Parallel robot modeling method considering omnidirectional motion error of flexible joint

Abstract

A parallel robot modeling method considering omni-directional motion errors of flexible joints comprises the steps that S1, the output pose of the tail end of a mechanism is defined, and a kinematic model of a robot is established based on a closed-loop vector method; s2, flexible joint output poses are constructed in combination with motion variables of the flexible joints, wherein the motion variables comprise the displacement amount and the rotation angle amount of the flexible joints in the non-functional direction; s3, establishing a local coordinate system in each flexible joint and each moving joint in the branch chains, and constructing homogeneous coordinate transformation matrixes and a transfer relation among the matrixes; s4, the mapping relation between the motion variables of all the flexible joints and the tail end output poses is constructed; s5, constructing a force and moment balance equation of the movable platform in the branched chain, the flexible joints and the movable joints; s6, all the equations are combined, and the tail end output pose of the mechanism is solved. According to the method, the motion error of the flexible joint in the non-functional direction is considered, the robot model with higher precision is established, and the operation precision and reliability of the robot are ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of parallel robot modeling, and particularly relates to a parallel robot modeling method considering omnidirectional motion error of flexible joints. BACKGROUND

[0002] 3-RPR planar flexible parallel robot is a three-degree-of-freedom planar motion mechanism, which is composed of a static platform, a dynamic platform and three RPR (rotation-translation-rotation) branch chains, each of which is connected to the dynamic platform and the static platform to realize precise motion control. The 3-RPR planar flexible parallel robot is widely used in important fields such as precise positioning and micro-nano operation, and a high-precision model is the basis for high-precision control. However, the existing modeling method does not consider the motion error of the flexible joint in the non-functional direction, which makes it difficult to ensure the accuracy of the model. SUMMARY

[0003] The technical problem to be solved by the present application is to provide a parallel robot modeling method considering omnidirectional motion error of flexible joints, which can solve the shortcomings of the prior art and realize high-precision modeling of 3-RPR planar flexible parallel mechanism by considering the motion error of flexible joints in the non-functional direction in the modeling process.

[0004] To achieve the above-mentioned purpose, the present application provides the following technical scheme:

[0005] A parallel robot modeling method considering omnidirectional motion error of flexible joints, comprising the steps of:

[0006] S1: defining the end output pose of the mechanism, and establishing a kinematic model of the robot based on the closed-loop vector method;

[0007] S2: constructing the output pose of the flexible joint in combination with the motion variable of the flexible joint, wherein the motion variable includes the displacement amount and the rotation angle amount of the flexible joint in the non-functional direction;

[0008] S3: establishing a local coordinate system in each flexible joint and moving joint in the branch chain, and constructing a homogeneous coordinate transformation matrix and a transmission relationship between the matrices;

[0009] S4: constructing a mapping relationship between the motion variable of each flexible joint and the end output pose;

[0010] S5: constructing a force and torque balance equation of the dynamic platform, each flexible joint and moving joint in the branch chain;

[0011] S6: solving the end output pose by simultaneously solving each equation.

[0012] Further, the mechanism is composed of a moving platform, a static platform and three branch chains, each of the branch chains comprises two flexible joints, one moving joint and a connecting rod, the first end of the connecting rod is connected to the moving platform through one of the flexible joints, the second end of the connecting rod is connected to the static platform through the other flexible joint, and the moving joint is arranged on the connecting rod and used for adjusting the length of the connecting rod.

[0013] Further, the motion variables in S4 comprise displacement δ x , δ y along the x-axis and y-axis directions and rotation angle γ z around the z-axis direction, and the flexible joint outputs a pose .

[0014] Further, S1 comprises:

[0015] S11, defining a moving coordinate system and a static coordinate system, and defining the end output pose , the moving coordinate system is fixed to the moving platform and moves with the moving platform, and the static coordinate system is fixed at the initial position of the moving platform;

[0016] S12, establishing the position vector of the center of each flexible joint on the moving platform in the moving coordinate system, establishing the position vector of the center of each flexible joint on the static platform in the static coordinate system, and constructing the position vector equation of each branch chain;

[0017] S13, combining the closed-loop constraint condition to obtain the closed-loop vector equation of the mechanism;

[0018] S14, squaring both sides of the closed-loop vector equation to establish the relationship model between the driving input displacement and the end output pose :

[0019]

[0020]

[0021] , and l is the initial length of the connecting rod.

[0022] Further,

[0023] Further, S3 comprises:

[0024] S31, respectively establishing local coordinate systems in each flexible joint and moving joint of the branch chain,

[0025] S32, combining the flexible joint output pose , and constructing the homogeneous transformation matrix between each local coordinate system , establish the homogeneous transformation relationship between each sub-matrix .

[0026] Further, the mapping relationship between the motion variables of the flexible joint and the moving joint in step S4 and the end output pose of the mechanism is , wherein M i is the mapping matrix between the motion variable P r,i and the end output pose X.

[0027] Further, the step S5 comprises:

[0028] S51, based on the force balance condition of the moving platform, construct the force and torque balance equation of the moving platform;

[0029] S52, isolate the flexible joint close to the moving platform alone, and establish two local coordinate systems in the upper and lower planes of the flexible joint, and construct the force and torque balance equation of the flexible joint;

[0030] S53, isolate the moving joint in the branch chain alone, and establish two local coordinate systems in the upper and lower planes of the moving joint, and construct the force and torque balance equation of the moving joint;

[0031] S54, isolate the flexible joint close to the static platform alone, and establish two local coordinate systems in the upper and lower planes of the flexible joint, and construct the force and torque balance equation of the flexible joint;

[0032] S54, repeat steps S51, S52 and S53 until the force and torque balance equations of each flexible joint and moving joint of each branch chain are obtained, and enter step S6.

[0033] Further, the force and torque acting on the lower plane of the flexible joint in step S52 are equal to the force and torque acting on the upper plane of the moving joint in step S53; the force and torque acting on the upper plane of the flexible joint in step S53 are equal to the force and torque acting on the lower plane of the moving joint in step S53.

[0034] Further, the force and torque balance equation in the step S5 comprises two force balance equations along the x-axis and y-axis directions, and a torque balance equation around the z-axis direction.

[0035] Further, the step S6 comprises:

[0036] S61, construct an equation set, the equation set comprising the force and torque balance equations of each flexible joint and moving joint, and the force and torque balance equation of the moving platform;

[0037] S62, forces and torques acting on the flexible joints and the moving joints are represented as forces and torques acting on the moving platform respectively;

[0038] S63, the end output pose is solved by substituting the force and torque balance equations of the moving platform.

[0039] The beneficial effects of the present application are:

[0040] 1. The parallel robot modeling method considering omnidirectional motion error of flexible joints provided by the present application comprises the following steps: S1: a kinematic model of the robot is established based on the closed-loop vector method; S2: the output pose of the flexible joint is constructed in combination with the motion variables of the flexible joint, the motion variables including the displacement amount and the rotation angle amount of the flexible joint in the non-functional direction; S3: local coordinate systems are established in each flexible joint and moving joint in the branch chain, and the transmission relationship between each homogeneous coordinate transformation matrix and each matrix is constructed; S4: the mapping relationship between the motion variables of each flexible joint and the output pose of the mechanism end is constructed; S5: force and torque balance equations of the moving platform, each flexible joint and moving joint in the branch chain are constructed; and S6: the end output pose of the mechanism is solved by simultaneously solving each equation. The present application considers the motion error of the flexible joint in the non-functional direction, establishes a robot model with higher accuracy compared to the prior art, and ensures the operation accuracy and reliability of the robot.

[0041] 2. The parallel robot modeling method considering omnidirectional motion error of flexible joints provided by the present application establishes local coordinate systems in each flexible joint and moving joint of the branch chain, and constructs the homogeneous transformation relationship between each local coordinate system in combination with the output pose of the flexible joint, thereby establishing a complete motion transmission path from the static platform to the moving platform. This not only realizes accurate mapping between the motion variables of each flexible joint and the end output pose, but also accurately describes the relative motion between each component in the branch chain, thereby significantly improving the accuracy and comprehensiveness of the motion transmission path description.

[0042] 3. The parallel robot modeling method considering omnidirectional motion error of flexible joints provided by the present application, in step S5, by separately isolating the flexible joints close to the moving platform and the static platform and the moving joints in the branch chain, and establishing local coordinate systems in the upper and lower planes to construct the force and torque balance equations, the forces and torques on each component can be accurately analyzed, thereby improving the overall accuracy and stability of the modeling. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0044] Figure 1 A modeling flowchart of a parallel robot modeling method considering omnidirectional motion error of flexible joints of the application;

[0045] Figure 2 A mechanism diagram of a 3-RPR flexible parallel robot in the embodiment.

[0046] Figure 3 A structure diagram of a 3-RPR flexible parallel robot in the embodiment.

[0047] Figure 4 A schematic diagram of a flexible joint of a 3-RPR flexible parallel robot in the embodiment.

[0048] In the figure, 10 is a static platform, 20 is a moving platform, 301 is a first branch chain, 302 is a second branch chain, 303 is a third branch chain, 401 is a flexible joint, 402 is a moving joint, and 403 is a connecting rod. DETAILED DESCRIPTION

[0049] The application will be described in detail below. Figures 1-4 The application will be described in detail below.

[0050] The embodiment provides a parallel robot modeling method considering omnidirectional motion error of flexible joints, as shown in the figure, comprising the following steps: Figure 1

[0051] S1: defining an end output pose of a mechanism, and establishing a kinematics model of the robot based on a closed-loop vector method;

[0052] S2: constructing a flexible joint output pose of the flexible joint 401 in combination with a motion variable of the flexible joint 401, the motion variable comprising a displacement amount and a rotation angle amount of the flexible joint 401 in a non-functional direction;

[0053] S3: establishing a local coordinate system in each flexible joint 401 and moving joint 402 in a branch chain, and constructing each homogeneous coordinate transformation matrix and a transmission relationship between the matrices;

[0054] S4: constructing a mapping relationship between the motion variable of each flexible joint 401 and the end output pose of the mechanism;

[0055] S5: constructing a force and torque balance equation of the moving platform 20, each flexible joint 401 and moving joint 402 in the branch chain;

[0056] S6: solving the end output pose of the mechanism by simultaneously solving each equation.

[0057] ​The scheme considers the motion error of the flexible joint 401 in the non-functional direction, so that the model is more in line with the actual working conditions, and the adaptability and reliability of the robot are improved. Specifically, the mechanism is composed of a moving platform 20, a static platform 10 and three branch chains, each branch chain includes two flexible joints 401, a moving joint 402 and a connecting rod 403, the first end of the connecting rod 403 is connected to the moving platform 20 through a flexible joint 401, and the second end is connected to the static platform 10 through another flexible joint 401. The connecting rod 403 adjusts the length through the sliding motion of the moving joint 402.

[0058] The motion variables include a rotation angle and two displacement amounts. Among them, the rotation angle is the motion of the flexible rotation joint in the functional direction, and the two displacement amounts are the motion errors of the flexible rotation joint in the non-functional direction. Specifically, the motion variables in S2 include the displacement amounts δ x , δ y along the x-axis and y-axis directions and the rotation angle γ z around the z-axis direction, and the output pose of the flexible joint is .

[0059] Step S1 includes:

[0060] S11, define the moving coordinate system and the static coordinate system, and define the end output pose , the moving coordinate system is fixed to the moving platform 20 and moves with it, and the static coordinate system is fixed at the initial position of the moving platform 20;

[0061] S12, establish the position vector of the center of each flexible joint 401 on the moving platform 20 in the moving coordinate system, establish the position vector of the center of each flexible joint 401 on the static platform 10 in the static coordinate system, and construct the position vector equation of each branch chain;

[0062] S13, combined with the closed loop constraint condition, the closed loop vector equation of the mechanism is obtained;

[0063] S14, square both sides of the closed loop vector equation, and establish the relationship model between the driving input displacement and the end output pose :

[0064]

[0065]

[0066] , l is the initial length of the connecting rod 403, q1, q2, q3 are the input values of the mechanism, x, y, γ are the output values of the mechanism, the distance between the second branch chain 302 and the third branch chain 303 is 2α, and the length of the moving platform 20 is 2d.

[0067] In other embodiments, step S1 further includes: S15, taking derivatives on both sides of the closed-loop vector equation to establish the drive input speed -End output speed Linear mapping relationship between , where J is the velocity Jacobian matrix of the mechanism.

[0068] In this embodiment, the mechanism is a 3-RPR planar flexible parallel robot, such as Figure 2 and Figure 3 As shown, the mobile platform 20 includes a static platform 10 and a dynamic platform 20. The first end of the dynamic platform 20 is connected to a first branch chain 301, and the second end is connected to a second branch chain 302 and a third branch chain 303 arranged in parallel with each other. A movable joint 402 is provided on a connecting rod 403, and the movable joint 402 is used to adjust the length of the connecting rod 403. The first branch chain 301, the second branch chain 302, and the third branch chain 303 are connected to the static platform 10. The dotted lines in the figure indicate the positions of the dynamic platform 20, the first branch chain 301, the second branch chain 302, and the third branch chain 303 after movement.

[0069] In other embodiments, the modeling of parallel robots with other dimensions and degrees of freedom can refer to the modeling steps of the 3-RPR flexible parallel robot and be adjusted according to the actual degrees of freedom.

[0070] Define a moving coordinate system and static coordinate system , then the static coordinate system Relative to the moving coordinate system The rotation transformation matrix can be expressed as:

[0071]

[0072] Define the centers of the three flexible joints 401 on the static platform 10 in the static coordinate system The position vector in is The centers of the three flexible joints 401 on the moving platform 20 are in the moving coordinate system The position vector in is , then the centers of the three flexible joints 401 on the moving platform 20 are in the static coordinate system The position vector in is: According to the geometric relationship, we can get:

[0073]

[0074]

[0075]

[0076] By solving the equation, we can get the inverse kinematics model of the 3-RPR planar parallel robot, that is, the driving input displacement and the terminal output pose The relationship model between:

[0077]

[0078]

[0079]

[0080] In the initial state, the length of the connecting rod 403 is The distance between the second branch chain 302 and the third branch chain 303 is 2α, and the length of the second end of the moving platform 20 is 2d.

[0081] Furthermore, step S3 includes:

[0082] S31, establish local coordinate systems in each flexible joint 401 and mobile joint 402 of the branch chain respectively,

[0083] S32, combined with flexible joint output posture , construct the homogeneous transformation matrix between each local coordinate system , establish the homogeneous transformation relationship between each sub-matrix .

[0084] Specifically, each sub-matrix can be expressed as:

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] , r is the radius of the side circle of the flexible joint 401.

[0091] In this embodiment, step S4 is: extracting the motion vectors of the flexible joint 401 and the mobile joint 402, and then , simplification is obtained to obtain the motion variables for constructing the flexible joint 401 and the mobile joint 402 The mapping relationship between the output pose of the robot end , where M i is the motion variable P r,i The mapping matrix between the terminal output pose X. For all the motion variables of the components, including the motion variables of the flexible joints 401 and the moving joints 402, refer to the flexible joint output pose in the foregoing .

[0092] Further, the step S5 includes:

[0093] S51, based on the force balance condition of the moving platform 20, construct the force and moment balance equation of the moving platform 20;

[0094] S52, isolate the flexible joint 401 close to the moving platform 20 separately, establish two local coordinate systems (as shown in Figure 4 ) in the upper and lower planes of the flexible joint 401 respectively, and construct the force and moment balance equation of the flexible joint 401;

[0095] S53, isolate the moving joint 402 in the branch chain separately, establish two local coordinate systems in the upper and lower planes of the moving joint 402 respectively, and construct the force and moment balance equation of the moving joint 402;

[0096] S54, isolate the flexible joint 401 close to the static platform 10 separately, establish two local coordinate systems in the upper and lower planes of the flexible joint 401 respectively, and construct the force and moment balance equation of the flexible joint 401; when the mechanism moves to the vicinity of the target pose, the components in the mechanism, including the flexible joint 401 and the moving joint 402, all reach the force balance condition. The flexible joint 401 is as shown in Figure 4 .

[0097] S54, repeat the steps S51, S52 and S53 until the force and moment balance equations of the flexible joints 401 and the moving joints 402 of each branch chain are obtained, and enter the step S6.

[0098] Specifically, the force and moment balance equation in the step S5 includes two force balance equations along the x-axis and y-axis directions, and one moment balance equation around the z-axis direction.

[0099] In this embodiment, the force and moment acting on the lower plane of the flexible joint 401 in the step S52 are equal to the force and moment acting on the upper plane of the moving joint 402 in the step S53; the force and moment acting on the upper plane of the flexible joint 401 in the step S53 are equal to the force and moment acting on the lower plane of the moving joint 402 in the step S53. In this step, by isolating each component in the branch chain separately and then constructing the equation based on the force balance condition, the force and moment on each component are accurately analyzed, and the overall accuracy and stability of the modeling are improved.

[0100] In this embodiment, the step S6 includes:

[0101] S61, construct equation set, the equation set includes force and torque balance equation of each flexible joint 401 and moving joint 402, and force and torque balance equation of moving platform 20;

[0102] S62, force and torque acting on flexible joint 401 and moving joint 402 are represented as force and torque acting on moving platform 20 respectively;

[0103] S63, force and torque acting on flexible joint 401 and moving joint 402 in S62 are substituted into force and torque balance equation of moving platform 20 , solve end output pose .

[0104] The parallel robot modeling method considering the omnidirectional motion error of flexible joint 401 provided by the application establishes a kinematic model through a closed-loop vector method, constructs an output pose expression of the flexible joint 401, establishes a homogeneous transformation relationship between coordinate systems of members in the branch chain, and realizes accurate description of the motion transmission path. Then, a mapping relationship between the motion variable of the flexible joint 401 and the end output pose is constructed, the mapping matrix is obtained through multiplication and simplification of the homogeneous coordinate transformation matrix, the force and torque balance equation of the end moving platform 20 is established according to the force balance condition, the force and torque balance equation of each flexible joint 401 and moving joint 402 in the branch chain is constructed, and finally the end output pose is solved by solving the equation set. The method comprehensively considers the omnidirectional motion error of the flexible joint 401 to solve the problem of insufficient accuracy of the existing method, establishes a high-precision input-output model, and provides a solid theoretical basis for high-precision control of the flexible parallel robot.

[0105] The above embodiments are only for illustrating the technical concept and characteristics of the application, the purpose is to enable those skilled in the art to understand the content of the application and implement it, and cannot limit the protection scope of the application. Any equivalent changes or modifications made according to the spirit and essence of the application shall be covered within the protection scope of the application.

Claims

1. A parallel robot modeling method considering omnidirectional motion errors of flexible joints, characterized in that: Including steps: S1: Define the end output pose of the mechanism and establish the robot's kinematic model based on the closed-loop vector method; S2: constructing the output posture of the flexible joint in combination with the motion variables of the flexible joint, wherein the motion variables include the displacement and rotation of the flexible joint in the non-functional direction; S3: establishing a local coordinate system in each of the flexible joints and mobile joints in the branch chain, and constructing a homogeneous coordinate transformation matrix and a transfer relationship between the matrices; S4: constructing a mapping relationship between the motion variables of each flexible joint and the output posture of the terminal; S5: constructing force and torque balance equations of the dynamic platform, the flexible joints and the mobile joints in the branch chain; S6: Solve the equations together to find the terminal output posture.

2. A parallel robot modeling method considering omnidirectional motion errors of flexible joints according to claim 1, characterized in that: The mechanism consists of a moving platform, a static platform and three branches, each of which includes two flexible joints, one movable joint and a connecting rod. The first end of the connecting rod is connected to the moving platform through a flexible joint, and the second end is connected to the static platform through another flexible joint. The movable joint is provided on the connecting rod and is used to adjust the length of the connecting rod.

3. A parallel robot modeling method considering omnidirectional motion errors of flexible joints as claimed in claim 2, characterized in that: The motion variables in S4 include displacements δ along the x-axis and y-axis directions x , δ y and the rotation angle γ around the z-axis z , the flexible joint output posture is .

4. A parallel robot modeling method considering omnidirectional motion errors of flexible joints as claimed in claim 3, characterized in that: Step S1 includes: S11, define the dynamic coordinate system and the static coordinate system, and define the terminal output posture , the moving coordinate system is fixed to the moving platform and moves with it, and the static coordinate system is fixed at the initial position of the moving platform; S12, establishing the position vector of the center of each flexible joint on the moving platform in the moving coordinate system, establishing the position vector of the center of each flexible joint on the static platform in the static coordinate system, and constructing the position vector equation of each branch chain; S13. Combining closed-loop constraints, obtaining a closed-loop vector equation of the mechanism; S14, square both sides of the closed-loop vector equation to establish the drive input displacement With the terminal output pose The relationship model between: ； ； , is the initial length of the connecting rod.

5. A parallel robot modeling method considering omnidirectional motion errors of flexible joints as claimed in claim 2, characterized in that: Step S3 includes: S31, establishing a local coordinate system in each of the flexible joints and mobile joints of the branch chain, S32, outputting the posture in combination with the flexible joint , construct the homogeneous transformation matrix between the local coordinate systems , establish the homogeneous transformation relationship between each sub-matrix .

6. A parallel robot modeling method considering omnidirectional motion errors of flexible joints as claimed in claim 2, characterized in that: The mapping relationship between the motion variables of the flexible joint and the mobile joint and the terminal output posture in step S4 is: , where M i is the motion variable P r,i The mapping matrix between the terminal output pose X.

7. A parallel robot modeling method considering omnidirectional motion errors of flexible joints as claimed in claim 2, characterized in that: The step S5 comprises: S51. Constructing a force and torque balance equation of the moving platform based on the force balance condition of the moving platform; S52, isolating the flexible joint close to the moving platform, establishing two local coordinate systems on the upper and lower planes of the flexible joint, and constructing the force and torque balance equations of the flexible joint; S53, isolating the mobile joint in the branch chain, establishing two local coordinate systems on the upper and lower planes of the mobile joint, and constructing the force and torque balance equation of the mobile joint; S54, isolating the flexible joint close to the static platform, establishing two local coordinate systems on the upper and lower planes of the flexible joint, and constructing the force and torque balance equations of the flexible joint; S54, repeat steps S51, S52 and S53 until the force and torque balance equations of each flexible joint and movable joint of each branch chain are obtained, and then proceed to step S6.

8. A parallel robot modeling method considering omnidirectional motion errors of flexible joints according to claim 7, characterized in that: The force and torque acting on the lower plane of the flexible joint in step S52 are equal to the force and torque acting on the upper plane of the mobile joint in step S53; the force and torque acting on the upper plane of the flexible joint in step S53 are equal to the force and torque acting on the lower plane of the mobile joint in step S53.

9. A parallel robot modeling method considering omnidirectional motion errors of flexible joints as claimed in claim 8, characterized in that: The force and torque balance equations in step S5 include two force balance equations along the x-axis and the y-axis, and a torque balance equation around the z-axis.

10. A parallel robot modeling method considering omnidirectional motion errors of flexible joints according to claim 2, characterized in that: The step S6 comprises: S61. Constructing a set of equations, wherein the set of equations includes force and torque balance equations of the flexible joints and the mobile joints, and force and torque balance equations of the dynamic platform; S62, expressing the force and torque acting on the flexible joint and the mobile joint by the force and torque acting on the moving platform respectively; S63: Substitute the force and torque balance equation of the dynamic platform into the equation to solve the terminal output posture.

Images