A Parametric Inverse Kinematics Solution Method for Arm Angles of a Seven-DOF Robotic Arm

Abstract

This invention relates to a parametric inverse kinematics solution method for the arm angles of a seven-DOF robotic arm, comprising the following steps: establishing a link coordinate system for an SRS-configured seven-DOF robotic arm based on the standard Denavit-Hartenberg parametric modeling method, and analyzing its forward kinematic equations; defining the arm angle parameters of the robotic arm based on the principle of minimum motion transformation, decomposing the minimum motion transformation model into two sub-motions: reference angle motion and arm angle self-motion, and analyzing them to obtain the elbow joint position in the zero arm angle plane; calculating the wrist joint posture rotation matrix corresponding to the zero arm angle based on the elbow joint position in the zero arm angle plane; solving for the elbow joint angle; and solving for the shoulder joint angle set and wrist joint angle set based on the optimal arm angle parameters, the wrist joint posture rotation matrix corresponding to the zero arm angle, and the forward kinematic equations. Compared with the prior art, this invention has the advantages of high solution accuracy, high computational efficiency, and good algorithm stability.

Description

Technical Field

[0001] This invention relates to the field of visual language multimodal fusion technology, and in particular to a method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm. Background Technology

[0002] The SRS-configured seven-DOF robotic arm, with its anthropomorphic arm design and redundant degrees of freedom, possesses highly flexible motion and manipulation capabilities. Solving its inverse kinematics is a key technology for maximizing these capabilities. Traditional arm angle parameterization methods, with their clear geometric meaning and ease of solution, are classic approaches for solving these types of robotic arms. However, traditional arm angle parameters have limitations in their definition, easily leading to algorithmic singularities during derivation. This necessitates the development of specialized exception handling algorithms in special cases, or the introduction of new parameters to address the undefined arm angle parameters in certain situations. While these methods largely solve the problem, they both increase the complexity of the solution algorithm. Summary of the Invention

[0003] The purpose of this invention is to provide a parameterized inverse kinematics solution method for the arm angle of a seven-degree-of-freedom robotic arm, redefine the arm angle parameters, solve the singularity problem in the inverse kinematics solution of the robotic arm, and improve the solution accuracy and speed.

[0004] The objective of this invention can be achieved through the following technical solutions:

[0005] A method for parametric inverse kinematics solution of arm angles of a seven-DOF robotic arm, comprising the following steps:

[0006] S1: Based on the standard Denavit-Hartenberg parametric modeling method, establish the link coordinate system of the SRS configuration seven-DOF manipulator and analyze its forward kinematic equations;

[0007] S2: Based on the principle of minimum motion transformation, the arm angle parameters of the robotic arm are defined, and the minimum motion transformation model is decomposed into two sub-motions: reference angle motion and arm angle self-motion. The analysis is performed to obtain the elbow joint position in the zero arm angle plane. The reference angle motion refers to the rotation transformation of the reference arm surface to the zero arm angle plane, and the arm angle self-motion refers to the movement of the elbow joint position on a circle with the shoulder and wrist vector as the axis. Each arm angle value corresponds to an elbow joint position.

[0008] S3: Calculate the wrist joint posture rotation matrix corresponding to the zero arm angle based on the elbow joint position in the zero arm angle plane;

[0009] S4: Solve for the elbow joint angle;

[0010] S5: Solve the shoulder joint angle set based on the optimal arm angle parameters, the wrist joint posture rotation matrix corresponding to zero arm angle, and the positive kinematic equation;

[0011] S6: Solve the wrist joint angle set based on the optimal arm angle parameters, the wrist joint posture rotation matrix corresponding to zero arm angle, and the positive kinematic equation.

[0012] Specifically, S1 involves: modeling the joint coordinate system of a seven-DOF robotic arm with an SRS configuration and no wrist offset; the formula for calculating the homogeneous transformation matrix of each joint is as follows:

[0013]

[0014] The above equation represents the homogeneous transformation matrix from the (i-1)th joint coordinate system to the ith joint coordinate system. Where θ represents the joint angle, α represents the torsion angle, d represents the link offset, and a represents the link length;

[0015] The end-effector pose matrix, i.e., the robot's forward kinematics equations, is calculated using matrix multiplication:

[0016]

[0017] Here, base is a special coordinate system used to align with the world coordinate system. Multiplying from the base coordinate system up to the 7th joint yields the pose matrix of the end-effector coordinate system.

[0018] The principle of minimum motion transformation refers to considering any configuration of the robotic arm as obtained from a reference posture through a minimum motion transformation process. The reference posture of the robotic arm is defined as the posture when the wrist point is located on the z0 axis and the elbow point E is located on the xOz plane, and the corresponding arm profile is the reference arm profile ΔS. * E * W * The zero arm angle plane is then selected as the reference plane ΔS. o E0W0, where z0 axis is the z-axis of coordinate system 0; x0z plane is the base reference system; S / s represents the shoulder point, E / e represents the elbow point, W / w represents the wrist point, the subscript 0 indicates the position of the corresponding joint point in the zero arm angle posture, and the superscript * indicates the position in the reference arm posture.

[0019] The reference angle motion transforms the reference arm profile to the zero arm angle plane, and its minimum motion transformation process is based on the normal vector V = S of the shoulder and wrist vector. * W * ×S0W0 is the rotation axis, which rotates the reference arm profile to the zero arm angle plane, where S * W *S0W0 refers to the shoulder and wrist vector in the baseline arm-angle posture, and S0W0 refers to the shoulder and wrist vector in the zero arm-angle posture. × is the vector cross product operation, and the rotation angle δ is S. * W * The formula for calculating the cosine value of the angle between the vectors of S0W0 and S0W0 is as follows:

[0020]

[0021] In the formula, d is the distance symbol, and the subscript indicates the joint point between the two endpoints of the line segment. sw This represents the distance from the shoulder point to the wrist point; p is a vector symbol, with its superscript indicating the reference coordinate system and its subscript indicating the specific vector.

[0022] The elbow joint position in the zero arm angle plane is:

[0023]

[0024] Here, rot is the rotation operation, with the first parameter representing the rotation axis and the second parameter representing the rotation angle, rot(V 0 ,δ) represents the orbit around V 0 The motion transformation is a counterclockwise rotation of the axis by an angle δ, and this motion transformation is applied to the vector multiplied on the right. superior, This represents the shoulder-elbow vector in the baseline arm posture within the 0th coordinate system. V represents the shoulder-elbow vector in coordinate system 0 under the zero arm angle posture. 0 Let V be the representation of V in coordinate system 0. The above formula corresponds to the reference angle motion, that is, the process of transforming from the reference angle attitude to the zero arm angle attitude.

[0025] Based on the elbow joint position in the zero arm angle plane, the elbow joint position corresponding to the arm angle parameter φ is determined as follows:

[0026]

[0027] in, This represents the shoulder point in coordinate system 0 when the arm angle parameter is φ. The above formula represents the elbow point in coordinate system 0. It corresponds to the arm angle self-motion, that is, the process of changing from the zero arm angle posture to the φ arm angle posture.

[0028] The wrist joint posture rotation matrix is ​​decomposed into three direction cosine unit vectors:

[0029]

[0030] in, This represents the orientation of the third coordinate system in the first coordinate system under the condition that the arm angle φ = 0. The third coordinate system is fixed at the wrist point, and the y-axis of the third coordinate system always points from the elbow point to the shoulder point.

[0031] Based on the geometric relationships that hold true in the robotic arm, the following equations are obtained:

[0032]

[0033] in, Equivalent to All are the representations of the shoulder and elbow vectors in coordinate system 0 under the zero arm angle posture. d represents the line segment distance, the subscripts represent the joint points corresponding to the two endpoints of the line segment, s represents the shoulder point, e represents the elbow point, and w represents the wrist point.

[0034]

[0035] in, This represents the shoulder-wrist vector in coordinate system 0 under the zero arm angle posture. The z-axis of coordinate system 4 under coordinate system 0 represents the zero arm angle posture. The z-axis of coordinate system 4 always points from the wrist point to the elbow point.

[0036]

[0037] The vector representation of the z-axis in coordinate system 4 in coordinate system 3 is given by s4 and c4, which are abbreviations for sin(θ4) and cos(θ4), respectively. θ represents the joint angle. In the Denavit-Hartenberg model, the following relationship exists:

[0038] Solving the system of equations simultaneously yields:

[0039]

[0040]

[0041] in, This represents the shoulder-wrist vector in coordinate system 0.

[0042] The solution obtained through the above steps is... This yields the complete expression for calculating the wrist joint posture rotation matrix corresponding to zero arm angle.

[0043] Specifically, S4 is:

[0044] Based on the geometric characteristics of the robotic arm, within the triangle formed by the shoulder-elbow vector and the elbow-wrist vector, joint 4 is the angle between the shoulder-elbow vector and the elbow-wrist vector. Given the target configuration, the lengths of the three sides of the triangle are calculable. According to the law of cosines, the wrist joint angle θ4 is calculated:

[0045]

[0046] Here, arccos is the inverse cosine operation, d represents the distance between line segments, the subscripts represent the joints of the two endpoints of the line segment, s represents the shoulder point, e represents the elbow point, and w represents the wrist point.

[0047] The shoulder joint angle group consists of the first three joints {θ1, θ2, θ3}. When the arm angle parameter is φ, the formula for calculating the elbow joint posture matrix is:

[0048]

[0049] In the formula, The rotational transformation matrix caused by the arm angle φ, as observed in the coordinates of joint 0, is obtained according to the Rodrigues formula for angular axis rotation:

[0050]

[0051] In the formula, I3 is a third-order identity matrix. For vectors skew-symmetric matrix;

[0052] right After sorting, we get:

[0053]

[0054] Among them, A s B s C s The calculation expression is:

[0055]

[0056] According to the forward kinematics model, we have:

[0057]

[0058] in, s represents the attitude of coordinate system i in coordinate system j. i sin(θ) i (abbreviation of ) i cos(θ) i (abbreviation)

[0059] By comparing the elements of the posture matrix of the shoulder joint angle group, the calculation expression for the shoulder joint angle group is obtained as follows:

[0060]

[0061] in, They represent A respectively S B S C S The element in the i-th row and j-th column of the matrix.

[0062] The wrist joint angle group consists of the last three joints {θ5, θ6, θ7}. When the arm angle parameter is φ, the wrist joint posture rotation matrix is:

[0063]

[0064] In the formula, A w B w C w The calculation formula is:

[0065]

[0066] According to the forward kinematics model, we have:

[0067]

[0068] By comparing the elements of the posture matrix, the calculation expression for the wrist joint angle group is obtained as follows:

[0069]

[0070] in, They represent A respectively w B w C w The element in the i-th row and j-th column of the matrix.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] (1) This invention proposes a new definition of arm angle parameters and a parametric inverse kinematics solution method for arm angles derived from a minimum motion transformation model. This method features high solution accuracy and fast computation speed. Compared with other arm angle parametric methods, it does not produce algorithm singularities due to configuration problems, effectively solving the algorithm singularity problem caused by the failure of the arm angle definition.

[0073] (2) The two-stage minimum motion transformation model proposed in this invention has reversibility in the algorithm flow of each stage, and can quickly implement its forward transformation algorithm and reverse transformation algorithm. This feature is of great help in problems such as motion obstacle avoidance and iterative search for the optimal arm angle. Attached Figure Description

[0074] Figure 1 This is a flowchart of the method of the present invention;

[0075] Figure 2 This is a schematic diagram of the solution process;

[0076] Figure 3 This is a schematic diagram of the SRS configuration seven-degree-of-freedom robotic arm structure of the present invention;

[0077] Figure 4 This is a schematic diagram of the minimum motion transformation model and its two-stage motion decomposition in the method of the present invention, wherein (4a) is the minimum motion transformation model, (4b) is a schematic diagram of the reference angle motion, and (4c) is a schematic diagram of the arm angle self-motion.

[0078] Figure 5 This is a flowchart of the forward algorithm for the minimum motion transformation model in the method of this invention;

[0079] Figure 6 This is a flowchart of the inverse algorithm of the minimum motion transformation model in the method of this invention. Detailed Implementation

[0080] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0081] This embodiment provides a method for parametric inverse kinematics solution of arm angles for a seven-degree-of-freedom robotic arm, such as... Figure 1 As shown in the diagram, the solution process is illustrated below. Figure 2 As shown, the specific steps include:

[0082] S1: Based on the standard Denavit-Hartenberg parametric modeling method, establish the link coordinate system of the SRS configuration seven-DOF manipulator and analyze its forward kinematic equations.

[0083] Based on the standard Denavit-Hartenberg parametric modeling method, and taking the positive rotation direction of each joint motor as the positive z-axis, with rotation angles θ1, θ2, θ3, θ4, θ5, θ6, and θ7 as joint variables, a seven-DOF robotic arm with an SRS configuration and no wrist offset (such as...) is modeled. Figure 3 As shown, perform joint coordinate system modeling.

[0084] In this embodiment, the parameter table for the SRS configuration seven-DOF robotic arm is shown in Table 1.

[0085] Table 1. DH Parameter Table for Seven-Axis Robotic Arm

[0086]

[0087] In this context, the subscript of the link offset d is the corresponding joint point, b is the base, s is the shoulder joint point, e is the elbow joint point, w is the wrist joint point, and f is the end flange.

[0088] The formula for calculating the homogeneous transformation matrix of each joint is as follows:

[0089]

[0090] The above equation represents the homogeneous transformation matrix from the (i-1)th joint coordinate system to the ith joint coordinate system. Where θ represents the joint angle, α represents the torsion angle, d represents the link offset, and a represents the link length.

[0091] The end-effector pose matrix, i.e., the robot's forward kinematics equations, is calculated using matrix multiplication:

[0092]

[0093] Here, base is a special coordinate system used to align with the world coordinate system. Multiplying from the base coordinate system up to the 7th joint yields the pose matrix of the end-effector coordinate system.

[0094] S2: Based on the principle of minimum motion transformation, the arm angle parameters of the robotic arm are defined, and the minimum motion transformation model is decomposed into two sub-motions: reference angle motion and arm angle self-motion. The analysis is then performed to obtain the elbow joint position in the zero arm angle plane.

[0095] Based on the principle of minimum motion transformation, the arbitrary position of the robotic arm is regarded as being obtained from the reference posture through the minimum motion transformation process. The motion of the robotic arm from the reference posture to the arbitrary posture is decomposed into two sub-motions: reference angle motion and arm angle self-motion. The former transforms the reference arm shape to obtain the zero arm angle plane, and the latter rotates the elbow point of the robotic arm under the zero arm angle around the shoulder and wrist vector by a certain angle to obtain the target pose under the corresponding arm angle.

[0096] The reference posture of the robotic arm is defined as the posture when the wrist point is located on the z0 axis (i.e., the z-axis of the 0th coordinate system) and the elbow point E is located in the xOz plane (i.e., the base reference system). The corresponding arm profile is the reference arm profile ΔS. * E * W * The zero arm angle plane is then selected as the reference plane ΔS. o E0W0. In this embodiment, shoulder points are uniformly represented by S / s, elbow points by E / e, and wrist points by W / w. The subscript 0 indicates the position of the corresponding joint point in the zero arm angle posture, and the superscript * indicates the position in the baseline arm posture.

[0097] The reference angle motion transforms the reference arm profile to the zero arm angle plane. Its minimum motion transformation process involves the normal vector V = S of the shoulder and wrist vectors. * W * ×S0W0 is the rotation axis, which rotates the reference arm profile to the zero arm angle plane, where S * W * S0W0 refers to the shoulder and wrist vector in the baseline arm-angle posture, and × represents the vector cross product operation. The rotation angle δ is S. * W * The angle between the vector and S0W0, such as Figure 4 As shown, the formula for calculating the cosine value is:

[0098]

[0099] In the formula, d is the distance symbol, and the subscript indicates the joint point between the two endpoints of the line segment. sw This represents the distance from the shoulder point to the wrist point; p is a vector symbol, with its superscript indicating the reference coordinate system and its subscript indicating the specific vector. For example, it represents the mathematical representation of the shoulder and wrist vector corresponding to the zero arm angle posture in the 0th coordinate system, and the interpretation of other vectors follows the same principle.

[0100] Arm angle self-motion refers to the movement of the elbow joint position on a circle with the shoulder-wrist vector as the axis. Each arm angle value corresponds to one elbow joint position, which in turn corresponds to a set of inverse joint solutions. The elbow joint position in the zero arm angle plane is:

[0101]

[0102] Here, rot is the rotation operation, with the first parameter representing the rotation axis and the second parameter representing the rotation angle, rot(V 0 ,δ) represents the orbit around V 0 The motion transformation is a counterclockwise rotation of the axis by an angle δ, and this motion transformation is applied to the vector multiplied on the right. superior, This represents the shoulder-elbow vector in the baseline arm posture within the 0th coordinate system. V represents the shoulder-elbow vector in coordinate system 0 under the zero arm angle posture. 0 Let V be the representation of V in coordinate system 0. The above formula corresponds to the reference angle motion, that is, the process of transforming from the reference angle attitude to the zero arm angle attitude.

[0103] Based on the elbow joint position in the zero arm angle plane, the elbow joint position corresponding to the arm angle parameter φ is determined as follows:

[0104]

[0105] in, This represents the shoulder point in coordinate system 0 when the arm angle parameter is φ. This represents the elbow point in coordinate system 0. Similar to the calculation of the elbow point at zero arm angle, the above formula corresponds to the arm angle self-motion, that is, the process of transforming from the zero arm angle posture to the φ arm angle posture.

[0106] Both stages of the minimum motion transformation model are mathematically invertible, meaning that the inverse joint solution can be solved based on specific arm angle parameters, and the current arm angle parameters can also be solved from a specific posture. The forward and inverse algorithm flows are described in detail below. Figure 5 and Figure 6 .

[0107] S3: Calculate the wrist joint posture rotation matrix corresponding to the zero arm angle based on the elbow joint position in the zero arm angle plane.

[0108] The wrist joint posture rotation matrix is ​​the key matrix for solving the expression for each joint angle. It can be decomposed into three direction cosine unit vectors:

[0109]

[0110] Where R is a 3*3 rotation matrix, which is a subset of matrix T mentioned earlier, consisting of the first 3 rows and the first 3 columns. The numbers in the upper right and lower right corners are similar to those in T, representing the index of the joint coordinate system. φ = 0 specifically refers to the arm angle condition. This represents the orientation of coordinate system 3 in coordinate system 0 under the condition that arm angle φ = 0. Coordinate system 3 is fixed at the wrist point, hence it is also called the wrist joint orientation rotation matrix. Here, the matrix to be solved... By performing cosine component decomposition on a matrix, we can calculate the result by solving for each of the three components separately. The advantage of decomposition is that it allows us to solve the problem by utilizing certain constant coordinate relationships that hold true during the movement of the robotic arm.

[0111] Based on the geometric relationships that hold true in the robotic arm, the following equations are obtained:

[0112]

[0113] For the sake of simplification, Equivalent to All of these are representations of the shoulder-elbow vector in coordinate system 0 under the zero arm angle posture. The following text... Similarly, the above formula represents the relationship between the shoulder-elbow vector and... In this relationship, the y-axis of coordinate system 3 always points from the elbow point to the shoulder point. This geometric relationship is referenced... Figure 3 The DH model.

[0114]

[0115] in, This represents the shoulder-wrist vector in coordinate system 0 under the zero arm angle posture. The above formula represents the z-axis of the fourth coordinate system under the zero arm angle posture in the zero coordinate system. The formula uses the relationship between the shoulder-elbow and elbow-wrist components and the shoulder-elbow vector. Similar to the previous text, the z-axis of the fourth coordinate system always points from the wrist point to the elbow point.

[0116]

[0117] The above formula utilizes attitude matrix multiplication. In addition to representing the attitude matrix of coordinate system 3 in coordinate system 0, it also represents the transformation matrix required to transform from coordinate system 0 to coordinate system 3. This matrix represents the vector representation of the z-axis of coordinate system 4 in coordinate system 3. The left multiplication of this matrix... Can Transform into a vector representation in coordinate system 0. s4 and c4 are abbreviations for sin(θ4) and cos(θ4), where θ represents the joint angle. In the Denavit-Hartenberg model, the following relationship exists:

[0118] Solving the system of equations simultaneously yields:

[0119]

[0120]

[0121] in, This represents the shoulder-wrist vector in coordinate system 0. sw is the rotation axis of the arm angle's self-motion; in the second stage of the decomposition, it is essentially a constant, and the value of the arm angle does not affect... The vector representation of .

[0122] Solve The cross product operation can then be used to solve the problem. The x, y, and z axes of the same coordinate system satisfy the right-hand screw rule.

[0123] The solution obtained through the above steps is... This yields the complete expression for calculating the wrist joint posture rotation matrix corresponding to zero arm angle.

[0124] S4: Solve for the elbow joint angle θ4.

[0125] Based on the geometric characteristics of the robotic arm, within the triangle formed by the shoulder-elbow vector and the elbow-wrist vector, joint 4 is the angle between the shoulder-elbow vector and the elbow-wrist vector. Given the target configuration, the lengths of the three sides of the triangle are calculable. According to the law of cosines, the wrist joint angle θ4 is calculated:

[0126]

[0127] Arccosine is the inverse cosine operation. In the ΔSEW triangle, the law of cosines can be used to solve for joint number 4.

[0128] S5: Based on the given optimal arm angle parameters, the wrist joint posture rotation matrix corresponding to zero arm angle, and the forward kinematic equation, calculate the posture matrix of the elbow joint in the corresponding arm angle self-motion, and solve the shoulder joint angle set {θ1, θ2, θ3} according to the identity relationship of the corresponding elements of the posture matrix.

[0129] The shoulder joint angle group consists of the first three joints {θ1, θ2, θ3}. When the arm angle parameter is φ, the formula for calculating the elbow joint posture matrix is:

[0130]

[0131] The above formula is given in the arm angle method literature (see Shimizu, M., Kakuya, H., Yoon, WK, Kitagaki, K., & Kosuge, K. (2008). Analytical inverse kinematic computation for 7-DOF redundant manipulators with joint limits and its application to redundancy resolution. IEEE Transactions on Robotics, 24(5), 1131-1142.), which assumes the existence of a rotation transformation matrix that depends only on φ. It can and expectations The attitude is related, and in fact, such a transformation matrix always exists.

[0132] In the above formula, The rotational transformation matrix caused by the arm angle φ, as observed in the coordinates of joint 0, is obtained according to the Rodrigues formula for angular axis rotation (i.e., matrix expansion of the rot operation):

[0133]

[0134] In the formula, I3 is a third-order identity matrix. For vectors A skew-symmetric matrix.

[0135] right After sorting, we get:

[0136]

[0137] Among them, A s B s C s The calculation expression is:

[0138]

[0139] According to the forward kinematics model, we have:

[0140]

[0141] in, s represents the attitude of coordinate system i in coordinate system j. i sin(θ) i (abbreviation of ) i cos(θ) i (abbreviation of ).

[0142] By comparing the elements of the posture matrix of the shoulder joint angle group, the calculation expression for the shoulder joint angle group is obtained as follows:

[0143]

[0144] in, They represent A respectively S B S C S The element in the i-th row and j-th column of the matrix.

[0145] S6: Based on the given optimal arm angle parameters, the wrist joint posture rotation matrix corresponding to zero arm angle, and the forward kinematic equation, calculate the posture matrix of the wrist joint in the corresponding arm angle self-motion. Combine the elbow posture matrix and the target posture matrix to calculate the wrist posture matrix, and solve the wrist joint angle set {θ5, θ6, θ7} according to the identity relationship of their corresponding elements.

[0146] The wrist joint angle group consists of the last three joints {θ5, θ6, θ7}. When the arm angle parameter is φ, the wrist joint posture rotation matrix is:

[0147]

[0148] In the formula, A w B w C w The calculation formula is:

[0149]

[0150] According to the forward kinematics model, we have:

[0151]

[0152] By comparing the elements of the posture matrix, the calculation expression for the wrist joint angle group is obtained as follows:

[0153]

[0154] in, They represent A respectively w B w C w The element in the i-th row and j-th column of the matrix.

[0155] Based on the above process, the inverse kinematics solution of the SRS configuration seven-DOF robot arm can be realized. The solution has high accuracy and fast calculation speed. It will not produce algorithm singularity due to configuration problems, and effectively solves the algorithm singularity problem caused by the failure of the arm angle definition.

[0156] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm, characterized in that, Includes the following steps: S1: Based on the standard Denavit-Hartenberg parametric modeling method, establish the link coordinate system of the SRS configuration seven-DOF manipulator and analyze its forward kinematic equations; S2: Based on the principle of minimum motion transformation, the arm angle parameters of the robotic arm are defined, and the minimum motion transformation model is decomposed into two sub-motions: reference angle motion and arm angle self-motion. The analysis is performed to obtain the elbow joint position in the zero arm angle plane. The reference angle motion refers to the rotation transformation of the reference arm surface to the zero arm angle plane, and the arm angle self-motion refers to the movement of the elbow joint position on a circle with the shoulder and wrist vector as the axis. Each arm angle value corresponds to an elbow joint position. S3: Calculate the wrist joint posture rotation matrix corresponding to the zero arm angle based on the elbow joint position in the zero arm angle plane; S4: Solve for the elbow joint angle; S5: Solve the shoulder joint angle set based on the optimal arm angle parameters, the wrist joint posture rotation matrix corresponding to zero arm angle, and the positive kinematic equation; S6: Solve the wrist joint angle set based on the optimal arm angle parameters, the wrist joint posture rotation matrix corresponding to zero arm angle, and the positive kinematic equation.

2. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 1, characterized in that, Specifically, S1 involves: modeling the joint coordinate system of a seven-DOF robotic arm with an SRS configuration and no wrist offset; the formula for calculating the homogeneous transformation matrix of each joint is as follows: The above equation represents the homogeneous transformation matrix from the (i-1)th joint coordinate system to the ith joint coordinate system. Where θ represents the joint angle, α represents the torsion angle, d represents the link offset, and A represents the link length; The end-effector pose matrix, i.e., the robot's forward kinematics equations, is calculated using matrix multiplication: Here, base is a special coordinate system used to align with the world coordinate system. Multiplying from the base coordinate system up to the 7th joint yields the pose matrix of the end-effector coordinate system.

3. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 1, characterized in that, The principle of minimum motion transformation refers to considering any configuration of the robotic arm as obtained from a reference posture through a minimum motion transformation process. The reference posture of the robotic arm is defined as the posture when the wrist point is located on the z0 axis and the elbow point E is located on the xOZ plane, and the corresponding arm profile is the reference arm profile ΔS. * E * W * The zero arm angle plane is selected as the reference plane ΔS0E0W0, where the z0 axis is the z-axis of the 0th coordinate system; the xOz plane is the base reference system; S / s represents the shoulder point, E / e represents the elbow point, and W / w represents the wrist point. The subscript 0 indicates the position of the corresponding joint point in the zero arm angle posture, and the superscript * indicates the position in the reference arm posture.

4. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 1, characterized in that, The reference angle motion transforms the reference arm profile to the zero arm angle plane, and its minimum motion transformation process is based on the normal vector V = S of the shoulder and wrist vector. * W * ×S0W0 is the rotation axis, which rotates the reference arm profile to the zero arm angle plane, where S * W * S0W0 refers to the shoulder and wrist vector in the baseline arm-angle posture, and S0W0 refers to the shoulder and wrist vector in the zero arm-angle posture. × is the vector cross product operation, and the rotation angle δ is S. * W * The formula for calculating the cosine value of the angle between the vectors of S0W0 and S0W0 is as follows: In the formula, d is the distance symbol, and the subscript indicates the joint point between the two endpoints of the line segment. sw This represents the distance from the shoulder point to the wrist point; p is a vector symbol, with its superscript indicating the reference coordinate system and its subscript indicating the specific vector.

5. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 4, characterized in that, The elbow joint position in the zero arm angle plane is: Here, rot is the rotation operation, with the first parameter representing the rotation axis and the second parameter representing the rotation angle, rot(V 0 ,δ) represents the orbit around V 0 The motion transformation is a counterclockwise rotation of the axis by an angle δ, and this motion transformation is applied to the vector multiplied on the right. superior, This represents the shoulder-elbow vector in the baseline arm posture within the 0th coordinate system. V represents the shoulder-elbow vector in coordinate system 0 under the zero arm angle posture. 0 Let V be the representation of V in coordinate system 0. The above formula corresponds to the reference angle motion, that is, the process of transforming from the reference angle attitude to the zero arm angle attitude.

6. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 5, characterized in that, Based on the elbow joint position in the zero arm angle plane, the elbow joint position corresponding to the arm angle parameter φ is determined as follows: in, This represents the shoulder point in coordinate system 0 when the arm angle parameter is φ. The above formula represents the elbow point in coordinate system 0. It corresponds to the arm angle self-motion, that is, the process of changing from the zero arm angle posture to the φ arm angle posture.

7. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 5, characterized in that, The wrist joint posture rotation matrix is ​​decomposed into three direction cosine unit vectors: in, This represents the orientation of coordinate system 3 within coordinate system 0, given an arm angle φ = 0. Coordinate system 3 is fixed at the wrist point, and its y-axis always points from the elbow point to the shoulder point. Based on the geometric relationships that hold true in the robotic arm, the following equations are obtained: in, Equivalent to All are the representations of the shoulder and elbow vectors in coordinate system 0 under the zero arm angle posture. d represents the line segment distance, the subscripts represent the joint points corresponding to the two endpoints of the line segment, s represents the shoulder point, e represents the elbow point, and w represents the wrist point. in, This represents the shoulder-wrist vector in coordinate system 0 under the zero arm angle posture. The z-axis of coordinate system 4 under coordinate system 0 represents the zero arm angle posture. The z-axis of coordinate system 4 always points from the wrist point to the elbow point. The vector representation of the z-axis of coordinate system 4 in coordinate system 3, where s4 and c4 are abbreviations for sin(θ4) and cos(θ4), and θ represents the joint angle. In the Denavit-Hartenberg model, the following relationship exists: Solving the system of equations simultaneously yields: in, This represents the shoulder-wrist vector in coordinate system 0. The solution obtained through the above steps is... This yields the complete expression for calculating the wrist joint posture rotation matrix corresponding to zero arm angle.

8. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 1, characterized in that, Specifically, S4 is: Based on the geometric characteristics of the robotic arm, within the triangle formed by the shoulder-elbow vector and the elbow-wrist vector, joint 4 is the angle between the shoulder-elbow vector and the elbow-wrist vector. Given the target configuration, the lengths of the three sides of the triangle are calculable. According to the law of cosines, the wrist joint angle θ4 is calculated: Here, arccos is the inverse cosine operation, d represents the distance between line segments, the subscripts represent the joints of the two endpoints of the line segment, s represents the shoulder point, e represents the elbow point, and w represents the wrist point.

9. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 7, characterized in that, The shoulder joint angle group consists of the first three joints {θ1, θ2, θ3}. When the arm angle parameter is φ, the formula for calculating the elbow joint posture matrix is: In the formula, The rotational transformation matrix caused by the arm angle φ, as observed in the coordinates of joint 0, is obtained according to the Rodrigues formula for angular axis rotation: In the formula, I3 is a third-order identity matrix. For vectors skew-symmetric matrix; right After sorting, we get: Among them, A s B s C s The calculation expression is: According to the forward kinematics model, we have: in, s represents the attitude of coordinate system i in coordinate system j. i sin(θ) i (abbreviation of ) i cosθ i (abbreviation) By comparing the elements of the posture matrix of the shoulder joint angle group, the calculation expression for the shoulder joint angle group is obtained as follows: in, They represent A respectively S B s C S The element in the i-th row and j-th column of the matrix.

10. The method for parametric inverse kinematics solution of arm angles of a seven-degree-of-freedom robotic arm according to claim 9, characterized in that, The wrist joint angle group consists of the last three joints {θ5, θ6, θ7}. When the arm angle parameter is φ, the wrist joint posture rotation matrix is: In the formula, A w B w C w The calculation formula is: According to the forward kinematics model, we have: By comparing the elements of the posture matrix, the calculation expression for the wrist joint angle group is obtained as follows: in, They represent A respectively W B w C w The element in the i-th row and j-th column of the matrix.

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