Closed-loop control method of two-degree-of-freedom parallel mechanism
By using a linear regression fitting method with composite variables, the forward and inverse kinematic relationships of a two-degree-of-freedom parallel mechanism are fitted, solving the problems of large computational load and large error, and achieving precise closed-loop control.
Patent Information
- Application Number
- CN202511219203.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-28
- Publication Date
- 2025-11-07
AI Technical Summary
In existing technologies, closed-loop control methods for two-degree-of-freedom parallel mechanisms suffer from problems such as large computational load, large errors, and difficulty in achieving precise control.
A linear regression fitting method with composite variables is used to fit the forward and inverse kinematic relationships of the parallel mechanism. A linear regression fitting variable matrix is established through experimental data to achieve closed-loop control of the parallel mechanism.
While reducing the amount of computation, the fitting accuracy was improved, and precise control of the parallel mechanism was achieved, solving the problems of large amount of computation and large error.
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Figure CN120901962A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of robot control, and relates to a closed-loop control method of a two-degree-of-freedom parallel mechanism. BACKGROUND
[0002] Compared with other types of robots, a humanoid robot has the advantage of being able to walk quickly on complex unstructured terrain. In order to achieve strong adaptability of the humanoid robot to complex terrain, the design of the ankle joint of the robot usually adopts a structure with two degrees of freedom of pitch and roll. At present, a common form is a two-degree-of-freedom parallel mechanism driven by two linear cylinders. The design structure of the parallel mechanism is more concise, and the pitch and roll degrees of freedom are driven by two linear cylinders. There is coupling in the forward and inverse kinematics of the structure, which is difficult to decouple, so it is difficult to realize closed-loop control of the structure.
[0003] In the prior art, the closed-loop control of the two-degree-of-freedom parallel mechanism is usually realized by calculating the analytical solution of the forward and inverse kinematics of the mechanism. The patent for utility model
Inverse kinematics solving method and device for ankle joint control of biped robot, CN 116859978
Control method and device for hydraulic drive parallel structure, CN 116238616
[0004] The technical problem solved by the present application is to overcome the shortcomings of the prior art and provide a closed-loop control method for a two-degree-of-freedom parallel mechanism.
[0005] The technical solution of the present application is:
[0006] The closed-loop control method for the two-degree-of-freedom parallel mechanism comprises the following steps:
[0007] Step one, making a two-degree-of-freedom parallel mechanism for legs and feet, comprising a calf inclination sensor, a calf rod, a foot, a foot inclination sensor, a left linear cylinder and a right linear cylinder; wherein the foot is horizontally placed; the calf rod is vertically arranged at the top of the foot; the calf inclination sensor is mounted on the front side wall of the calf inclination sensor; the foot inclination sensor is mounted on the instep of the foot; the rear side wall of the calf rod is connected to the root of the foot through the left linear cylinder and the right linear cylinder;
[0008] Step two, setting the x-axis as the rotation axis of the foot pitch direction, the z-axis as the rotation axis of the foot roll direction, and the y-axis as the vertical direction; setting the pitch angle of the foot as θ p , the roll angle of the foot as θ r ; setting the length of the left linear cylinder as l1 and the length of the right linear cylinder as l2; establishing the calculation equations of θ p , θ r , l1 and l2; recording θ p , θ r , l1 and l2 corresponding to the pitch and roll full motion stroke angle range of the two-degree-of-freedom parallel mechanism;
[0009] Step three, constructing a linear regression fitting variable matrix Θ of the inverse kinematics of the two-degree-of-freedom parallel mechanism;
[0010] Step four, performing linear regression fitting according to the linear regression fitting variable matrix Θ and the calculation equations of l1 and l2 to establish the inverse kinematics relationship of the two-degree-of-freedom parallel mechanism;
[0011] Step five, constructing a linear regression fitting variable matrix L' of the forward kinematics of the two-degree-of-freedom parallel mechanism;
[0012] Step six, performing linear regression fitting according to the linear regression fitting variable matrix L' of the forward kinematics in step five and the θ p , θ r data obtained in step two to establish the forward kinematics relationship of the two-degree-of-freedom parallel mechanism;
[0013] Step seven, calculating the forward kinematics velocity relationship according to the forward kinematics relationship of the two-degree-of-freedom parallel mechanism.
[0014] Step eight, according to the inverse kinematics relationship of the two-degree-of-freedom parallel mechanism in step four and the forward kinematics relationship of the two-degree-of-freedom parallel mechanism in step six, a closed-loop controller of the two-degree-of-freedom parallel mechanism is established; and the closed-loop control of the two-degree-of-freedom parallel mechanism is completed.
[0015] In the closed-loop control method of the two-degree-of-freedom parallel mechanism, in step one, a foot pad is mounted on the bottom of the foot; the bottom end of the calf rod is connected with the foot through a cross hinge; and the left linear cylinder and the right linear cylinder are symmetrically arranged with the axial direction vertical.
[0016] In the closed-loop control method of the two-degree-of-freedom parallel mechanism, in step two, θ p , θ r are calculated by the following equations respectively:
[0017] θ p = θ 1x - θ 2x - 90°
[0018] θ r = θ 1y - θ 2y
[0019] In the equations, θ 1x , θ 1z are the x-axis angle and the z-axis angle of the calf inclination sensor respectively.
[0020] θ 2x , θ2 are the x-axis angle and the z-axis angle of the foot inclination sensor respectively.
[0021] In the closed-loop control method of the two-degree-of-freedom parallel mechanism, in step two, the calculation equations of l1 and l2 are as follows respectively:
[0022] l1 = (α1-α0)×S
[0023] l2 = (α2-α0)×S
[0024] In the equations, α1 and α2 are the angles of the left linear cylinder driving motor and the right linear cylinder driving motor respectively.
[0025] α0 is the angle of the linear cylinder driving motor in the zero position.
[0026] S is the lead of the linear cylinder screw.
[0027] In the closed-loop control method of the two-degree-of-freedom parallel mechanism, in step three, the linear regression fitting variable matrix Θ of the inverse kinematics is expressed as:
[0028]
[0029] In the formula, 1 n×1 is an n row × 1 column matrix, and all elements are 1; n is the n group of experimental data;
[0030] Θ p is the n group of experimental data of foot pitch angle; Θ p = [θ p1 , θ p2 , … θ pn ] T , θ p1 , θ p2 , … θ pn are the experimental data of the first group, …, the n group of foot pitch angle, respectively;
[0031] Θ r is the n group of experimental data of foot roll angle; Θ r = [θ r1 , θ r2 , … θ rn ] T , θ r1 , θ r2 , … θ rn are the experimental data of the first group, …, the n group of foot roll angle, respectively.
[0032] In the closed-loop control method of the two-degree-of-freedom parallel mechanism described above, in step four, the inverse kinematics relationship of the two-degree-of-freedom parallel mechanism is:
[0033] L = C1Θ
[0034] In the formula, L is a set of experimental data of the length of the two linear cylinders; L = [L1, L2] T ; wherein L1 is the n group of experimental data of the length of the left linear cylinder; L1 = [l 11 , l 12 , … l 1n ] T ; L2 is the n group of experimental data of the length of the right linear cylinder; L2 = [l 21 , l 22 , … l 2n ] T ;
[0035] C1 is the first variable coefficient.
[0036] In the closed-loop control method of the two-degree-of-freedom parallel mechanism described above, in step five, the linear regression fitting variable matrix L' of the forward kinematics is:
[0037]
[0038] In the closed-loop control method of the two-degree-of-freedom parallel mechanism, in the step six, the forward kinematics relationship of the two-degree-of-freedom parallel mechanism is:
[0039] Θ′=C2L′
[0040] In the formula, Θ′ is a pitch angle and a roll angle set of the two-degree-of-freedom parallel mechanism; Θ′=[Θ p , Θ r ] T , wherein Θ p is a pitch angle set of the two-degree-of-freedom parallel mechanism; and Θ r is a roll angle set of the two-degree-of-freedom parallel mechanism.
[0041] C2 is a second variable coefficient.
[0042] In the closed-loop control method of the two-degree-of-freedom parallel mechanism, in the step seven, the forward kinematics velocity relationship is:
[0043]
[0044] In the formula, Θ′ is a pitch angle and a roll angle set of the two-degree-of-freedom parallel mechanism; is a pitch angle and a roll angle set of the two-degree-of-freedom parallel mechanism; , wherein Θ is a pitch angle set of the two-degree-of-freedom parallel mechanism; and Θ is a roll angle set of the two-degree-of-freedom parallel mechanism.
[0045] is a derivative of the two linear cylinder length composite variables.
[0046] In the closed-loop control method of the two-degree-of-freedom parallel mechanism, in the step eight, the two-degree-of-freedom parallel mechanism closed-loop controller is:
[0047]
[0048] In the formula, T is a target torque set of the two-degree-of-freedom parallel mechanism pitch and roll;
[0049] K p is a proportional coefficient;
[0050] Θ des is a target pitch angle and roll angle set;
[0051] Θ act is a feedback actual pitch angle and roll angle set;
[0052] is a feedback actual pitch angle and roll angle set;
[0053] K d is a differential coefficient.
[0054] The beneficial effects of the present application compared with the prior art are:
[0055] (1) The present application adopts a composite variable linear regression fitting method combining powers and trigonometric functions to fit the kinematics of a two-degree-of-freedom parallel mechanism. Compared with the expression obtained by geometric analysis, the operation amount is smaller and the real-time performance is better. Compared with the interpolation fitting method containing only power variables, the fitting accuracy is higher while ensuring real-time performance.
[0056] (2) The present application records the actual pitch and roll angles and the elongation data of the two linear cylinders of the parallel mechanism as the reference for fitting through experimental sampling. Compared with using the geometric analysis results as the reference, the fitting error caused by the inconsistency between the parameters in the expression and the actual values is effectively avoided, and the precise control problem of the two-degree-of-freedom parallel mechanism is solved.
[0057] (3) The present application (3) can fit the forward and inverse kinematics by using the composite variable linear regression fitting method, so that closed-loop control of the parallel mechanism can be realized, and the problem of precise control of the two-degree-of-freedom parallel mechanism through closed-loop control is solved. BRIEF DESCRIPTION OF DRAWINGS
[0058] Figure 1 is a schematic diagram of the two-degree-of-freedom parallel mechanism of the present application;
[0059] Figure 2 is a schematic diagram of the two-degree-of-freedom parallel mechanism of the present application. DETAILED DESCRIPTION
[0060] The present application will be further described below in conjunction with examples.
[0061] The present application overcomes the problems of large error or large operation amount in the expression of the kinematics of the two-degree-of-freedom parallel mechanism in the prior art, and the lack of forward kinematics expression method. A closed-loop control method for a two-degree-of-freedom parallel mechanism is proposed, which uses a linear regression fitting method of composite variables to fit the forward and inverse kinematics of the parallel mechanism. The error is smaller while ensuring a lower operation amount, and the closed-loop control of the parallel mechanism is realized, solving the problem of precise control of the parallel mechanism.
[0062] The closed-loop control method for a two-degree-of-freedom parallel mechanism specifically includes the following steps:
[0063] Step one, make a leg-foot two-degree-of-freedom parallel mechanism, such as Figure 1As shown, specifically includes calf angle sensor 1, calf bar 2, foot 3, foot angle sensor 4, left linear cylinder 6 and right linear cylinder 7; wherein the foot 3 is placed horizontally; the calf bar 2 is vertically arranged at the top of the foot 3; the front side wall of the calf angle sensor 1 is mounted with the calf angle sensor 1; the upper instep of the foot 3 is mounted with the foot angle sensor 4; the rear side wall of the calf bar 2 is connected with the root of the foot 3 through the left linear cylinder 6 and the right linear cylinder 7; the sole of the foot 3 is installed with the foot cushion 5; the bottom end of the calf bar 2 is connected with the foot 3 through the cross hinge 8; the left linear cylinder 6 and the right linear cylinder 7 are symmetrical and vertically arranged in the axial direction.
[0064] Step two, set x axis as the pitch direction rotation axis of the foot 3, z axis as the roll direction rotation axis of the foot 3, y axis as the vertical direction; as shown Figure 2 The pitch angle of the foot 3 is set as θ p , the roll angle of the foot 3 is set as θ r ; the length of the left linear cylinder 6 is set as l1, the length of the right linear cylinder 7 is set as l2; the calculation equation of θ p , θ r , l1, l2 is established; record θ p , θ r , l1, l2 corresponding to the pitch and roll full motion stroke angle range of the two degree of freedom parallel mechanism. Specifically:
[0065] The calculation equation of θ p , θ r is respectively:
[0066] θ p = θ 1x - θ 2x - 90°
[0067] θ r = θ 1y - θ 2y
[0068] In the formula, θ 1x , θ 1z are the x axis angle and z axis angle of the calf angle sensor 1 respectively;
[0069] θ 2x , θ2 are the x axis angle and z axis angle of the foot angle sensor 4 respectively.
[0070] The calculation equation of l1, l2 is respectively:
[0071] l1 = (α1-α0)×S
[0072] l2 = (α2-α0)×S
[0073] In the formula, α1, α2 are the driving motor angle of the left linear cylinder 6 and the driving motor angle of the right linear cylinder 7 respectively;
[0074] α0 is the linear cylinder driving motor angle in zero position state;
[0075] S is the lead of linear cylinder screw.
[0076] The zero position state is defined as θ p = 0 and the roll angle θ r = 0.
[0077] Step three, construct the linear regression fitting variable matrix Θ of inverse kinematics of the two-degree-of-freedom parallel mechanism.
[0078] The variable matrix is preferably combined with a compound variable of power and trigonometric function, and the linear regression fitting variable matrix Θ of inverse kinematics is expressed as:
[0079]
[0080] In the formula, 1 n×1 is an n-row × 1-column matrix, and the elements are all 1; n is the n sets of experimental data;
[0081] Θ p is the n sets of experimental data of the pitch angle of the foot 3; Θ p = [θ p1 , θ p2 ,... θ pn ] T , θ p1 , θ p2 ,... θ pn are the experimental data of the pitch angle of the foot 3 of the first group,..., the n th group, respectively;
[0082] Θ r is the n sets of experimental data of the roll angle of the foot 3; Θ r = [θ r1 , θ r2 ,... θ rn ] T , θ r1 , θ r2 ,... θ rn are the experimental data of the roll angle of the foot 3 of the first group,..., the n th group, respectively.
[0083] Step four, according to the calculation equation of the linear regression fitting variable matrix Θ and l1, l2, linear regression fitting is carried out to establish the inverse kinematics relationship of the two-degree-of-freedom parallel mechanism.
[0084] The inverse kinematics relationship of the two-degree-of-freedom parallel mechanism is:
[0085] L = C1Θ
[0086] In the formula, L represents the set of experimental data for the length of two linear cylinders; L = [L1, L2] T Where L1 represents n sets of experimental data for the length of the left linear cylinder 6; L1 = [l 11 , l 12 , ...l 1n ] T L2 represents n sets of experimental data for the length of the right linear cylinder 7; L2 = [l 21 , l 22 , ...l 2n ] T ;
[0087] C1 is the coefficient of the first variable.
[0088] C1 can be calculated using the least squares method:
[0089] C1=(Θ T Θ) -1 Θ T L
[0090] Step 5: Construct the linear regression fitting variable matrix L′ for the forward kinematics of the two-degree-of-freedom parallel mechanism.
[0091] The linear regression fitting variable matrix L′ for positive kinematics is:
[0092]
[0093] Step 6: Fit the variable matrix L′ using the linear regression of the positive kinematics from Step 5 and the θ obtained in Step 2. p θ r The data is used to perform linear regression fitting to establish the positive kinematic relationship of the two-degree-of-freedom parallel mechanism.
[0094] The forward kinematics of a two-degree-of-freedom parallel mechanism are as follows:
[0095] Θ′=C2L′
[0096] In the formula, Θ′ is the set of pitch and roll angles of a two-degree-of-freedom parallel mechanism; Θ′=[Θ p Θ r ] T , where Θ p Θ is the set of pitch angles for a two-degree-of-freedom parallel mechanism. r This is the set of roll angles for a two-degree-of-freedom parallel mechanism;
[0097] C2 is the coefficient of the second variable.
[0098] C2 can be calculated using the least squares method:
[0099] C2=(L ′T L′) -1L ′T Θ′
[0100] Step seven, according to the positive kinematics relationship of the two-degree-of-freedom parallel mechanism, a positive kinematics velocity relationship is calculated.
[0101] The positive kinematics velocity relationship is:
[0102]
[0103] In the formula, is a pitch angle velocity and a roll angle velocity set of the two-degree-of-freedom parallel mechanism; wherein, is respectively a pitch angle velocity set and a roll angle velocity set of the two-degree-of-freedom parallel mechanism;
[0104] is a derivative of the length composite variable of the two linear cylinders.
[0105] Specifically,
[0106]
[0107] wherein is respectively a linear velocity of the left and right two linear cylinders of the two-degree-of-freedom parallel mechanism.
[0108] Step eight, according to the inverse kinematics relationship of the two-degree-of-freedom parallel mechanism in step four and the positive kinematics relationship of the two-degree-of-freedom parallel mechanism in step six, a closed-loop controller of the two-degree-of-freedom parallel mechanism is established; and the closed-loop control of the two-degree-of-freedom parallel mechanism is completed.
[0109] The closed-loop controller of the two-degree-of-freedom parallel mechanism is:
[0110]
[0111] In the formula, T is a target torque set of the pitch and roll of the two-degree-of-freedom parallel mechanism;
[0112] K p is a proportional coefficient;
[0113] Θ des is a target pitch angle and roll angle set;
[0114] Θ act is a feedback actual pitch angle and roll angle set;
[0115] is a feedback actual pitch angle velocity and roll angle velocity set;
[0116] K d is a differential coefficient.
[0117] Specifically, T = [τ p , τ r ] T , τ p , τ r are target moments of pitch and roll of the two-degree-of-freedom parallel mechanism, respectively; Θ des = [θ pdes , θ rdes ] T , θ pdes , θ rdes are target pitch and roll angles, respectively; Θ act = [θ pact , θ ract ] T , θ pdes , θ rdes are feedback actual pitch and roll angles, respectively. are feedback actual pitch and roll angular velocities, respectively.
[0118] Then, the target pitch and roll angles can be converted into target lengths of the left and right linear cylinders according to the inverse kinematics relationship obtained in step four, and can be specifically expressed as:
[0119]
[0120] wherein L des = [l 1des , l 2des ] T , l 1des , l 2des are target lengths of the left and right linear cylinders, respectively. is a variable matrix form of the target pitch and roll angles, and can be specifically expressed as:
[0121]
[0122] The actual pitch and roll angles can be obtained through the actual lengths of the left and right linear cylinders according to the forward kinematics relationship obtained in step five, and can be specifically expressed as:
[0123]
[0124] wherein, is a variable matrix form of the actual lengths of the left and right linear cylinders, and can be specifically expressed as:
[0125]
[0126] wherein, l 1act and l 2act are actual lengths of the left and right linear cylinders, respectively.
[0127] The actual pitch and roll angular velocities can be obtained according to the forward kinematics velocity relationship obtained in step six, through the actual linear velocities of the left and right linear cylinders, and can be specifically represented as:
[0128]
[0129] wherein, are actual pitch and roll angular velocities, respectively; is the derivative of the variable matrix form of the actual lengths of the left and right linear cylinders, and is specifically:
[0130]
[0131] wherein, are actual linear velocities of the left and right linear cylinders, respectively.
[0132] The compound variable linear regression fitting method combining the power and trigonometric functions is adopted to fit the kinematics of the two-degree-of-freedom parallel mechanism, and compared with the expression obtained by geometric analysis, the operation amount is smaller, and the real-time performance is better; compared with the interpolation fitting method containing only the power variable, the fitting accuracy is higher while ensuring real-time performance.
[0133] The actual pitch and roll angles and the elongation data of the two linear cylinders of the parallel mechanism are recorded by experimental sampling as the reference for fitting, compared with the geometric analysis results as the reference, the fitting error caused by the inconsistency between the parameters in the expression and the actual situation is effectively avoided, and the accurate control problem of the two-degree-of-freedom parallel mechanism is solved.
[0134] The compound variable linear regression fitting method adopted by the present application can be used to fit the forward and inverse kinematics relationship, so that the closed-loop control of the parallel mechanism is realized, and the problem that the two-degree-of-freedom parallel mechanism is difficult to realize accurate control through closed-loop is solved.
[0135] Although the present application has been disclosed with the above preferred embodiments, it is not intended to limit the present application, and any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not deviate from the technical solutions of the present application, belongs to the protection scope of the present application.
Claims
1. A closed-loop control method of a two-degree-of-freedom parallel mechanism, characterized by: The application relates to a two-degree-of-freedom parallel mechanism, and belongs to the field of robot control. Step one: a two-degree-of-freedom parallel mechanism is prepared, which comprises a calf inclination sensor (1), a calf rod (2), a foot (3), a foot inclination sensor (4), a left linear cylinder (6) and a right linear cylinder (7); wherein the foot (3) is horizontally placed; the calf rod (2) is vertically arranged on the top of the foot (3); the calf inclination sensor (1) is arranged on the front side wall of the calf inclination sensor (1); the foot inclination sensor (4) is arranged on the upper instep of the foot (3); the rear side wall of the calf rod (2) is connected with the root of the foot (3) through the left linear cylinder (6) and the right linear cylinder (7); Step two, set the x-axis as the foot (3) pitch direction rotation axis, the z-axis as the foot (3) roll direction rotation axis, and the y-axis as the vertical direction; Set the pitch angle of the foot (3) as θ p , the roll angle of the foot (3) as θ r ; Set the length of the left linear cylinder (6) as l1 and the length of the right linear cylinder (7) as l2; Establish the calculation equation of θ p , θ r , l1 and l2; Record θ p , θ r , l1 and l2 corresponding to the pitch and roll full motion stroke angle range of the two-degree-of-freedom parallel mechanism Step three: a linear regression fitting variable matrix Θ of inverse kinematics of the two-degree-of-freedom parallel mechanism is constructed; Step four: linear regression fitting is carried out according to the linear regression fitting variable matrix Θ and the calculation equation of l1 and l2, and an inverse kinematics relationship of the two-degree-of-freedom parallel mechanism is established; Step five: a linear regression fitting variable matrix L' of forward kinematics of the two-degree-of-freedom parallel mechanism is constructed; Step six, according to the linear regression fitting variable matrix L' in the forward kinematics in step five and θ p , θ r data obtained in step two, linear regression fitting is performed to establish the forward kinematics relationship of the two-degree-of-freedom parallel mechanism; Step seven: a forward kinematics velocity relationship is calculated according to the forward kinematics relationship of the two-degree-of-freedom parallel mechanism; Step eight: a closed-loop controller of the two-degree-of-freedom parallel mechanism is established according to the inverse kinematics relationship of the two-degree-of-freedom parallel mechanism in step four and the forward kinematics relationship of the two-degree-of-freedom parallel mechanism in step six, and the closed-loop control of the two-degree-of-freedom parallel mechanism is completed.
2. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 1, characterized in that: In the step one, a foot bottom cushion (5) is arranged on the foot sole of the foot (3); the bottom end of the calf rod (2) is connected with the foot (3) through a cross hinge (8); the left linear cylinder (6) and the right linear cylinder (7) are symmetrically arranged and vertically arranged in the axial direction.
3. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 1, characterized in that: In the second step, θ p , θ r The calculation equation is respectively: θ p = θ 1x - θ 2x - 90° θ r = θ 1y - θ 2y In the formula, θx, θz, and θy are the x-axis angle, the z-axis angle, and the y-axis angle of the thigh angle sensor (1), respectively. 1x , θx 1z , and θy are the x-axis angle, the z-axis angle, and the y-axis angle of the calf angle sensor (1), respectively. θ 2x θ1, θ2 are x-axis angle, z-axis angle of the foot inclination sensor (4), respectively.
4. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 3, characterized in that: In the step two, the calculation equations of l1 and l2 are respectively: l1＝(α1-α0)×S l2＝(α2-α0)×S In the formula, alpha1 and alpha2 are respectively the driving motor angles of the left linear cylinder (6) and the right linear cylinder (7); alpha0 is the driving motor angle of the linear cylinder in the zero position state; S is the lead of the linear cylinder screw.
5. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 4, characterized in that: In the step three, the linear regression fitting variable matrix Θ of inverse kinematics is represented as: In the formula, 1 n×1 is an n row x 1 column matrix, all elements of which are 1; n is the n group of experimental data; Θ p n sets of experimental data of the pitch angle of the foot (3); Θ p = [θ p1 , θ p2 ,... θ pn ] T , θ p1 , θ p2 ,... θ pn are the experimental data of the pitch angle of the foot (3) of the 1st set,..., the nth set, respectively; Θ r n sets of experimental data of the roll angle of the foot (3); Θ r = [θ r1 , θ r2 ,... θ rn ] T , θ r1 , θ r2 ,... θ rn are the experimental data of the roll angle of the foot (3) of the 1st set,..., nth set, respectively.
6. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 5, characterized in that: In the step four, the inverse kinematics relationship of the two-degree-of-freedom parallel mechanism is: L=C1Θ In the formula, L is a set of experimental data of lengths of two linear cylinders; L = [L1, L2] T ; wherein L1 is n sets of experimental data of lengths of left linear cylinders (6); L1 = [l 11 , l 12 ,... l 1n ] T ; L2 is n sets of experimental data of lengths of right linear cylinders (7); L2 = [l 21 , l 22 ,... l 2n ] T ; C1 is the first variable coefficient.
7. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 6, characterized in that: In the step five, the linear regression fitting variable matrix L' of forward kinematics is:
8. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 7, characterized in that: In the step six, the forward kinematics relationship of the two-degree-of-freedom parallel mechanism is: Θ'=C2L' In the formula, Θ' is a pitch angle and a roll angle set of the two-degree-of-freedom parallel mechanism; Θ' = [Θ p , Θ r ] T , wherein Θ p is a pitch angle set of the two-degree-of-freedom parallel mechanism; and Θ r is a roll angle set of the two-degree-of-freedom parallel mechanism. C2 is the second variable coefficient.
9. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 8, characterized in that: In the step seven, the forward kinematics velocity relationship is: wherein is the pitch angular velocity and roll angular velocity set of the 2-DOF parallel mechanism; wherein is the pitch angular velocity set and roll angular velocity set of the 2-DOF parallel mechanism, respectively. is the derivative of the two straight cylinder length composite variable.
10. The closed-loop control method of a two-degree-of-freedom parallel mechanism according to claim 9, wherein: In the step eight, the closed-loop controller of the two-degree-of-freedom parallel mechanism is: In the formula, T is a target torque set of the two-degree-of-freedom parallel mechanism in pitching and rolling. K p is a proportionality factor; Θ des Θ des Θ des Θ des Θ des Θ des Θ <000 Θ act a set of actual pitch, roll angles for feedback; a set of actual pitch and roll angular velocities for feedback; K d is the differential coefficient.