Redundant six-degree-of-freedom parallel heavy-load electric stabilized platform and control method

Abstract

The invention relates to the technical field of automatic control and precision engineering, in particular to a redundant six-degree-of-freedom parallel heavy-load electric stabilized platform and a control method.The electric stabilized platform comprises an upper platform, a lower platform, six telescopic motion branch chains, three redundant branch chains, a first hooke joint assembly and a second hooke joint assembly; the upper ends and the lower ends of the six telescopic motion branch chains are hinged to the lower surface of the upper platform and the upper surface of the lower platform through first hooke joint assemblies correspondingly, and the upper ends and the lower ends of the three redundant branch chains are hinged to the lower surface of the upper platform and the upper surface of the lower platform through second hooke joint assemblies correspondingly. The control method adopts a force-position hybrid control method, and the six telescopic motion branch chains adopt position servo control to realize stable attitude control of the electric stable platform; the three redundant branch chains achieve platform and load gravity compensation through force servo control. The bearing capacity of the stable platform is improved by adding the three redundant branch chains, and the heavy-load high-frequency motion tracking requirement is met by adopting a force-position hybrid control method.

Description

Technical Field

[0001] The present invention relates to the field of automation control and precision engineering technology, and in particular to a redundant six-degree-of-freedom parallel heavy-load electric stable platform and a control method thereof. Background Art

[0002] A stable platform is a device that can maintain its own posture or the position and posture of the object it carries relatively stable in the presence of external interference. For example, on a ship, although the waves will cause the hull to shake, the stable platform can maintain a relatively stable working environment for some precision instruments. Compared with the serial stable platform, the parallel stable platform has the following advantages: first, high precision and no error accumulation; second, strong bearing capacity, high rigidity, and good stability; third, fast dynamic response, and relatively easy position inversion, which is easy to control. The Stewart platform is a typical parallel mechanism. At present, a large number of literatures have been studied on its characteristics and control as a stable platform. The Stewart platform can accurately control the position and posture of the platform through the coordinated work of multiple retractable branches, and has the characteristics of high rigidity, strong bearing capacity, high precision, and fast dynamic response. It can effectively isolate external interference and realize the stability function. It is widely used in many fields such as ship stable platform and optical instrument stabilization. The hydraulic Stewart platform has the advantages of high bearing capacity, high rigidity, and good dynamic response, but its structure is complex, the precision control is complex, and it is easy to leak and contaminate. At present, electric Stewart platforms are widely used and studied due to their advantages such as high control accuracy, fast response speed, clean and environmental protection, simple structure, and easy maintenance. However, the load-bearing capacity of electric Stewart platforms is far less than that of hydraulic Stewart platforms. Large mass loads will seriously increase the structural size of the electric Stewart platform and reduce safety and response speed. Redundant parallel mechanisms can make up for the shortcomings of the Stewart mechanism. Adding redundant branches can reduce singular configurations, provide additional support force, balance the driving force of the branches, and improve safety and reliability. Therefore, the present invention aims to provide a redundant six-degree-of-freedom parallel heavy-load electric stable platform and control method to improve the load-bearing capacity and response speed of electric Stewart platforms of the same size. Summary of the invention

[0003] The present invention aims to solve the problems of insufficient load-bearing capacity and slow dynamic response of the electric Stewart stabilized platform. A redundant six-degree-of-freedom parallel heavy-load electric stabilized platform and a control method are proposed. The load-bearing capacity of the stabilized platform is improved by adding three redundant branches, and a force-position hybrid control method is adopted to meet the heavy-load high-frequency motion tracking requirements.

[0004] To achieve the above purpose, the technical solution adopted is:

[0005] The present invention provides a redundant six-degree-of-freedom parallel heavy-load electric stable platform, comprising an upper platform, a lower platform, six retractable motion branches, three redundant branches, a Hooke's hinge assembly 1 and a Hooke's hinge assembly 2. The upper and lower ends of the six retractable motion branches are respectively hinged to the lower surface of the upper platform and the upper surface of the lower platform through the Hooke's hinge assembly 1, and the upper and lower ends of the three redundant branches are respectively hinged to the lower surface of the upper platform and the upper surface of the lower platform through the Hooke's hinge assembly 2.

[0006] According to the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, further, the Hooke's hinge assembly 1 includes a Hooke's hinge mounting seat A and a Hooke's hinge; three Hooke's hinge mounting seats A are fixed to the lower surface of the upper platform, with the center of the upper platform as the center and r A The three Hooke hinge mounting seats A are fixed on the upper surface of the lower platform, with the center of the lower platform as the center and the radius r B The three Hooke's hinge mounting seats A on the upper platform and the three Hooke's hinge mounting seats A on the lower platform are evenly distributed in an alternating manner; two Hooke's hinges are arranged on the Hooke's hinge mounting seats A, and the telescopic motion branch chain is connected to the Hooke's hinge.

[0007] According to the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, further, the radius r of the circle where the three Hooke's joint mounting seats A of the lower platform are located B Greater than the radius r of the circle where the three Hooke hinge mounting seats A of the upper platform are located A , so that the telescopic motion branch chain is inclined inward from bottom to top and is arranged between the upper platform and the lower platform.

[0008] According to the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, further, the second Hooke's hinge assembly includes a Hooke's hinge mounting seat B and a Hooke's hinge, and three Hooke's hinge mounting seats B are fixed to the lower surface of the upper platform, with the center of the upper platform as the center and r A The three Hooke hinge mounting seats B are fixed on the upper surface of the lower platform, with the center of the lower platform as the center and the radius r C The three Hooke's hinge mounting seats B on the upper platform are evenly distributed at the same angle as the three Hooke's hinge mounting seats B on the lower platform; a Hooke's hinge is provided on the Hooke's hinge mounting seat B, and the redundant branch chain is connected to the Hooke's hinge.

[0009] According to the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, further, the radius r of the circle where the three Hooke's joint mounting seats B of the lower platform are located C Smaller than the radius r of the circle where the three Hooke hinge mounting seats B on the upper platform are located A , so that the redundant branch chain is inclined outward from bottom to top and is set between the upper platform and the lower platform.

[0010] Furthermore, the present invention also proposes a control method based on the redundant six-degree-of-freedom parallel heavy-load electric stable platform as mentioned above. The control method adopts a force-position hybrid control method, and the six retractable motion branches adopt position servo control to realize the posture stability control of the electric stable platform; the three redundant branches adopt force servo control to realize the gravity compensation of the platform and the load.

[0011] Further, according to the control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, the system model adopted by the control method is:

[0012] Kinematic model: Given the spatial position of the motion carrier connection system, calculate the extension and contraction of each actuator: l i =t p +R bp A i -B i , t p A is the position vector of the upper platform of the moving carrier connection system relative to the moving carrier, i is the coordinates of the upper hinge points of the moving carrier connection system, B i is the coordinates of the lower hinge points of the moving carrier connection system, R bp is the Euler transformation matrix, i is 1, 2, 3, 4, 5, 6; the matrix form of the extension and retraction speed of the six actuators is obtained as follows: J represents the Jacobian matrix from the upper platform velocity to the actuator extension velocity, Indicates q p The first-order differential of , i.e., the generalized velocity of the center of mass of the upper platform in the moving carrier connection system;

[0013] Dynamic model: The dynamic model was established using the Kane method, and the dynamic equation of the stable platform fixed on the motion carrier was expressed as: M p represents the relative motion mass matrix of the stable platform, C p Represents the centrifugal force / Coriolis force matrix of the relative motion of the stable platform; G p represents the gravity term of the stable platform, M b represents the mass matrix of the motion coupling between the stable platform and the moving carrier, C b represents the centrifugal force / Coriolis force matrix of the motion coupling between the stable platform and the moving carrier, f a represents the actuator driving force vector, Indicates q p The second-order differential of is the generalized acceleration of the center of mass of the upper platform in the motion carrier connection system. Indicates q b The second-order differential of is the generalized acceleration of the center of mass of the lower platform in the inertial coordinate system.

[0014] Further, according to the control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, the position servo control adopts an adaptive anti-interference robust control algorithm composed of Critic-Actor neural network compensation, interference estimation compensation and sliding mode control terms, and the expression is:

[0015] f a =f an +f ad +f ar

[0016] In the formula, f an 、f ad 、f ar They represent the neural network fitting uncertainty compensation, disturbance estimation compensation and sliding mode control terms respectively.

[0017] Furthermore, according to the control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, the force servo control adopts an admittance control algorithm based on PID position control to realize force compliance control.

[0018] Furthermore, according to the control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform of the present invention, the admittance control algorithm detects the force exerted on the redundant branch chain through a force sensor, and then calculates the displacement of the redundant branch chain in the next control cycle based on the force and impedance parameters, so that the redundant branch chain can achieve follow-up control while maintaining a given supporting force.

[0019] The beneficial effects achieved by adopting the above technical solution are:

[0020] The present invention uses six retractable motion branches and three redundant branches in combination with upper and lower platforms to realize the construction of a parallel platform and meet the needs of six-degree-of-freedom motion. The six retractable motion branches complete position control, and the three redundant branches realize load and platform gravity compensation, thereby improving the carrying capacity of the stable platform. The force-position hybrid control method is used to reduce the coupling interference between the retractable motion branches, so as to realize high-precision and high-dynamic posture tracking of the platform under heavy load. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings of the embodiments of the present invention, wherein the drawings are only used to illustrate some embodiments of the present invention, but not to limit all embodiments of the present invention thereto.

[0022] Figure 1 This is one of the structural schematic diagrams of a redundant six-degree-of-freedom parallel heavy-load electric stable platform according to an embodiment of the present invention;

[0023] Figure 2 This is the second structural schematic diagram of the redundant six-degree-of-freedom parallel heavy-load electric stable platform according to an embodiment of the present invention;

[0024] Figure 1 and Figure 2 In the middle, 1 represents the upper platform, 2 represents the lower platform, 3 represents the retractable motion branch chain, 4 represents the redundant branch chain, 5 represents the Hooke's hinge mounting seat A, and 6 represents the Hooke's hinge mounting seat B;

[0025] Figure 3 is a schematic diagram of coordinates of a stable platform according to an embodiment of the present invention;

[0026] Figure 4 It is an overall framework diagram of a control method of a redundant six-degree-of-freedom parallel heavy-load electric stable platform according to an embodiment of the present invention;

[0027] Figure 5 is a schematic diagram of a position servo control algorithm according to an embodiment of the present invention;

[0028] Figure 6 4 is a schematic diagram of an admittance control algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The following will be combined with the drawings of specific embodiments of the present invention to clearly and completely describe the exemplary scheme of the embodiment of the present invention. Unless otherwise defined, the technical terms or scientific terms used in the present invention should be the common meanings understood by people with ordinary skills in the field.

[0030] like Figure 1 and Figure 2 As shown, this embodiment discloses a redundant six-degree-of-freedom parallel heavy-load electric stable platform including an upper platform 1, a lower platform 2, six retractable motion branches 3, three redundant branches 4, a Hooke's hinge assembly 1 and a Hooke's hinge assembly 2. The lower surface of the upper platform and the upper surface of the lower platform are both provided with the Hooke's hinge assembly 1 and the Hooke's hinge assembly 2. The upper and lower ends of the six retractable motion branches are respectively hinged to the lower surface of the upper platform and the upper surface of the lower platform through the Hooke's hinge assembly 1, and the upper and lower ends of the three redundant branches are respectively hinged to the lower surface of the upper platform and the upper surface of the lower platform through the Hooke's hinge assembly 2.

[0031] The Hook hinge assembly 1 includes a Hook hinge mounting seat A5 and a Hook hinge. The three Hook hinge mounting seats A are fixed to the lower surface of the upper platform, with the center of the upper platform as the center and the center of the circle r A The three Hooke's hinge mounting seats A are evenly distributed on a circle with a radius of r (the lines connecting the three Hooke's hinge mounting seats A and the center of the upper platform form an angle of 120° with each other). BThe three Hooke's hinge mounting seats A on the upper platform and the three Hooke's hinge mounting seats A on the lower platform are evenly distributed on a circle with a radius of 120° (the lines connecting the three Hooke's hinge mounting seats A and the center of the lower platform form an angle of 120° with each other). The three Hooke's hinge mounting seats A on the upper platform and the three Hooke's hinge mounting seats A on the lower platform are staggered and evenly distributed. Two Hooke's hinges are arranged on the Hooke's hinge mounting seats A, and the retractable motion branch chain is connected to the upper platform and the lower platform through the Hooke's hinge. The retractable motion branch chain is tiltedly arranged between the upper platform and the lower platform, thereby realizing the six-degree-of-freedom posture adjustment of the platform.

[0032] The radius r of the circle where the three Hooke hinge mounting seats A of the lower platform are located B Greater than the radius r of the circle where the three Hooke hinge mounting seats A of the upper platform are located A , so that the retractable motion branch chain is arranged between the upper platform and the lower platform from bottom to top and tilted inward, which is beneficial to the stability of the platform.

[0033] The second Hooke hinge assembly includes a Hooke hinge mounting seat B6 and a Hooke hinge. The three Hooke hinge mounting seats B are fixed to the lower surface of the upper platform, with the center of the upper platform as the center and r A The three Hooke's hinge mounting seats B are evenly distributed on a circle with a radius of r (the lines connecting the three Hooke's hinge mounting seats B and the center of the upper platform form an angle of 120° with each other). C The three Hook hinge mounting seats B on the upper platform and the three Hook hinge mounting seats B on the lower platform are evenly distributed at the same angle. A Hook hinge is provided on the Hook hinge mounting seat B, and the redundant branch chain is connected to the upper platform and the lower platform through the Hook hinge. The redundant branch chain is tilted between the upper platform and the lower platform to support the upper platform and the lower platform, offset a certain load and the gravity of the upper platform, and meet the requirements of the parallel mechanism with a large load.

[0034] The radius r of the circle where the three Hooke hinge mounting seats B of the lower platform are located C Smaller than the radius r of the circle where the three Hooke hinge mounting seats B on the upper platform are located A , so that the redundant branch chain is tilted outward from bottom to top and is set between the upper platform and the lower platform, so that the posture change of the lower platform has less impact on the redundant branch chain.

[0035] This embodiment also discloses a control method for a redundant six-degree-of-freedom parallel heavy-load electric stable platform. The overall process is as follows: Figure 4As shown in the figure, the control method adopts a force-position hybrid control method. The six retractable motion branches use position servo control to achieve attitude stability control of the electric stable platform, and the three redundant branches use force servo control to achieve platform and load gravity compensation. The position servo control adopts an anti-interference robust control algorithm composed of neural network fitting uncertainty compensation, interference estimation compensation and sliding mode control terms, which can effectively reduce the influence of adverse factors such as model uncertainty, coupling interference and motion interference, and improve the accuracy of attitude stability control. The force servo control adopts an admittance control algorithm based on PID position control to achieve force compliance control, and reduce the influence of position control coupling on the basis of compensating the platform and load gravity.

[0036] The system model used in the control method is:

[0037] ① Coordinate system establishment

[0038] In order to conveniently describe the dynamic model of the stable platform mechanical system, three coordinate systems are established, such as Figure 3 As shown:

[0039] Motion carrier connection system b -X b Y b Z b , fixed on a movable carrier (such as a ship, vehicle, etc.), where the origin O b It is the center of the motion carrier and also the center of the motion sensor.

[0040] Platform Connection System p -X p Y p Z p , fixed on the upper platform of Stewart, where the origin O p It is the center of the upper platform. When in the middle position, the directions of its axes are parallel to the corresponding axes in the motion carrier connection system.

[0041] The inertial reference system O0-X0Y0Z0 is fixed on the ground. In the initial position, the coordinate axes of the inertial reference system and the motion carrier connection system have the same attitude.

[0042] In order to analyze the dynamic characteristics of the stable platform, we must first mathematically describe the state of the moving carrier and define the origin O b The generalized coordinates of where t b =(x b ,y b ,z b ) T is the position vector of the moving carrier in the inertial reference frame, ψ b ,θ b and The moving carrier is around Zb Axis, Y b Axis and X b The rotation angle of the axis; in addition, the posture of the moving carrier relative to the inertial reference system can be described by the following Euler transformation matrix:

[0043]

[0044] The origin O of the platform on the stable platform p Generalized coordinates of relative motion carrier t p =(x p ,y p ,z p ) T is the position vector of the upper platform relative to the motion carrier in the motion carrier connection system. The posture of the upper platform relative to the motion carrier connection system can be expressed by the Euler transformation matrix R bp describe:

[0045]

[0046] For the convenience of description, the values ​​of subscript i in the whole text are 1, 2, 3, 4, 5, 6, and the values ​​of j are 7, 8, 9.

[0047] ② Kinematic model

[0048] The inverse solution of the parallel mechanism is to find the expansion and contraction amount of each actuator when the spatial position of the motion carrier connection system is known. Figure 3 The space vector relationship shown in Figure 1 gives the actuator length vector (the vector formed by the upper and lower hinge points):

[0049] l i =t p +R bp A i -B i (3)

[0050] In the formula, A i represents the coordinates of the upper hinge points of the moving carrier connection system, B i Represents the coordinates of each lower hinge point under the motion carrier connection system.

[0051] Define l = [l1,l2,l3,l4,l5,l6] T , the matrix form of the extension and retraction speed of the six actuators is obtained as:

[0052]

[0053] Where J represents the Jacobian matrix from the upper platform velocity to the actuator extension velocity, Indicates q p The first-order differential of L is the generalized velocity of the center of mass of the upper platform in the moving carrier connection system,n represents the actuator unit vector matrix, Indicates t p The first-order differential of is the linear velocity of the upper platform under the motion carrier connection system, ω pb It represents the angular velocity of the upper platform under the motion carrier connection system.

[0054] ③ Kinetic model

[0055] In order to reduce the computational complexity and facilitate programming, the Kane method was used to establish the dynamic model. Here, the inertial force, inertia moment, gravity and driving force are projected into the task space as generalized inertial force and generalized driving force through the Jacobian matrix. Then, the dynamic equations are obtained based on the D'Alembert principle.

[0056] The dynamic equation of the stable platform is expressed as:

[0057]

[0058] Where M p represents the relative motion mass matrix of the stable platform, C p Represents the centrifugal force / Coriolis force matrix of the relative motion of the stable platform; G p represents the gravity term of the stable platform, M b represents the mass matrix of the motion coupling between the stable platform and the moving carrier, C b represents the centrifugal force / Coriolis force matrix of the motion coupling between the stable platform and the moving carrier, f a represents the actuator driving force vector, Indicates q p The second-order differential of is the generalized acceleration of the center of mass of the upper platform in the motion carrier connection system. Indicates q b The second-order differential of is the generalized acceleration of the center of mass of the lower platform in the inertial coordinate system.

[0059] The first two terms on the left side of formula (5) describe the force generated by the relative motion of the stable platform, and the last two terms describe the coupling between the stable platform and the motion of the motion carrier. The difference from the static-based six-degree-of-freedom parallel platform lies in this coupling. Therefore, the driving force generated by the actuator is first transformed by the system Jacobian matrix, and then divided into three parts: the first part is used to drive the force generated by relative motion, the second part is used to drive the force generated by the involved motion, and the third part is used to overcome gravity, and this part of gravity is also affected by the position of the motion carrier.

[0060] Since the displacement sensor is generally installed on the actuator, in order to facilitate the controller design, both sides of equation (5) are multiplied by J T , we get the joint space dynamic equation:

[0061]

[0062] Considering the uncertainty of model parameters, the parameters of the dynamic model can be expressed as M l =M l0 +ΔM l , C l =C l0 +ΔC l , G l =G l0 +ΔG l 、M G =M G0 +ΔM G and C G =C G0 +ΔC G Therefore, the dynamic equation can be further expressed as:

[0063]

[0064] In the formula,

[0065] like Figure 5 As shown in the figure, the position servo control adopts an adaptive anti-interference robust control algorithm composed of Critic-Actor neural network compensation, disturbance estimation compensation and sliding mode control terms, which can effectively reduce the influence of adverse factors such as model uncertainty, coupling interference and motion interference, and improve the accuracy of attitude stability control. Therefore, the position servo control can be written as:

[0066] f a =f an +f ad +f ar (8)

[0067] In the formula, f an 、f ad 、f ar They represent the neural network fitting uncertainty compensation, disturbance estimation compensation and sliding mode control terms respectively.

[0068] ①Critic-Actor neural network compensation

[0069] The short-term cost function is designed as:

[0070]

[0071] Where M and Q are the positive definite matrices to be designed, d Indicates the desired length of the actuator.

[0072] Using the short-term cost function, the long-term cost function is designed as:

[0073]

[0074] Here, ψ is a constant.

[0075] Based on the approximate ability of neural networks, It can be expressed as ω c =[ω c1 ,ω c2 ,…,ω ch ] T is the optimal weight coefficient, h represents the number of nodes in the hidden layer, e1=[e 11 ,e 12 ,e 13 ,e 14 ,e 15 ,e 16 ] T is the input vector of the neural network, ε c is the approximation error, σ c (e1) is a Gaussian function. Gaussian function σ c The specific expression of (e1) is: in is the center of the Gaussian function, is the width of the Gaussian function.

[0076] It can be approximated by neural network, and its fitting value It can be expressed as:

[0077]

[0078] For the cost function (9), the approximation error of the remaining cost function is defined as:

[0079]

[0080] In order to obtain the weight coefficient update rate of the Critic network, define the function E c =(1 / 2)λ 2 Based on the gradient descent method, the weight coefficient update rate of the Critic network can be expressed as:

[0081]

[0082] Substituting formula (12) into formula (13) yields:

[0083]

[0084] In the formula, δ c is the learning rate of the Critic network.

[0085] definition in Formula (14) can be further expressed as:

[0086]

[0087] Use smooth mapping Ensure the boundedness of the critic network weight coefficients. Therefore, Approximation Can be modified to Then the weight coefficient of the critic network is limited to a known bounded interval

[0088] Based on the approximate ability of neural networks, f Δ It can be expressed as where ω a =[ω a1 ,ω a2 ,…,ω a6 ] T , ε a =[ε a1 ,ε a2 ,…,ε a6 ] T . Using the output of the RBF neural network Approximate model uncertainty f Δ , It can be expressed as:

[0089]

[0090] In the formula, ω ai =[ω ai1 ,ω ai2 ,…,ω aim ] T is the weight coefficient vector, is the input vector of the RBF neural network, is a Gaussian function.

[0091] The approximation error of the Actor network can be expressed as:

[0092]

[0093] In the formula, make Representing the expected cost function of the future state, using formulas (11) and (17), the error of the Actor network can be expressed as:

[0094]

[0095] In the formula, is a coefficient. Define Ea =ln(cosh(e a ), the update rate of Actor network weight coefficient can be derived as:

[0096]

[0097] In the formula, δ a >0 is the designed learning rate coefficient. a It is unknowable and unmeasurable. Formula (19) can be modified as follows:

[0098]

[0099] Use smooth mapping Ensure the boundedness of the Actor network weight coefficient. Therefore, f Δi Approximation Can be modified to Furthermore, the weight coefficients of the Actor network are limited to a known bounded interval

[0100] The smooth mapping function vector π(·) can be expressed as in, Any parameter The estimated value of p = 1, 2, ..., r is a smooth non-decreasing mapping function with bounded n-1 derivatives, which is expressed as:

[0101]

[0102] Among them, ε ωp is an arbitrarily small positive real number, ω pmin and ω pmax They are ω p The minimum and maximum values ​​of .

[0103] Neural network fitting compensation f an Designed for:

[0104]

[0105] (2) Interference Estimation Compensation

[0106] In order to construct non-singular sliding mode variables, the following function is defined:

[0107]

[0108] In the formula, ε i >0 is a small constant, α<1, sign(·) represents the sign function.

[0109] The fast terminal sliding surface is designed as:

[0110] s=e2+ξ1e1+ξ2λ(e1) (24)

[0111] Where, ξ1=diag{ξ 11 ,ξ 12 ,ξ 13 ,ξ 14 ,ξ 15 ,ξ 16} and ξ2=diag{ξ 21 ,ξ 22 ,ξ 23 ,ξ 24 ,ξ 25 ,ξ 26} coefficient diagonal matrix, λ(e1)=diag{λ1(e 11 ),…,λ6(e 16 )}.

[0112] Using formula (7), the dynamics of the sliding surface can be expressed as

[0113]

[0114] In the formula,

[0115] It can be estimated by the following disturbance observer:

[0116]

[0117] In the formula, It is interference The estimated value of k1=diag{k 11 ,k 12 ,k 13 ,k 14 ,k 15 ,k 16}, k2 = diag{k 21 ,k 22 ,k 23 ,k 24 ,k 25 ,k 26}, k3 = diag{k 31 ,k 32 ,k 33 ,k 34 ,k 35 ,k 36}, k4=diag{k 41 ,k 42 ,k 43 ,k 44 ,k45 ,k 46}.

[0118] Disturbance estimation compensation f ad Designed for:

[0119]

[0120] (3) Sliding mode control term

[0121] According to formula (25), the sliding mode control term can be designed as:

[0122]

[0123] (4) Proof of stability

[0124] definition Substituting formula (28) into formula (25) yields:

[0125]

[0126] According to formula (26), we can get:

[0127]

[0128] Analyzing the above derivation process, we can assume is bounded, that is

[0129] For the convenience of expression and understanding, formulas (29) and (30) are expressed in scalar form:

[0130]

[0131] Proof: To facilitate the proof, define an auxiliary variable:

[0132]

[0133] Therefore, the system can be rewritten as:

[0134]

[0135] In the formula,

[0136] Next, we need to prove that the vector η converges to a bounded region. The Lyapunov function is chosen as:

[0137]

[0138] Therefore, P is a positive definite symmetric matrix.

[0139] The derivative of the Lyapunov function V can be rearranged as:

[0140]

[0141] In the formula, and

[0142] Control gain k 1i , k 2i , k 3i and k 4i is properly designed so that Ω1 and Ω2 are positive definite. According to the positive definiteness of the matrix, the following inequality holds.

[0143]

[0144] Using inequality (36), we can get:

[0145]

[0146] Substituting inequalities (36) and (37) into inequality (35), we obtain:

[0147]

[0148] In the formula, γ pδ =2δ max λ max (P).

[0149] Obviously, if the control gain k 1i , k 2i , k 3i , k 4i and L are reasonably chosen to satisfy the condition λ 11 -λ 12 >0, the state of the dynamic system (31) can converge to 0.

[0150] Force servo control uses an admittance control algorithm based on PID position control to achieve force compliance control. The principle of the admittance control algorithm is as follows: Figure 6 As shown, on the basis of compensating the gravity of the platform and the load, the influence on the position control coupling is reduced.

[0151] The force exerted by the 9 branch chains on the moving platform is f = [f p ,f f ] T , where f p =[f1,f2,f3,f4,f5,f6] T and f f =[f7,f8,f9] T The force F and moment M of the load on the moving platform are expressed as F = [F x ,F y,F z ] T and M=[M x ,M y ,M z ] T When the moving platform is in a state of force balance, the resultant force acting on the moving platform is 0, and the force balance equation of the moving platform is: and Among them, n m is the unit direction vector of each branch, r m is the position vector of the moving hinge point in the moving platform coordinate system. The dynamic platform force balance equation is expressed in matrix form It is not difficult to see that J F is the force transfer matrix between the parallel mechanism moving platform and each branch chain, that is, the force Jacobian matrix The goal of driving force optimization is to minimize the bi-norm of f. Therefore, using the least squares optimization method, we can get

[0152] There are three redundant branches in the stable platform. Controlling the output of the redundant branches can improve the force on other drive branches. The essence of redundant branch force control is compliance control, that is, when the redundant branches are subjected to external forces, the force sensors detect the external forces and feed them back to the controller, and the controller drives the branches to achieve compliance. The admittance control method is adopted to achieve force compliance control. The admittance control algorithm detects the external force F on the redundant branches through force sensors. exj , and then according to this external force and impedance parameter M d , D d , K d Calculate the displacement l of the redundant branch chain in the next control cycle d , so that the redundant branch chain maintains a given support force f r The follow-up control is realized under the condition of

[0153] In admittance control, it is necessary to be able to obtain force information and control the joint position of the robot. The position controller can be implemented using the PID control algorithm:

[0154]

[0155] In order to achieve the designed control force f rj Make the external force F exj and tracking error e j = l dj -l 0j The mass-spring-damper dynamic relationship is established between The admittance control law is designed as:

[0156]

[0157] By integrating the above formula, we can get the expected position l0j .

[0158] Those skilled in the art will appreciate that all or part of the steps in the above method can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a disk or an optical disk. Optionally, all or part of the steps in the above embodiment can also be implemented using one or more integrated circuits, and accordingly, each module / unit in the above embodiment can be implemented in the form of hardware or in the form of software function modules. The present invention is not limited to any specific form of combination of hardware and software.

[0159] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or replace some of the technical features therein by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A redundant six-degree-of-freedom parallel heavy-load electric stable platform, characterized in that: It includes an upper platform, a lower platform, six retractable motion branches, three redundant branches, a Hooke's hinge assembly 1 and a Hooke's hinge assembly 2. The upper and lower ends of the six retractable motion branches are respectively hinged to the lower surface of the upper platform and the upper surface of the lower platform through the Hooke's hinge assembly 1, and the upper and lower ends of the three redundant branches are respectively hinged to the lower surface of the upper platform and the upper surface of the lower platform through the Hooke's hinge assembly 2.

2. The redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 1, characterized in that: The Hooke's hinge assembly 1 includes a Hooke's hinge mounting seat A and a Hooke's hinge; three Hooke's hinge mounting seats A are fixed to the lower surface of the upper platform, with the center of the upper platform as the center and r A The three Hooke hinge mounting seats A are fixed on the upper surface of the lower platform, with the center of the lower platform as the center and the radius r B The three Hooke's hinge mounting seats A on the upper platform and the three Hooke's hinge mounting seats A on the lower platform are evenly distributed in an alternating manner; two Hooke's hinges are arranged on the Hooke's hinge mounting seats A, and the telescopic motion branch chain is connected to the Hooke's hinge.

3. The redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 2, characterized in that: The radius r of the circle where the three Hooke hinge mounting seats A of the lower platform are located B Greater than the radius r of the circle where the three Hooke hinge mounting seats A of the upper platform are located A , so that the telescopic motion branch chain is inclined inward from bottom to top and is arranged between the upper platform and the lower platform.

4. The redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 1, characterized in that: The second Hooke's hinge assembly includes a Hooke's hinge mounting seat B and a Hooke's hinge. The three Hooke's hinge mounting seats B are fixed to the lower surface of the upper platform. A The three Hooke hinge mounting seats B are fixed on the upper surface of the lower platform, with the center of the lower platform as the center and the radius r C The three Hooke's hinge mounting seats B on the upper platform are evenly distributed at the same angle as the three Hooke's hinge mounting seats B on the lower platform; a Hooke's hinge is provided on the Hooke's hinge mounting seat B, and the redundant branch chain is connected to the Hooke's hinge.

5. The redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 4, characterized in that: The radius r of the circle where the three Hooke hinge mounting seats B of the lower platform are located C Smaller than the radius r of the circle where the three Hooke hinge mounting seats B on the upper platform are located A , so that the redundant branch chain is inclined outward from bottom to top and is set between the upper platform and the lower platform.

6. A control method based on the redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claims 1 to 5, characterized in that: The control method adopts a force-position hybrid control method. The six retractable motion branches use position servo control to achieve attitude stability control of the electric stable platform; the three redundant branches use force servo control to achieve platform and load gravity compensation.

7. The control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 6, characterized in that: The system model adopted by the control method is: Kinematic model: Given the spatial position of the motion carrier connection system, calculate the extension and contraction of each actuator: l i =t p +R bp A i -B i , t p A is the position vector of the upper platform of the moving carrier connection system relative to the moving carrier, i is the coordinates of the upper hinge points of the moving carrier connection system, B i is the coordinates of the lower hinge points of the moving carrier connection system, R bp is the Euler transformation matrix, i is 1, 2, 3, 4, 5, 6; the matrix form of the extension and retraction speed of the six actuators is obtained as J represents the Jacobian matrix from the upper platform velocity to the actuator extension velocity, Indicates q p The first-order differential of , i.e., the generalized velocity of the center of mass of the upper platform in the moving carrier connection system; Dynamic model: The dynamic model was established using the Kane method, and the dynamic equation of the stable platform fixed on the motion carrier was expressed as: M p represents the relative motion mass matrix of the stable platform, C p Represents the centrifugal force / Coriolis force matrix of the relative motion of the stable platform; G p represents the gravity term of the stable platform, M b represents the mass matrix of the motion coupling between the stable platform and the moving carrier, C b represents the centrifugal force / Coriolis force matrix of the motion coupling between the stable platform and the moving carrier, f a represents the actuator driving force vector, Indicates q p The second-order differential of is the generalized acceleration of the center of mass of the upper platform in the motion carrier connection system. Indicates q b The second-order differential of is the generalized acceleration of the center of mass of the lower platform in the inertial coordinate system.

8. The control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 6, characterized in that: The position servo control adopts an adaptive anti-interference robust control algorithm consisting of Critic-Actor neural network compensation, disturbance estimation compensation and sliding mode control terms, and the expression is: f a =f an +f ad +f ar In the formula, f an 、f ad 、f ar They represent the neural network fitting uncertainty compensation, disturbance estimation compensation and sliding mode control terms respectively.

9. The control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 6, characterized in that: The force servo control adopts an admittance control algorithm based on PID position control to achieve force compliance control.

10. The control method of the redundant six-degree-of-freedom parallel heavy-load electric stable platform according to claim 9, characterized in that: The admittance control algorithm detects the force on the redundant branch chain through a force sensor, and then calculates the displacement of the redundant branch chain in the next control cycle based on the force and impedance parameters, so that the redundant branch chain can achieve follow-up control while maintaining a given supporting force.

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