A parallel robot modeling method considering omni-directional motion error of flexible joint

Abstract

A parallel robot modeling method considering omni-directional motion error of flexible joint comprises the following steps: S1: defining mechanism end output pose, and establishing kinematics model of robot based on closed loop vector method; S2: combining motion variable of flexible joint to construct flexible joint output pose, and the motion variable comprises displacement amount and rotation angle amount of flexible joint in non-functional direction; S3: establishing local coordinate system in each flexible joint and moving joint in branch chain, and constructing homogeneous coordinate transformation matrix and transmission relationship among each matrix; S4: constructing mapping relationship between motion variable of each flexible joint and end output pose; S5: constructing force and torque balance equation of each flexible joint and moving joint in branch chain; S6: solving end output pose of mechanism by simultaneously solving each equation.The present application considers motion error of flexible joint in non-functional direction, establishes robot model with higher precision, and ensures operation precision and reliability of robot.

Description

Technical Field

[0001] This invention relates to the field of parallel robot modeling technology, and in particular to a parallel robot modeling method that considers the omnidirectional motion error of flexible joints. Background Technology

[0002] The 3-RPR planar flexible parallel robot is a three-degree-of-freedom planar motion mechanism consisting of a static platform, a moving platform, and three RPR (rotation-translation-rotation) chains. Each chain connects the moving platform and the static platform respectively, achieving precise motion control. 3-RPR planar flexible parallel robots are widely used in important fields such as precision positioning and micro / nano manipulation, and high-precision models are the foundation for high-precision control. However, existing modeling methods have not considered the motion errors of flexible joints in non-functional directions, making it difficult to guarantee model accuracy. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a parallel robot modeling method that considers the omnidirectional motion error of flexible joints, which can overcome the shortcomings of the prior art. By taking the motion error of flexible joints in non-functional directions into account in the modeling process, high-precision modeling of 3-RPR planar flexible parallel mechanisms can be achieved.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for modeling parallel robots that considers omnidirectional motion errors of flexible joints, comprising the following steps:

[0006] S1: Define the end-effector pose of the mechanism and establish the kinematic model of the robot based on the closed-loop vector method;

[0007] S2: Construct the output pose of the flexible joint by combining 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;

[0008] S3: Establish a local coordinate system in each of the flexible joints and moving joints within the branch, and construct each homogeneous coordinate transformation matrix and the transfer relationship between the matrices;

[0009] S4: Construct the mapping relationship between the motion variables of each flexible joint and the end-effector output pose;

[0010] S5: Construct the force and torque balance equations for the moving platform, the flexible joints and the movable joints within the branch chain;

[0011] S6: Solve the equations simultaneously to obtain the terminal output pose.

[0012] Furthermore, the mechanism consists of a moving platform, a stationary platform, and three branches. Each branch includes two flexible joints, a movable joint, and a connecting rod. The first end of the connecting rod is connected to the moving platform through one of the flexible joints, and the second end is connected to the stationary platform through another of the flexible joints. The movable joint is located on the connecting rod and is used to adjust the length of the connecting rod.

[0013] Furthermore, the motion variables described 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 outputs the pose as follows: .

[0014] Furthermore, step S1 includes:

[0015] S11. Define the dynamic coordinate system and the static coordinate system, and define the end-effector output pose. The moving coordinate system is fixed to the moving platform and moves with it, while the static coordinate system is fixed at the initial position of the moving platform.

[0016] S12. Establish the position vector of the center of each flexible joint on the moving platform in the moving coordinate system, establish the position vector of the center of each flexible joint on the static platform in the static coordinate system, and construct the position vector equation of each branch.

[0017] S13. Combining the closed-loop constraint conditions, the closed-loop vector equation of the mechanism is obtained;

[0018] S14. Squaring both sides of the closed-loop vector equation establishes the driving input displacement. With the end output pose Relationship model:

[0019] ;

[0020] ;

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

[0022] Furthermore,

[0023] Furthermore, step S3 includes:

[0024] S31. Establish local coordinate systems in each of the flexible joints and movable joints of the branch chain.

[0025] S32, Output pose in conjunction with the flexible joint Construct homogeneous transformation matrices between the local coordinate systems. Establish homogeneous transformation relationships between submatrices. .

[0026] Furthermore, the mapping relationship between the motion variables of the flexible joint and the movable joint in step S4 and the output pose of the mechanism end effector is as follows: M i Let P be the motion variable r,i The mapping matrix between the terminal output pose X and the terminal pose X.

[0027] Furthermore, step S5 includes:

[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 near the moving platform separately, and establish two local coordinate systems on the upper and lower planes of the flexible joint to construct the force and torque balance equation of the flexible joint.

[0030] S53. Isolate the movable joint within the branch chain separately, and establish two local coordinate systems on the upper and lower planes of the movable joint to construct the force and torque balance equation of the movable joint; subsequently, isolate the flexible joint near the static platform separately, and establish two local coordinate systems on the upper and lower planes of the flexible joint to construct the force and torque balance equation of the flexible joint.

[0031] S54. Repeat steps S51, S52 and S53 until the force and torque balance equations of each flexible joint and movable joint of each branch are obtained, and proceed to step S6.

[0032] Furthermore, in step S52, the force and torque acting on the lower plane of the flexible joint are equal to the force and torque acting on the upper plane of the movable joint; in step S53, the force and torque acting on the upper plane of the flexible joint are equal to the force and torque acting on the lower plane of the movable joint.

[0033] Furthermore, the force and torque balance equations in step S5 include two force balance equations along the x-axis and y-axis directions, and a torque balance equation around the z-axis direction.

[0034] Furthermore, step S6 includes:

[0035] S61. Construct a set of equations, which includes force and torque balance equations for each of the flexible joints and the movable joints, as well as force and torque balance equations for the moving platform.

[0036] S62. The forces and torques acting on the flexible joint and the movable joint are respectively represented by the forces and torques acting on the moving platform;

[0037] S63. Substitute the force and torque balance equations of the moving platform to solve for the end-effector output pose.

[0038] The beneficial effects of this invention are:

[0039] 1. This invention proposes a parallel robot modeling method considering omnidirectional motion errors of flexible joints, comprising the following steps: S1: Establishing a kinematic model of the robot based on the closed-loop vector method; S2: Constructing the output pose of the flexible joints by combining the motion variables of the flexible joints, including the displacement and rotation of the flexible joints in non-functional directions; S3: Establishing local coordinate systems in each flexible joint and phasing joint within the branch, and constructing each homogeneous coordinate transformation matrix and the transfer relationship between the matrices; S4: Constructing the mapping relationship between the motion variables of each flexible joint and the end-effector output pose of the mechanism; S5: Constructing the force and torque balance equations for the moving platform, each flexible joint, and phasing joint within the branch; S6: Solving the equations simultaneously to obtain the end-effector output pose of the mechanism. This invention considers the motion errors of the flexible joints in non-functional directions, establishing a robot model with higher accuracy than existing technologies, ensuring the robot's operational accuracy and reliability.

[0040] 2. This invention proposes a parallel robot modeling method considering omnidirectional motion errors of flexible joints. Local coordinate systems are established in each flexible joint and moving joint of the branch, and homogeneous transformation relationships between these local coordinate systems are constructed by combining the output poses of the flexible joints, thereby establishing a complete motion transmission path from the static platform to the moving platform. This not only achieves accurate mapping between the motion variables of each flexible joint and the end-effector output pose, but also accurately describes the relative motion between components within the branch, significantly improving the accuracy and comprehensiveness of the motion transmission path description.

[0041] 3. The parallel robot modeling method proposed in this invention, which considers the omnidirectional motion error of flexible joints, isolates the flexible joints near the moving platform and the stationary platform, as well as the moving joints in the branch in step S5, and establishes a local coordinate system in the upper and lower planes to construct the force and torque balance equation. This allows for accurate analysis of the forces and torques on each component, improving the overall accuracy and stability of the modeling. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a modeling flowchart of a parallel robot modeling method that considers the omnidirectional motion error of flexible joints according to the present invention.

[0044] Figure 2 This is a simplified diagram of the mechanism of the 3-RPR flexible parallel robot in this embodiment.

[0045] Figure 3 This is a structural diagram of the 3-RPR flexible parallel robot in this embodiment.

[0046] Figure 4 This is a schematic diagram of the flexible joint of the 3-RPR flexible parallel robot in this embodiment.

[0047] In the diagram, 10 is the static platform; 20 is the moving platform; 301 is the first branch; 302 is the second branch; 303 is the third branch; 401 is the flexible joint; 402 is the sliding joint; and 403 is the connecting rod. Detailed Implementation

[0048] The following is combined Figure 1-4 The present invention will be described in detail below.

[0049] This embodiment provides a parallel robot modeling method that considers the omnidirectional motion error of flexible joints, such as... Figure 1 As shown, the steps include:

[0050] S1: Define the end-effector pose of the mechanism and establish the kinematic model of the robot based on the closed-loop vector method;

[0051] S2: Construct the flexible joint output pose of the flexible joint 401 by combining the motion variables of the flexible joint 401. The motion variables include the displacement and rotation of the flexible joint 401 in the non-functional direction.

[0052] S3: Establish a local coordinate system in each flexible joint 401 and movable joint 402 within the branch, and construct each homogeneous coordinate transformation matrix and the transfer relationship between the matrices.

[0053] S4: Construct the mapping relationship between the motion variables of each flexible joint 401 and the end-effector pose of the mechanism;

[0054] S5: Force and torque balance equations for the construction of the moving platform 20, the flexible joints 401 and the movable joints 402 within the branch chain;

[0055] S6: Solve the equations simultaneously to find the end-effector pose of the mechanism.

[0056] This design considers the motion error of the flexible joint 401 in non-functional directions, making the model more consistent with actual working conditions and improving the robot's adaptability and reliability. Specifically, the mechanism consists of a moving platform 20, a stationary platform 10, and three branches. Each branch includes two flexible joints 401, a sliding joint 402, and a link 403. The first end of the link 403 is connected to the moving platform 20 through a flexible joint 401, and the second end is connected to the stationary platform 10 through another flexible joint 401. The link 403 adjusts its length through the sliding motion of the sliding joint 402.

[0057] The motion variables include one rotation angle and two displacements. The rotation angle represents the movement of the flexible rotary joint in the functional direction, and the two displacements represent the motion errors of the flexible rotary joint in the non-functional directions. Specifically, the motion variables in S2 include displacements δ along the x-axis and y-axis. x δ y and the rotation angle γ about the z-axis z The flexible joint outputs the pose as .

[0058] Step S1 includes:

[0059] S11. Define the dynamic coordinate system and the static coordinate system, and define the end-effector output pose. The moving coordinate system is fixed to the moving platform 20 and moves with it, while the static coordinate system is fixed at the initial position of the moving platform 20.

[0060] 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.

[0061] S13. Combining the closed-loop constraint conditions, the closed-loop vector equation of the mechanism is obtained;

[0062] S14. Squaring both sides of the closed-loop vector equation establishes the driving input displacement. With end-output pose Relationship model:

[0063]

[0064]

[0065] l is the initial length of link 403, q1, q2, and q3 are the input values ​​of the mechanism, x, y, and γ are the output values ​​of the mechanism, the distance between the second branch 302 and the third branch 303 is 2α, and the length of the moving platform 20 is 2d.

[0066] In other embodiments, step S1 further includes: S15, differentiating both sides of the closed-loop vector equation to establish the driving input speed. -Terminal output speed Linear mapping relationship between , where J is the velocity Jacobian matrix of the mechanism.

[0067] In this embodiment, the mechanism is a 3-RPR planar flexible parallel robot, such as... Figure 2 and Figure 3 As shown, the system includes a static platform 10 and a moving platform 20. A first branch 301 is connected to the first end of the moving platform 20, and a second branch 302 and a third branch 303, which are arranged parallel to each other, are connected to the second end. A movable joint 402 is mounted on a connecting rod 403 and is used to adjust the length of the connecting rod 403. The first branch 301, second branch 302, and third branch 303 are connected to the static platform 10. The dashed lines in the attached figure indicate the positions of the moving platform 20, the first branch 301, the second branch 302, and the third branch 303 after movement.

[0068] 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 can be adjusted according to the actual degrees of freedom.

[0069] Define a moving coordinate system static coordinate system Then the static coordinate system Relative to the moving coordinate system The rotation transformation matrix can be expressed as:

[0070]

[0071] 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 The centers of the three flexible joints 401 on the moving platform 20 are in the static coordinate system. The position vector in is: Based on geometric relationships, we can obtain:

[0072]

[0073]

[0074]

[0075] By solving the equations, the inverse kinematics model of the 3-RPR planar parallel robot can be obtained, i.e., the driving input displacement. With end-output pose Relationship model:

[0076]

[0077]

[0078]

[0079] In the initial state, the length of link 403 is The distance between the second branch 302 and the third branch 303 is 2α, and the length of the second end of the moving platform 20 is 2d.

[0080] Furthermore, step S3 includes:

[0081] S31. Establish local coordinate systems in each flexible joint 401 and movable joint 402 of the branch chain, respectively.

[0082] S32, Combine flexible joints to output pose Construct homogeneous transformation matrices between local coordinate systems Establish homogeneous transformation relationships between submatrices. .

[0083] Specifically, each submatrix can be represented as:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] r is the radius of the lateral circle of the flexible joint 401.

[0090] In this embodiment, step S4 is: extracting the motion vectors of the flexible joint 401 and the movable joint 402, and establishing a motion transformation relationship. The motion variables of the flexible joint 401 and the movable joint 402 are obtained by simplification. Mapping relationship between the robot's end effector output pose and the robot's end effector output pose M i Let P be the motion variable r,i The mapping matrix between the terminal output pose X and the terminal pose X. For the motion variables of all components, including the motion variables of flexible joint 401 and locating joint 402, refer to the flexible joint output pose in the previous text. .

[0091] Furthermore, step S5 includes:

[0092] S51. Based on the force balance condition of the moving platform 20, construct the force and torque balance equations of the moving platform 20;

[0093] S52. Isolate the flexible joint 401 near the moving platform 20, and establish two local coordinate systems (e.g., on the upper and lower planes of the flexible joint 401 respectively) Figure 4 As shown), construct the force and moment balance equations for the flexible joint 401;

[0094] S53. Isolate the movable joint 402 in the branch separately, establish two local coordinate systems on the upper and lower planes of the movable joint 402 respectively, and construct the force and torque balance equation of the movable joint 402.

[0095] The flexible joint 401 near the static platform 10 is isolated. Two local coordinate systems are established on the upper and lower planes of the flexible joint 401, respectively, and the force and torque balance equations of the flexible joint 401 are constructed. When the mechanism moves to the vicinity of the target pose, all components inside the mechanism reach the force balance condition. The components include the flexible joint 401 and the locating joint 402. The flexible joint 401 is as follows: Figure 4 As shown.

[0096] S54. Repeat steps S51, S52 and S53 until the force and torque balance equations of each flexible joint 401 and movable joint 402 of each branch are obtained, and proceed to step S6.

[0097] Specifically, the force and torque balance equations in step S5 include two force balance equations along the x-axis and y-axis, and one torque balance equation around the z-axis.

[0098] In this embodiment, in step S52, the force and torque acting on the lower plane of the flexible joint 401 are equal to the force and torque acting on the upper plane of the movable joint 402; in step S53, the force and torque acting on the upper plane of the flexible joint 401 are equal to the force and torque acting on the lower plane of the movable joint 402. In this step, by isolating each component within the branch and constructing equations based on force balance conditions, the force and torque on each component can be accurately analyzed, thus improving the overall accuracy and stability of the modeling.

[0099] In this embodiment, step S6 includes:

[0100] S61. Construct a set of equations, which includes the force and moment balance equations for each flexible joint 401 and movable joint 402, as well as the force and moment balance equations for the moving platform 20.

[0101] S62. The forces and torques acting on the flexible joint 401 and the movable joint 402 are respectively represented by the forces and torques acting on the moving platform 20;

[0102] S63. Substitute the forces and moments acting on the flexible joint 401 and the movable joint 402 in S62 into the force and moment balance equation of the moving platform 20. Solve for the end-effector output pose .

[0103] This invention proposes a parallel robot modeling method considering the omnidirectional motion error of the flexible joint 401. It establishes a kinematic model using the closed-loop vector method, constructs the output pose expression of the flexible joint 401, and establishes homogeneous transformation relationships between the coordinate systems of each component within the branch, achieving a precise description of the motion transmission path. Then, it constructs a mapping relationship between the motion variables of the flexible joint 401 and the end-effector output pose, obtaining the mapping matrix through multiplication and simplification of homogeneous coordinate transformation matrices. Next, based on the force balance condition, it establishes the force and torque balance equations for the end-effector moving platform 20, constructs the force and torque balance equations for each flexible joint 401 and the moving joint 402 within the branch, and finally solves the system of equations to obtain the end-effector output pose. This method comprehensively considers the omnidirectional motion error of the flexible joint 401, addressing the insufficient accuracy of existing methods, and establishes a high-precision input-output model, providing a solid theoretical foundation for high-precision control of flexible parallel robots.

[0104] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand and implement the present invention. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A parallel robot modeling method considering omni-directional motion error of a flexible joint, characterized in that, The method comprises the steps of: S1: defining an end output pose of a mechanism, and establishing a kinematics model of the robot based on a closed loop vector method; S2: constructing an output pose of a flexible joint based on a motion variable of the flexible joint, the motion variable comprising a displacement amount and a rotation angle amount of the flexible joint in a non-functional direction; S3: establishing a local coordinate system in each flexible joint and moving joint in a branch, and constructing a homogeneous coordinate transformation matrix and a transmission relationship between the matrices; S4: constructing a mapping relationship between the motion variable of each flexible joint and the end output pose; S5: constructing a force and torque balance equation of a moving platform, each flexible joint and moving joint in the branch; S6: solving the end output pose by simultaneously solving the equations. The mechanism comprises a moving platform, a static platform and three branches, each branch comprising two flexible joints, a moving joint and a connecting rod, a first end of the connecting rod being connected to the moving platform through one flexible joint, a second end of the connecting rod being connected to the static platform through the other flexible joint, and the moving joint being arranged on the connecting rod and used for adjusting a length of the connecting rod.

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