupled and optimally allocated according to Step 1 in a loop. At the same time, the states of each actuator are estimated to estimate the overall state and total disturbance of the platform. Further, according to Step 2, an error polynomial sliding mode surface combined with a fractional-order differential operator is proposed, and a control law is constructed by combining the power approach and adaptive gain strategy to quickly converge the system state to the desired trajectory, complete the fast-converging tracking of the trajectory, and thus realize the overall motion planning of the redundant parallel platform.

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