Six-degree-of-freedom parallel robot with large attitude angle and control method thereof

Abstract

A six-degree-of-freedom parallel robot with large attitude angle and a control method thereof belong to the technical field of large attitude angle parallel robots. A moving platform is connected with a fixed frame through four PUS branch chains and three UPS branch chains. Drive joints of the branch chains are connected with the moving platform through connecting rods. A vertical linear motion module of the PUS branch chain is fixedly arranged on the fixed frame. An E-shaped Hooke joint is arranged between the drive joint and the connecting rod. An E-shaped spherical pair is arranged between the connecting rod and the moving platform. An inclined linear motion module of the UPS is arranged between the fixed frame and the H-shaped Hooke joint. The drive joint and the connecting rod are fixedly connected. A U-shaped spherical pair is arranged between the connecting rod and the moving platform. Through optimization of the geometric relationship between the joints, cooperation of different control strategies of the normal group branch chain and the rotation group branch chain, the pose accuracy of the moving platform is ensured. The driving force of each drive joint can be intervened and adjusted, so that the moving platform can continuously adjust the large-angle attitude.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of large attitude angle parallel robots, in particular to a six-degree-of-freedom parallel robot with large attitude angle and a control method thereof. BACKGROUND

[0002] Parallel robots have many advantages such as large stiffness, strong carrying capacity, small inertia, good dynamic response, and no cumulative error, and are widely used in large attitude adjustment platforms, precision optical machine structures, and mechanical processing fields. A parallel robot is usually composed of a moving platform, a fixed platform, and a plurality of branch chains connected between the two. A certain link in each branch chain is selected as a driving joint, and the number of driving joints is comparable to the number of degrees of freedom of the parallel robot mechanism. For a six-degree-of-freedom parallel robot, the large-scale movement of the moving platform will cause interference between the branch chains, resulting in limited activity space and attitude adjustment range of the six-degree-of-freedom parallel robot. In addition, due to the strong coupling between the branch chains of the parallel robot, there are many singular points in the working space. In order to avoid them, the working route of the parallel robot will be discontinuous, which reduces the operation ability of the robot.

[0003] At present, with the continuous development of industrial level, the processing demand for special parts is increasing, and the potential of parallel robots in the field of mechanical processing needs to be further tapped. The problems of small working range and attitude adjustment range of six-degree-of-freedom parallel robots and many singular points in the working space need to be solved. Through the redesign of the Hooke joint and the spherical pair and the reasonable configuration of the branch chains of the parallel robot, the working space can be ensured to a certain extent, and the attitude adjustment range of the parallel robot can be increased. For the problem of many singular points in the working space of the parallel robot, the singular shape of the expected working path can be avoided through the form of redundant degrees of freedom, or the singular points of the parallel robot can be eliminated through the way of redundant driving.

[0004] For example, the applicant's prior application for a Chinese invention patent with application number 202310694440.0, application date June 12, 2023, and name of a 4PUS-3UPS redundant drive parallel robot, its branch chain includes four PUS branch chains and three UPS branch chains. Through the redesign of the Hooke joint and the spherical pair, the moving platform can realize large-angle attitude adjustment, and the way of redundant driving is proposed to eliminate the singular points in the working space. However, the joint layout proposed in this scheme has a loss of stability singularity in some poses, which cannot be avoided by the redundant driving method proposed, and the patent also does not propose a specific redundant driving control strategy applicable to the proposed parallel robot.

[0005] Therefore, it is necessary to further optimize the design of the six-degree-of-freedom parallel robot with large attitude angle and propose a control method to solve the adverse effects of loss of stability singularity on the parallel robot. SUMMARY

[0006] To solve the problems in the background art, the application provides a six-degree-of-freedom parallel robot with a large attitude angle and a control method thereof, which eliminates the instability singularity in the attitude change process by optimizing the geometric relationship between the hinges of the parallel robot, and uses the cooperation of different control strategies of the normal group of branches and the rotation group of branches to intervene in the adjustment of the driving force of each branch driving joint while ensuring the pose accuracy of the moving platform, so that the moving platform can continuously adjust the large-angle attitude.

[0007] To achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0008] A six-degree-of-freedom parallel robot with a large attitude angle, comprising a fixed frame and a moving platform arranged inside the fixed frame, wherein the moving platform and the fixed frame are connected by seven branches, including four PUS branches and three UPS branches, characterized in that: the four PUS branches are all vertical linear motion modules and are respectively installed at the top positions of the four corners of the fixed frame, the three UPS branches are all inclined linear motion modules and are respectively installed between the top of the fixed frame and the moving platform, the vertical linear motion module and the inclined linear motion module are both movably provided with a driving joint, and the driving joints of the seven branches are respectively connected with the moving platform through connecting rods.

[0009] The vertical linear motion module is fixedly arranged with the fixed frame, the driving joint and the upper end of the connecting rod are connected through an E-type Hooke joint, and the lower end of the connecting rod and the moving platform are connected through an E-type spherical pair.

[0010] The upper end of the inclined linear motion module is connected with the fixed frame through an H-type Hooke joint, the driving joint of the inclined linear motion module is fixedly connected with the upper end of the connecting rod, the lower end of the connecting rod and the moving platform are connected through a U-type spherical pair, and the connecting rod is located on the center line of the H-type Hooke joint and the U-type spherical pair.

[0011] In the initial state, the moving platform is in a horizontal position, the centers of rotation of the four E-shaped Hooke joints are arranged according to four end points of an isosceles trapezoid in the horizontal projection, the centers of rotation of the three H-shaped Hooke joints are arranged according to three end points of an isosceles right triangle in the horizontal projection, the hypotenuse of the isosceles right triangle in which the centers of rotation of the H-shaped Hooke joints are located is arranged to coincide with the center line of the isosceles trapezoid in which the centers of rotation of the E-shaped Hooke joints are located in the top view, and the midpoint of the hypotenuse of the isosceles right triangle in which the centers of rotation of the H-shaped Hooke joints are located is located on the axis of the moving platform; the centers of rotation of the four E-shaped spherical pairs are arranged according to four end points of a rectangle in the horizontal projection and are arranged at two ends of the moving platform, the centers of rotation of the three U-shaped spherical pairs are arranged according to three end points of an isosceles right triangle in the horizontal projection and are arranged at edges of the surface of the moving platform, the hypotenuse of the isosceles right triangle in which the centers of rotation of the U-shaped spherical pairs are located is arranged to be perpendicular to the hypotenuse of the isosceles right triangle in which the centers of rotation of the H-shaped Hooke joints are located in the top view, and the midpoint of the hypotenuse of the isosceles right triangle in which the centers of rotation of the U-shaped spherical pairs are located is located on the axis of the moving platform.

[0012] Further, the vertical linear motion module and the oblique linear motion module both adopt ball screws as execution mechanisms and are matched with moving pairs as driving joints.

[0013] A control method of a six-degree-of-freedom parallel robot with a large attitude angle, comprising the following steps:

[0014] The seven branch chains are numbered as 1#PUS branch chain, 2#PUS branch chain, 3#PUS branch chain, 4#PUS branch chain, and 5#UPS branch chain, 6#UPS branch chain, and 7#UPS branch chain, wherein the H-shaped Hooke joint and the U-shaped spherical pair of the 5#UPS branch chain are arranged at the vertices of the corresponding isosceles right triangle, and the 6#UPS branch chain and the 7#UPS branch chain are center-symmetric structures, so that the seven branch chains are divided into two groups, including a normal group branch chain and a rotation group branch chain, the normal group branch chain is composed of the 1#PUS branch chain, the 2#PUS branch chain, the 3#PUS branch chain, the 4#PUS branch chain, and the 5#UPS branch chain, and the rotation group branch chain is composed of the 6#UPS branch chain and the 7#UPS branch chain.

[0015] First, a reference coordinate system and a motion coordinate system are defined, the reference coordinate system O A -X A Y A Z A The origin O is located below the plane in which the centers of rotation of the H-shaped Hooke joints in the three UPS branch chains, the intersection point of the median line and the vertical bisector of the lower base of the isosceles trapezoid in which the centers of rotation of the E-shaped Hooke joints of the four PUS branch chains coincide, Y A The Y-axis is horizontal to the left, and the Z-axis is vertical downward, the motion coordinate system O A -X A Y B Y B Y BZ B The origin O of the reference coordinate system is located at the center of the four PUS branch chains A The center Y of the circle where the E-type spherical deputy revolves is located at the center of the circle of the four PUS branch chains B The Z-axis is perpendicular to the left surface of the moving platform B The X-axis is vertical downward A The Y-axis is perpendicular to the X-axis and the Z-axis B The X-axis, the Y-axis and the Z-axis all comply with the right-hand rule

[0016] The pose of the moving platform in the workspace is described by the pose of the motion coordinate system in the reference coordinate system, expressed as (x o ,y o ,z o ), the attitude is conventionally the X-Y-Z Euler angle, expressed as (α B ,β B ,γ B ), and the generalized pose coordinate of the space motion of the moving platform is expressed as X=[x o y o z o α B β B γ B ] T ;

[0017] The drive joint of the said alternate group branch chain is driven by a sliding mode controller for drive force control through an alternate condition, and the other drive joint of the alternate group branch chain and all the drive joints of the said normal group branch chain are controlled in position according to a dynamics model, and the said alternate condition is defined as the condition number of the velocity Jacobian matrix J6 and J7, if the condition number of J6 is smaller, the drive joint of the 6#UPS branch chain is controlled in drive force, and if the condition number of J7 is smaller, the drive joint of the 7#UPS branch chain is controlled in drive force

[0018] The velocity Jacobian matrix J6 and J7 are defined as follows:

[0019] J6=[J h1 J h2 J h3 J h4 J h5 J h6 ]W v

[0020] J7=[J h1 J h2 J h3 J h4 J h5 J h7 ]W v

[0021] In the formula, J hmm=1,2,...,6,7 represents the velocity Jacobian matrix of each driving joint, W v is a variable weight matrix, expressed as follows:

[0022]

[0023] Among them, E 3×3 is the 3×3 identity matrix, O 3×3 is a 3×3 zero matrix, L v is the root mean square of the velocity Jacobian matrix corresponding to the velocity component vector modulus of the moving platform, L ω is the root mean square of the vector modulus of the angular velocity component of the moving platform corresponding to the velocity Jacobian matrix, which is calculated as follows:

[0024]

[0025] Where n represents the J in the velocity Jacobian matrix J6 and J7. hm The nth child of ;

[0026] Define the total velocity Jacobian matrix J including J6 and J7 A ∈R 6×7 And the driving force matrix τ∈R 7×1 as follows:

[0027]

[0028] τ=[τ1τ2τ3τ4τ5τ6τ7] T

[0029] The dynamic model is as follows:

[0030]

[0031] The generalized inverse method is used to obtain the least squares solution of the dynamic model and define J A The generalized right pseudo-inverse matrix of Then the least squares norm solution of the dynamic model is obtained:

[0032]

[0033] Where A∈R 6×6 Represents the acceleration coefficient matrix, C∈R 6×6 Represents the velocity term coefficient matrix, Q∈R 6×6 represents the gravity coefficient matrix, E3 is the 3rd-order identity matrix, O3 is the 3rd-order zero matrix, [FM] T ∈R 6×1 It represents the external force applied to the moving platform by the external load;

[0034] The established dynamic model is converted from the workspace to the joint space, and the joint space velocity coordinates are defined It contains seven elements, which correspond to the Cartesian coordinate movement speed of the seven driving joints respectively, and the spatial motion generalized velocity coordinates of the moving platform and the joint space velocity coordinates are expressed as follows:

[0035]

[0036] In the formula, J = [J h1 J h2 J h3 J h4 J h5 J h6 J h7 ];

[0037] Solving it, define the generalized left pseudo-inverse matrix J + of J as J T J) -1 J T , and the mapping relationship is converted to:

[0038]

[0039] Taking the derivative of both sides of the equation gives:

[0040]

[0041] Where,

[0042] Substitute the dynamic model and do not consider the external load, get:

[0043]

[0044] By multiplying the generalized right pseudo-inverse matrix J A of J A + Solving the joint space described dynamic model:

[0045]

[0046] In the formula,

[0047] Considering the modeling error of the dynamic model and external disturbance, both are integrated into the error term d ∈ R 7×1 , Add the error term to the above formula, get:

[0048]

[0049] Let the joint space position tracking error be e ∈ R7×1 The joint space velocity tracking error is

[0050] e = q d -q

[0051]

[0052] wherein,

[0053] q d = [q 1d q 2d q 3d q 4d q 5d q 6d q 7d ] T

[0054]

[0055] wherein, q md m = 1, 2, …, 6, 7 represent the desired position of each driving joint;

[0056] The nonsingular terminal fast sliding mode surface is designed as:

[0057]

[0058] wherein, the coefficient matrix Λ = diag(λ1, λ2, λ3, λ4, λ5, λ6, λ7) and λ m > 0, a and b are positive odd numbers, b > a, and

[0059] The derivative of the sliding mode surface is obtained as:

[0060]

[0061] Let the exponential-based sliding mode approach rate be:

[0062]

[0063] Finally, the upper bound-based sliding mode control method is adopted to design the sliding mode controller as follows:

[0064]

[0065] wherein, sgn(s) is a sign function, ε > 0, and k > 0.

[0066] Further, the hyperbolic tangent function tanh(sη) is adopted in the sliding mode controller to replace the sign function sgn(s).

[0067] Compared with the prior art, the present application has the following advantages:

[0068] The six-degree-of-freedom parallel robot of the present application has the spatial layout of the centers of rotation of the Hooke joints and the spherical pairs designed as non-single scaling relationship, eliminates partial instability singularities of the parallel robot in the workspace, has seven driving branched chains, is redundantly driven, the control method provided uses different control strategies for the normal group branched chains and the alternate group branched chains, is a typical force-position hybrid driving logic, can ensure the motion control precision while also intervening in the distribution of the driving force of each driving joint, makes the distribution of the driving force more uniform, can ensure the continuous adjustment and change of the large attitude angle in the workspace, and has no singularities that need to be avoided. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 is the overall structure isometric view of the six-degree-of-freedom parallel robot of the present application;

[0070] Figure 2 is the branched chain number diagram of the six-degree-of-freedom parallel robot of the present application;

[0071] Figure 3 is the spatial distribution diagram of the Hooke joints of the six-degree-of-freedom parallel robot of the present application;

[0072] Figure 4 is the spatial distribution diagram of the spherical pairs of the six-degree-of-freedom parallel robot of the present application;

[0073] Figure 5 is the positive direction large attitude angle state diagram of the B axis of the six-degree-of-freedom parallel robot of the present application;

[0074] Figure 6 is the negative direction large attitude angle state diagram of the B axis of the six-degree-of-freedom parallel robot of the present application;

[0075] Figure 7 is the two kinds of mechanism singularities of the six-degree-of-freedom parallel robot of the present application;

[0076] Figure 8 is the comparison diagram of the sign function and the hyperbolic tangent function. DETAILED DESCRIPTION

[0077] The technical solutions in the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0078] As Figures 1-7As shown, the application is optimized and improved on the basis of the typical Gough-Stewart configuration, one UPS branch is added, and the joint order of four UPS branches is changed to PUS, combined with Figure 1 As shown, the inside of the fixed frame 9 is provided with the moving platform 8, and seven branches are connected between the moving platform 8 and the fixed frame 9, including four PUS branches and three UPS branches, so that the number of drives is more than the number of degrees of freedom of the mechanism to facilitate the formation of redundant drive control. Combined with Figure 2 As shown, the four PUS branches are numbered 1#PUS branch 1, 2#PUS branch 2, 3#PUS branch 3 and 4#PUS branch 4 in anticlockwise direction in plan view, and the three UPS branches are numbered 5#UPS branch 5, 6#UPS branch 6 and 7#UPS branch 7 in clockwise direction in plan view. Combined with Figure 5 As shown, the four PUS branches all adopt vertical linear motion modules 11 and are respectively installed at the top positions of the four corners of the fixed frame 9, and the three UPS branches all adopt inclined linear motion modules 51 and are respectively installed between the top of the fixed frame 9 and the moving platform 8, the vertical linear motion modules 11 and the inclined linear motion modules 51 all adopt ball screws as execution mechanisms and are matched with moving pairs as driving joints, and the driving joints of the seven branches are respectively connected with the moving platform 8 through connecting rods. Among them, the vertical linear motion modules 11 of the four PUS branches are fixedly arranged with the fixed frame 9, the driving joints of the vertical linear motion modules 11 are connected with the upper ends of the connecting rods through E-type hooke joints 12, and the lower ends of the connecting rods are connected with the moving platform 8 through E-type spherical pairs 13; the upper ends of the inclined linear motion modules 51 of the three UPS branches are connected with the fixed frame 9 through H-type hooke joints 52, the driving joints of the inclined linear motion modules 51 are fixedly connected with the upper ends of the connecting rods, and the lower ends of the connecting rods are connected with the moving platform 8 through U-type spherical pairs 53, wherein the connecting rods are on the center line of rotation of the H-type hooke joint 52 and the U-type spherical pair 53.

[0079] On this basis, the application provides a six-degree-of-freedom parallel robot with large attitude angle, the core of which is to eliminate the instability singularity of the parallel robot in the attitude change process by optimizing the geometric relationship between the joints. In the initial state, the moving platform 8 is in a horizontal position, combined with Figure 3 As shown, the centers of rotation of the E-type hooke joints 12 of the four PUS branches are arranged according to the four endpoints of the isosceles trapezoid in horizontal projection, the centers of rotation of the H-type hooke joints 52 of the three UPS branches are arranged according to the three endpoints of the isosceles right triangle in horizontal projection, the hypotenuse of the isosceles right triangle where the center of rotation of the H-type hooke joint 52 is located coincides with the center line of the isosceles trapezoid where the center of rotation of the E-type hooke joint 12 is located in plan view, and the midpoint of the hypotenuse of the isosceles right triangle where the center of rotation of the H-type hooke joint 52 is located is located on the axis of the moving platform 8; combined with Figure 4As shown, the rotation centers of the E-type ball joints 13 of the four PUS branches are arranged at the ends of the moving platform 8 according to the four endpoints of a rectangle in horizontal projection. The rotation centers of the U-type ball joints 53 of the three UPS branches are arranged at the edge of the surface of the moving platform 8 according to the three endpoints of an isosceles right triangle in horizontal projection. The hypotenuse of the isosceles right triangle where the rotation centers of the U-type ball joints 53 are located is perpendicular to the hypotenuse of the isosceles right triangle where the rotation centers of the H-type Hooke's hinges 52 are located, and the midpoint of the hypotenuse of the isosceles right triangle where the rotation centers of the U-type ball joints 53 are located is located on the axis of the moving platform 8. Among the three UPS branches, the H-type Hooke's hinge 52 and the U-type ball joint 53 of the 5# UPS branch chain are respectively arranged at the vertices of the corresponding right angles of the isosceles right triangle, while the 6# UPS branch chain 6 and the 7# UPS branch chain 7 are centrosymmetrical structures. The geometric layout of the hinge asymmetric scaling is helpful to avoid the movement singularity of the mechanism. The combination of redundant drive control can avoid the two singular configurations in the B-axis direction. Figure 5 、 Figure 6 As shown, the parallel robot can achieve large-angle posture adjustment in the positive and negative directions of the B-axis.

[0080] For the proposed six-degree-of-freedom parallel robot with a large attitude angle, the seven branches are divided into two groups, including normal group branches and rotation group branches. The normal group branches consist of 1#PUS branch 1, 2#PUS branch 2, 3#PUS branch 3, 4#PUS branch 4 and 5#UPS branch 5, and the rotation group branches consist of 6#UPS branch 6 and 7#UPS branch 7. The normal group branches and the rotation group branches adopt different control strategies. The normal group branches are mainly involved in the determination of the posture of the dynamic platform 8, and the rotation group branches are used to adjust the distribution of driving force of all driving joints and participate in the determination of the posture of the dynamic platform 8.

[0081] First, define the reference coordinate system and motion coordinate system in the 4PUS-3UPS parallel mechanism. Reference coordinate system O A -X A Y A Z A Located below the plane where the rotation center of the H-type Hook hinge 52 is located in the three UPS branches, the origin O A The intersection of the median line of the isosceles trapezoid and the perpendicular bisector of the lower base where the rotation center of the E-type Hooke's hinge 12 coincides with the four PUS branches, Y A Axis horizontal to the left, Z A The axis is vertically downward, and the motion coordinate system is O B -X B Y B Z B Origin O A Located at the center of the circle where the rotation center of the E-type ball pair 13 is located in the four PUS branches, Y BThe axis is perpendicular to the left surface of the moving platform 8, Z B The axis is vertical downward, X A The axis and X B The axes all conform to the right-hand rule.

[0082] The reference coordinate system is fixed in the workspace and does not move, and the moving coordinate system is located on the moving platform 8 and moves with the moving platform 8. Further, the pose of the moving platform 8 in the workspace can be described by the pose of the moving coordinate system in the reference coordinate system. Wherein, the position is the coordinates of the origin of the moving coordinate system in the reference coordinate system, denoted as (x o ,y o ,z o ), and the attitude can be agreed as X-Y-Z Euler angle, denoted as (α B ,β B ,γ B ), then the pose of the moving platform 8 in the workspace can be represented by (x o ,y o ,z o ,α B ,β B ,γ B ), and the spatial motion generalized pose coordinates of the moving platform 8 can be represented as X = [x o y o z o α B β B γ B ] T .

[0083] As shown in Figure 7 , since the 4PUS-3UPS parallel mechanism has two typical singular poses, when one or more links in the PUS branch are parallel to the reference coordinate system O A -X A Y A Z A plane, the moving platform 8 will lose part of the translational ability in the reference coordinate system O A -X A Y A Z A plane at this moment; when one or more links in the PUS branch are parallel to the moving coordinate system O B -X B Y B Z B plane, the moving platform 8 will lose part of the translational ability in the moving coordinate system O B -X B Y B Z B plane at this moment.

[0084] The application selects one driving joint of the rotation group branch chain to be driven by a sliding mode controller based on a dynamic model for driving force control according to a rotation condition, and the other driving joint of the rotation group branch chain and all driving joints of the normal group branch chain are controlled according to a dynamic model for position control.

[0085] The rotation condition is to compare the condition numbers of velocity Jacobian matrices J6 and J7, if the condition number of J6 is smaller, the driving joint of the 6# UPS branch chain 6 is controlled for driving force, if the condition number of J7 is smaller, the driving joint of the 7# UPS branch chain 7 is controlled for driving force.

[0086] Wherein, the velocity Jacobian matrix J6 is a six-order velocity Jacobian matrix based on a normalized variable weighting matrix, containing the 1# PUS branch chain 1, the 2# PUS branch chain 2, the 3# PUS branch chain 3, the 4# PUS branch chain 4, the 5# UPS branch chain 5 and the 6# UPS branch chain 6, and the velocity Jacobian matrix J7 is a six-order velocity Jacobian matrix based on a normalized variable weighting matrix, containing the 1# PUS branch chain 1, the 2# PUS branch chain 2, the 3# PUS branch chain 3, the 4# PUS branch chain 4, the 5# UPS branch chain 5 and the 7# UPS branch chain 7.

[0087] The variable weighting matrix W is defined as follows: v And the velocity Jacobian matrices J6 and J7 are as follows:

[0088]

[0089] J6 = [J h1 J h2 J h3 J h4 J h5 J h6 ]W v

[0090] J7 = [J h1 J h2 J h3 J h4 J h5 J h7 ]W v

[0091] In the formula, E 3×3 is a 3×3 unit matrix, O 3×3 is a 3×3 zero matrix, J hm (m = 1, 2,..., 6, 7) represents the velocity Jacobian matrix of each driving joint, L v is the root mean square of the velocity Jacobian matrix corresponding to the moving platform moving speed component vector, and L ω is the root mean square of the velocity Jacobian matrix corresponding to the moving platform rotating angular velocity component vector, and is calculated as follows:

[0092]

[0093] where n represents the n-th sub-item of J hm .

[0094] The parallel robot has six degrees of freedom and seven driving joints, is redundantly driven, and its dynamic model has infinite solutions, which provides the possibility for driving force redistribution.

[0095] The total velocity Jacobian matrix J A ∈R 6×7 and the driving force matrix τ∈R 7×1 are defined as follows:

[0096]

[0097] τ=[τ1τ2τ3τ4τ5τ6τ7] T

[0098] The dynamic model of the 4PUS-3UPS parallel mechanism considering the action of the load is as follows:

[0099]

[0100] where A∈R 6×6 represents the acceleration term coefficient matrix, C∈R 6×6 represents the velocity term coefficient matrix, Q∈R 6×6 represents the gravity term coefficient matrix, E3 is a 3-order unit matrix, O3 is a 3-order zero matrix, [F M] T ∈R 6×1 represents the external force applied by the external load on the moving platform.

[0101] Since the 4PUS-3UPS parallel mechanism has six degrees of freedom and seven driving joints, the Jacobian matrix J A is not a square matrix, so the dynamic model cannot be directly solved by simultaneously left multiplying the inverse matrix of J A on both sides of the equation. And from the relationship between the rows and columns of J A , it can be seen that the dynamic model does not have a unique solution, and there are multiple combinations of driving forces that make the equation true, which also provides the possibility for the distribution of the driving force of the 4PUS-3UPS parallel mechanism.

[0102] For this driving force multiple solution problem, the method of generalized inverse is adopted in this paper to obtain the least two norm solution of the dynamic model, which can make the distribution of the driving force more uniform, and the generalized right pseudo-inverse matrix of J A is defined as and the solution of the dynamic model is obtained, which is the least two norm solution:

[0103]

[0104] A dynamically adjusted force-position hybrid control strategy is selected. In order to enable the dynamic platform 8 to move according to the expected trajectory, a sliding mode controller is designed based on the dynamic model.

[0105] Since the trajectory tracking target is the position and velocity error of the driving joint space, before designing the sliding mode controller, the established dynamic model is first converted from the workspace to the joint space and the velocity coordinates of the joint space are defined. It contains seven elements, corresponding to the Cartesian coordinate movement speeds of the seven driving joints. The velocity mapping relationship between the spatial motion generalized velocity coordinates of the moving platform 8 and the joint space velocity coordinates is expressed as follows:

[0106]

[0107] Where, J = [J h1 J h2 J h3 J h4 J h5 J h6 J h7 ].

[0108] To solve it, just multiply both sides of the equation by the generalized left pseudo-inverse matrix of the velocity Jacobian matrix J. Define the generalized left pseudo-inverse matrix J of J as + =(J T J) -1 J T , then the mapping relationship can be converted to:

[0109]

[0110] Taking the derivative of both sides of the equation we get:

[0111]

[0112] in,

[0113] Substituting into the dynamic model and ignoring the external load, we can get:

[0114]

[0115] By multiplying both sides of the above formula by J A The generalized right pseudo-inverse matrix J A + The dynamic model describing the joint space can be solved:

[0116]

[0117] wherein,

[0118] Considering the modeling error of the dynamic model and the external disturbance, both are integrated into the error term d∈R 7×1 Adding the error term to the above equation, we get:

[0119]

[0120] Let the joint space position tracking error be e∈R 7×1 , and the joint space velocity tracking error be

[0121] e = q d - q

[0122]

[0123] wherein,

[0124] q d = [q 1d q 2d q 3d q 4d q 5d q 6d q 7d ] T

[0125]

[0126] wherein, q md (m = 1, 2, …, 6, 7) represents the desired position of each driving joint.

[0127] The nonsingular terminal fast sliding mode surface is designed as:

[0128]

[0129] wherein, the coefficient matrix Λ = diag(λ1, λ2, λ3, λ4, λ5, λ6, λ7) and λ m > 0, a and b are positive odd numbers, b > a, and

[0130] The derivative of the sliding mode surface is:

[0131]

[0132] Let the exponential-based sliding mode approach rate be:

[0133]

[0134] wherein, ε > 0, k > 0.

[0135] Finally, the upper bound based sliding mode control method is adopted to design the sliding mode controller as follows:

[0136]

[0137] In order to verify the stability of the sliding mode controller, the Lyapunov function is set as follows:

[0138]

[0139] The Lyapunov function is a quadratic function, so the Lyapunov equation is positive definite, and the derivative of the Lyapunov function is taken again:

[0140]

[0141] Wherein, Then:

[0142]

[0143] In the formula, -s T ks≤0 is always true, and the equality holds only when s=0. Since the disturbance term d is finite, there is an upper bound There is an upper bound. When is always true, and the equality holds only when s=0. Therefore, the derivative of the Lyapunov function is negative, and the system is asymptotically stable, and the sliding mode controller can be used.

[0144] In addition, in the sliding mode controller designed above, the sign function sgn(s) introduced by the exponential convergence rate It is possible to cause high-frequency vibration of the control input, and in severe cases, it can also make the motor switch positive and negative at an unreasonable frequency, causing damage to the motor and the driver. Therefore, the hyperbolic tangent function tanh(s / η) can be used instead of the sign function sgn(s). In combination Figure 8 The images of the sign function and the hyperbolic tangent function in the same coordinate system are compared, where η=0.1.

[0145] The control method provided above can ensure that the parallel robot proposed in the application can continuously adjust the posture in the workspace by a large margin, without needing to avoid singular shapes, Figure 5 and Figure 6 The 90° posture adjustment of the moving platform 8 of the proposed parallel robot around the same axis in the positive and negative directions is shown.

[0146] It is apparent to a person skilled in the art that the present application is not limited to the details of the above-described exemplary embodiments, but that it can be implemented in other embodiments without departing from the spirit or essential characteristics of the application. Therefore, the embodiments should be considered in all respects as illustrative and not restrictive, the scope of the application being defined by the appended claims rather than by the above description, and all changes coming within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. No reference signs in the claims should be considered as limiting the scope of the claims to the features to which the reference signs are attached.

[0147] Furthermore, it should be understood that although the description is made on embodiments, not every embodiment contains only one independent technical solution, and the description is made in this way only for the sake of clarity, and a person skilled in the art should consider the description as a whole, and the technical solutions in each embodiment can also be combined appropriately to form other embodiments that can be understood by a person skilled in the art.

Claims

1. A six-degree-of-freedom parallel robot with a large attitude angle, comprising a fixed frame (9) and a moving platform (8) arranged inside the fixed frame, wherein the moving platform (8) and the fixed frame (9) are connected by seven branches, including four PUS branches and three UPS branches, characterized in that: The four PUS branches all use vertical linear motion modules (11) and are respectively installed at the top positions of the four corners of the fixed frame (9); the three UPS branches all use oblique linear motion modules (51) and are respectively installed between the top of the fixed frame (9) and the moving platform (8); the vertical linear motion modules (11) and the oblique linear motion modules (51) are both movably provided with driving joints, and the driving joints of the seven branches are respectively connected to the moving platform (8) through connecting rods; The vertical linear motion modules (11) are fixedly arranged on the fixed frame (9), and the driving joints are connected to the upper ends of the connecting rods via E-type Hooke's joints (12), and the lower ends of the connecting rods are connected to the moving platform (8) via E-type ball joints (13); The upper end of the oblique linear motion module (51) is connected to the fixed frame (9) via an H-shaped Hooke's hinge (52), the driving joint of the oblique linear motion module (51) is fixedly connected to the upper end of the connecting rod, and the lower end of the connecting rod is connected to the moving platform (8) via a U-shaped ball pair (53), and the connecting rod is located on the rotation center connection line of the H-shaped Hooke's hinge (52) and the U-shaped ball pair (53); In the initial state, the moving platform (8) is in a horizontal position, the rotation centers of the four E-type Hooke's hinges (12) are arranged according to the four endpoints of an isosceles trapezoid in horizontal projection, and the rotation centers of the three H-type Hooke's hinges (52) are arranged according to the three endpoints of an isosceles right triangle in horizontal projection, the hypotenuse of the isosceles right triangle where the rotation center of the H-type Hooke's hinge (52) is located and the center line of the isosceles trapezoid where the rotation center of the E-type Hooke's hinge (12) is located are arranged to coincide with each other in a top-down view, and the midpoint of the hypotenuse of the isosceles right triangle where the rotation center of the H-type Hooke's hinge (52) is located is located on the axis of the moving platform (8); The rotation centers of the four E-type ball pairs (13) are arranged at both ends of the moving platform (8) according to the four endpoints of a rectangle in horizontal projection, and the rotation centers of the three U-type ball pairs (53) are arranged at the edge of the surface of the moving platform (8) according to the three endpoints of an isosceles right triangle in horizontal projection. The hypotenuse of the isosceles right triangle where the rotation center of the U-type ball pair (53) is located is perpendicular to the hypotenuse of the isosceles right triangle where the rotation center of the H-type Hooke's hinge (52) is located when viewed from above, and the midpoint of the hypotenuse of the isosceles right triangle where the rotation center of the U-type ball pair (53) is located is located on the axis of the moving platform (8).

2. The six-degree-of-freedom parallel robot with a large attitude angle according to claim 1, characterized in that: The vertical linear motion module (11) and the oblique linear motion module (51) both use ball screws as actuators and are matched with moving pairs as driving joints.

3. A control method for a six-degree-of-freedom parallel robot with a large attitude angle, characterized by: The six-degree-of-freedom parallel robot according to claim 2, wherein the control method comprises the following steps: The seven branches are numbered as 1#PUS branch (1), 2#PUS branch (2), 3#PUS branch (3), 4#PUS branch (4), 5#UPS branch (5), 6#UPS branch (6), and 7#UPS branch (7), wherein the H-type Hooke's hinge (52) and the U-type ball pair (53) of the 5#UPS branch (5) are respectively arranged at the vertices of the right angles of the corresponding isosceles right triangle, and the 6#UPS branch (6) and the 7#UPS branch (7) are centrally symmetrical structures. The seven branches are divided into two groups, including a normal group branch and a rotation group branch. The normal group branch consists of the 1#PUS branch (1), the 2#PUS branch (2), the 3#PUS branch (3), the 4#PUS branch (4), and the 5#UPS branch (5), and the rotation group branch consists of the 6#UPS branch (6) and the 7#UPS branch (7); First, define the reference coordinate system and the motion coordinate system. A -X A Y A Z A Located below the plane where the rotation center of the H-type Hooke's hinge (52) in the three UPS branches is located, the origin O A The intersection of the median line of the isosceles trapezoid and the perpendicular bisector of the lower base where the rotation center of the E-type Hooke hinge (12) coincides with the four PUS branches, Y A Axis horizontal to the left, Z A The axis is vertically downward, and the motion coordinate system is O B -X B Y B Z B Origin O A Located at the center of the circle where the E-type ball pair (13) of the four PUS branches is located, Y B The axis is perpendicular to the left surface of the moving platform (8), Z B The axis is vertically downward, X A Axis and X B The axes all conform to the right-hand rule; The position of the moving platform (8) in the workspace is described by the position of the motion coordinate system in the reference coordinate system, which is expressed as (x o ,y o ,z o ), the posture is agreed to be XYZ Euler angle, expressed as (α B ,β B ,γ B ), then the spatial motion generalized pose coordinates of the moving platform (8) are expressed as X = [x o y o z o α B β B γ B ] T ; The rotation group branch chain selects a driving joint through the rotation condition and adopts a sliding mode controller to perform driving force control. The other driving joint of the rotation group branch chain and all the driving joints of the normal group branch chain are position-controlled according to the dynamic model. The rotation condition is agreed to compare the condition numbers of the velocity Jacobian matrices J6 and J7. If the condition number of J6 is smaller, the driving joint of the 6#UPS branch chain (6) is controlled by the driving force. If the condition number of J7 is smaller, the driving joint of the 7#UPS branch chain (7) is controlled by the driving force. The velocity Jacobian matrices J6 and J7 are defined as follows: J6=[J h1 J h2 J h3 J h4 J h5 J h6 ]W v J7=[J h1 I h2 I h3 I h4 I h5 I h7 ]W v Where, J hm m=1,2,...,6,7 represents the velocity Jacobian matrix of each driving joint, W v is a variable weight matrix, expressed as follows: Among them, E 3×3 is the 3×3 identity matrix, O 3×3 is a 3×3 zero matrix, L v is the root mean square of the velocity Jacobian matrix corresponding to the velocity component vector modulus of the moving platform, L ω is the root mean square of the vector modulus of the angular velocity component of the moving platform corresponding to the velocity Jacobian matrix, which is calculated as follows: Where n represents the J in the velocity Jacobian matrix J6 and J7. hm The nth child of ; Define the total velocity Jacobian matrix J including J6 and J7 A ∈R 6×7 And the driving force matrix τ∈R 7×1 as follows: τ=[τ1τ2τ3τ4τ5τ6τ7] T The dynamic model is as follows: The generalized inverse method is used to obtain the least squares solution of the dynamic model and define J A The generalized right pseudo-inverse matrix of Then the least squares norm solution of the dynamic model is obtained: Where A∈R 6×6 Represents the acceleration coefficient matrix, C∈R 6×6 Represents the velocity term coefficient matrix, Q∈R 6×6 represents the gravity coefficient matrix, E3 is the 3rd-order identity matrix, O3 is the 3rd-order zero matrix, [FM] T ∈R 6×1 It represents the external force applied to the moving platform by the external load; Convert the established dynamic model from the workspace to the joint space and define the velocity coordinates in the joint space It contains seven elements, corresponding to the Cartesian coordinate movement speeds of the seven driving joints. The velocity mapping relationship between the spatial motion generalized velocity coordinates of the moving platform (8) and the joint space velocity coordinates is expressed as follows: Where, J = [J h1 J h2 J h3 J h4 J h5 J h6 J h7 ]; To solve it, define the generalized left pseudo-inverse matrix J of J + =(J T J) -1 J T , then the mapping relationship is converted to: Taking the derivative of both sides of the equation we get: in, Substituting into the dynamic model and ignoring the external load, we get: By multiplying both sides of the above formula by J A The generalized right pseudo-inverse matrix of Solve the dynamic model described by the joint space: Where, Taking into account the modeling error of the dynamic model and external interference, the two are combined into the error term d∈R 7×1 , adding the error term to the above formula, we get: Assume that the joint space position tracking error is e∈R 7×1 , the joint space velocity tracking error is e=q d -q in, q d =[q 1d q 2d q 3d q 4d q 5d q 6d q 7d ] T Where q md m=1,2,...,6,7 represents the desired position of each driven joint; The non-singular terminal fast sliding surface is designed as: Among them, the coefficient matrix Λ = diag (λ1, λ2, λ3, λ4, λ5, λ6, λ7) and λ m > 0, a and b are positive odd numbers, b>a, and Taking the derivative of the sliding surface, we get: Assume that the index-based synovial approach rate is: Finally, the sliding mode control method based on the upper bound is adopted to design the sliding mode controller as follows: Where sgn(s) is the sign function, ε>0, k>0.

4. The control method of a six-degree-of-freedom parallel robot with a large attitude angle according to claim 3, characterized in that: The sliding mode controller uses the hyperbolic tangent function tanh(s / η) to replace the sign function sgn(s).

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