Geometric inverse solution method for seven-degree-of-freedom humanoid arm with shoulder joint offset
By combining the inverse solution method of geometric method and algebra method, the problems of low computational efficiency and limited accuracy of the seven-degree-of-freedom robot arm are solved, especially for the seven-degree-of-freedom human arm with shoulder joint bias, an efficient and accurate inverse solution method is provided.
Patent Information
- Application Number
- CN202510377896.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-28
- Publication Date
- 2025-07-22
AI Technical Summary
In the prior art, the inverse solution method of the seven-axis robotic arm has problems of low computational efficiency and limited accuracy, especially the inverse solution problem of the seven-degree-of-freedom human-like arm with shoulder joint bias has not been effectively solved.
The inverse solution method combining geometric method and algebraic method is adopted to establish the DH coordinate system of the seven-degree-freedom human arm, calibrate its parameters, and use geometric relationships and algebraic formulas to solve the joint angle, including preset joint limits and geometric solution steps, to expand the inverse solution method for the seven-degree-freedom human arm with shoulder joint bias.
The inverse solution with small calculation volume, high efficiency and reliable accuracy is achieved, and is suitable for seven-degree-of-freedom robotic arms with shoulder joint bias, which complements the shortcomings of the prior art.
Smart Images
Figure CN120354879A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of robots, and in particular to a geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset. Background Art
[0002] When a robot moves in three-dimensional space, its end needs to satisfy three position constraints and three attitude constraints. Therefore, generally, a robotic arm requires six degrees of freedom. Compared with a six-degree-of-freedom robotic arm, a seven-degree-of-freedom redundant arm has an additional degree of freedom, so it has higher flexibility, which is specifically manifested in avoiding singular configurations, optimizing motion paths, expanding the operating space, and fault tolerance, etc., and the functions that can be achieved are more similar to the human arm structure. Compared with a non-offset arm, an offset arm has the advantages of a more reasonable mechanism form, a larger working range, and elimination of singularities.
[0003] The solution methods for the inverse kinematics of a robotic arm include: closed solution methods and numerical solution methods. The closed solution methods include algebraic methods and geometric methods, and they all have their own characteristics. Among them, the geometric method has a small amount of calculation, but is only applicable to specific configurations; the algebraic method has a relatively complex analytical process and needs to satisfy the Pieper criterion; the numerical method has high versatility, but the calculation accuracy is limited, and some algorithms have problems such as slow convergence speed.
[0004] Due to kinematic redundancy, while increasing flexibility and offset, a seven-axis robotic arm also increases the difficulty of kinematic modeling and solution. Currently, the inverse solution problem of a seven-axis robotic arm with an offset in the first three axis axes in this configuration has not been solved. Summary of the Invention
[0005] The present invention is to overcome the above-mentioned deficiencies in the prior art, and provides a geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset, which has high calculation efficiency and reliable accuracy.
[0006] In order to achieve the above object, the present invention adopts the following technical solutions:
[0007] A geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset, based on a seven-degree-of-freedom humanoid arm, the humanoid arm has a shoulder joint offset, and the three axes of the wrist joint of the humanoid arm are orthogonal to one point; the origin position of the 0 coordinate system of the humanoid arm is the intersection point of the first joint axes of the left and right arms, and the inverse solution method of the humanoid arm includes the following steps:
[0008] S1. Establish a DH coordinate system for the seven-degree-of-freedom humanoid arm and calibrate its DH parameters;
[0009] S2. Perform forward kinematics solution of the humanoid arm according to the DH parameters set in step S1;
[0010] S3. According to the joint limits of the humanoid arm, preset the link angle θ2 of the second joint of the humanoid arm 2 as a constant within the value range to degrade the degrees of freedom;
[0011] S4. Solve the link angle θ4 of the fourth joint of the shaft part 4 and the link angle θ1 of the first joint through the geometric method;
[0012] S5. Solve the link angle θ3 of the third joint;
[0013] S6. Solve the link angles θ5, θ6, and θ7 of the three joints of the humanoid arm wrist, namely the fifth joint, the sixth joint, and the seventh joint.
[0014] The purpose of the present invention is to provide an inverse solution method of geometric-algebra method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset in combination with the geometric method and the algebraic method in view of the deficiencies of the existing technology. Based on the arm angle and the basic geometric structure relationship in space, on the basis of the existing algebraic solution method, a set of geometric-algebra inverse solution methods for this special configuration of a seven-degree-of-freedom humanoid arm with a shoulder joint offset is extended. This method combines the geometric method and the algebraic method, has the advantages of small calculation amount, high efficiency, reliable calculation accuracy, and easy implementation method, and supplements the inverse solution method for the seven-degree-of-freedom manipulator with a shoulder joint offset for this configuration.
[0015] Preferably, in step S1, specifically:
[0016] Establish a DH coordinate system for the seven-degree-of-freedom humanoid arm and calibrate its DH parameters: α i-1 、α i-1 、θ i 、d i , that is, the link rotation angle α i-1 , the link length a i-1 , the link angle θ i , the link offset d i ;
[0017] Among them, the coordinate system i = 1 to 7, α i-1 represents the angle between z i-1 and z i-1 as seen from the direction of x i , a i-1 represents the distance between z i-1 and z i-1 along the direction of x i , θ i represents the angle between x i and x i-1 as seen from the direction of z i , positive clockwise and negative counterclockwise, d i represents the distance between x i and x i-1 along the direction of z i .
[0018] Preferably, in step S2, specifically:
[0019] Solve the forward kinematics of the robotic arm according to the DH parameters set in step S1, and describe the coordinate system i in the coordinate system i-1
[0020] where c represents cos and s represents sin.
[0021] The homogeneous transformation matrix of forward kinematics is:
[0022]
[0023] where nx, ny, and nz are the components of the unit vector of the x-axis of the 7 coordinate system in the 0 coordinate system, sx, sy, and sz are the components of the unit vector of the y-axis of the 7 coordinate system in the 0 coordinate system, ax, ay, and az are the components of the unit vector of the z-axis of the 7 coordinate system in the 0 coordinate system, and px, py, and pz are the coordinates of the origin of the 7 coordinate system in the 0 coordinate system.
[0024] Preferably, in step S3, if the link angle θ2 of joint 2 needs to move, first change the link angle θ2, and then perform steps S4 to S6 to solve the inverse kinematics.
[0025] Preferably, in step S4, the specific steps are as follows:
[0026] S41. The intersection point of the upper arm l3 of the humanoid arm and the rotation axis z1 of joint 1 is always on the same straight line and is always tangent to the sphere O2, which is centered at the origin o2 of the 2 coordinate system with a radius of a2; according to the above geometric relationship, find the intersection point A1 of the extension line of the upper arm l3 of the humanoid arm and the rotation axis z1 of joint 1, and the tangent point A2 with the sphere O2; in triangle Ao4o5, two solutions θ 41 、θ 42 ; of the joint angle θ4 can be obtained by the cosine theorem
[0027] S42. When the link angle θ2 of joint 2 of the humanoid arm is a constant, the spatial position of the origin o4 of the shaft joint coordinate system is a circle with the joint angle θ1 of joint 1 as the only variable; obtain the homogeneous transformation matrix through the forward kinematics obtained in step S2
[0028]
[0029] where t11~t33 represent terms that can be ignored. Arbitrarily assign 3 different angle values to the joint angle θ1 of joint 1, and substitute them into formula (2) respectively to obtain the spatial positions o 41 、o 42 、o 43, the center o of the spatial position circle of the origin o4 of the shaft joint coordinate system can be obtained by the three-point circle method a and the radius r;
[0030] Transform the coordinate origin of the base coordinate system o0 to the center o a and rotate it around the x-axis to obtain a new coordinate system with the center o a as the origin, and the homogeneous transformation matrix is The representation of the position of the origin of the 7-coordinate system in the new coordinate system is:
[0031]
[0032] Given the center coordinates, radius, position point o′7 of the circle o a and the connection length l4 with the circle o a , the positions p1 and p2 of the origin o4 of the shaft joint coordinate system can be determined through geometric analysis in space. Then, substitute the positions p1 and p2 into the formula (2) respectively to obtain the 1-joint angles θ 11 , θ 12 .
[0033] Preferably, in step S5, specifically:
[0034] According to formula (1), the joint angles affecting the position of the origin of the 7-coordinate system are θ1, θ2, θ3, θ4. Substitute the constant joint angle θ2 and the obtained variable joint angles θ1, θ4 to obtain the 3-joint angles θ 31 , θ 32 , θ 33 , θ 34 , corresponding to θ 11 , θ 41 , θ 11 , θ 42 , θ 12 , θ 41 and θ 12 , θ 42 . Thus, 4 groups of joint angles can be obtained.
[0035] Preferably, in step S6, specifically:
[0036] According to formula (1), the joint angles θ5, θ6, θ7 do not affect the position of the origin of the 7-coordinate system. Just perform attitude calculation on θ5, θ6, θ7. Denote the attitude of the 7-coordinate system as R p :
[0037]
[0038] The rotation transformation of the joint angles θ5, θ6, θ7 is:
[0039]
[0040] It can be obtained from the forward kinematics that:
[0041]
[0042] By transposing the above equation, it can be obtained that:
[0043]
[0044] Combining equations (5) and (7), two sets of joint angles can be obtained:
[0045] θ 51 = atan2(r23, r13)
[0046]
[0047] θ 71 = atan2(r32, -r31) (8)
[0048] θ 52 = atan2(r23, r13) + π
[0049]
[0050] θ 72 = atan2(r32, -r31) + π (9)
[0051] So far, the 8 sets of inverse solutions of the humanoid arm can be obtained:
[0052]
[0053] The beneficial effects of the present invention are as follows: Since it combines geometric and algebraic methods, it has the advantages of small computational amount, high efficiency, reliable calculation accuracy, and easy implementation method, and supplements the inverse solution method for the seven-degree-of-freedom manipulator with a shoulder joint offset for this configuration. Description of the Drawings
[0054] Figure 1 is a schematic diagram of the humanoid arm prototype of the present invention;
[0055] Figure 2 is a schematic diagram of the joints of the humanoid arm of the present invention;
[0056] Figure 3 is a schematic diagram for solving the angle of the link of joint 2;
[0057] Figure 4 is a schematic diagram for solving the position of joint 4. Detailed Embodiment
[0058] The present invention will be further described below in conjunction with the drawings and specific embodiments.
[0059] As Figure 1 , Figure 2 described in the embodiments, a geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset. Based on the seven-degree-of-freedom humanoid arm, the humanoid arm has a shoulder joint offset, and the wrist joint of the humanoid arm is orthogonal to a point in three axes; the origin position of the 0 coordinate system of the humanoid arm is the intersection point of the 1 joint axes of the left and right arms, and the direction is as Figure 1 , Figure 2 shown; the inverse solution method of the humanoid arm includes the following steps:
[0060] S1. Establish a DH coordinate system for the seven-degree-of-freedom humanoid arm and calibrate its DH parameters; specifically:
[0061] Establish a DH coordinate system for the seven-degree-of-freedom humanoid arm and calibrate its DH parameters: the link rotation angle α i-1 , the link length α i-1 , the link angle θ i , the link offset d i ;
[0062] As Figure 1 , Figure 2 shown, the origin O0 of the base coordinate system O 0-x0y0z0 is the intersection point of the 1 joint axes of the left and right arms, the z0 direction is vertically upward, the x0 direction is outward from the paper plane, and the y0 direction is calibrated according to the right-hand system principle.
[0063] Among them, the coordinate system i = 1 to 7, α i-1 represents the angle between z i-1 and z i-1 viewed from the direction of x i , α i-1 represents the distance between z i-1 and z i-1 along the direction of x i , θ i represents the angle between x i and x i-1 viewed from the direction of z i , positive clockwise and negative counterclockwise, d i represents the distance between x i and x i-1 along the direction of z i .
[0064] The DH parameters of the left and right arms are specifically shown in Table 1 below:
[0065] Table 1. DH Parameter Table
[0066]
[0067]
[0068] The left and right arms of the humanoid arm are symmetrical to each other and have the same configuration. Therefore, the right arm is taken as an example for solution.
[0069] S2. Solve the forward kinematics of the humanoid arm according to the DH parameters set in step S1; specifically:
[0070] Solve the forward kinematics of the robotic arm according to the DH parameters set in step S1, and the description of the coordinate system i in the coordinate system i-1
[0071] where c represents cosine and s represents sine.
[0072] The forward kinematics homogeneous transformation matrix is:
[0073]
[0074] where nx, ny, nz are the components of the unit vector of the x-axis of the coordinate system 7 in the coordinate system 0, sx, sy, sz are the components of the unit vector of the y-axis of the coordinate system 7 in the coordinate system 0, ax, ay, az are the components of the unit vector of the z-axis of the coordinate system 7 in the coordinate system 0, and px, py, pz are the coordinates of the origin of the coordinate system 7 in the coordinate system 0.
[0075] S3. According to the joint limit of the humanoid arm, the value range of the 2nd joint of the humanoid arm is Preset the link angle θ2 of the 2nd joint of the humanoid arm as a constant within the value range to degrade the degree of freedom;
[0076] If the link angle θ2 of the 2nd joint needs to move, first change the link angle θ2, and then perform steps S4 to S6 to solve the inverse kinematics.
[0077] S4. Solve the link angle θ4 of the 4th joint of the shaft part and the link angle θ1 of the 1st joint through the geometric method; the specific steps are as follows:
[0078] S41. From Figure 1 , Figure 2 It can be seen that the intersection point of the upper arm l3 of the humanoid arm and the rotation axis z1 of the 1st joint is always on the same straight line and is always tangent to the sphere O2, which is centered at the origin o2 of the coordinate system 2 and has a radius of a2; according to the above geometric relationship, the intersection point A1 of the extension line of the upper arm l3 of the humanoid arm and the rotation axis z1 of the 1st joint and the tangent point A2 of the sphere O2 are obtained;
[0079] As Figure 3 shown, in the triangle Ao4o5, the two solutions θ 41 , θ 42 of the link angle θ4 of the 4th joint can be obtained through the cosine theorem;
[0080]
[0081] θ 42 =-θ 41
[0082] Wherein, o4o5 = l4. When -π / 6 ≤ θ2 < π / 3, point A takes intersection point A1, corresponding to Figure 3 (a), at this time AO4 = l A1A2 + l3; when -1.878 ≤ θ2 < -π / 6, point A takes intersection point A1, corresponding to Figure 3 (b), at this time AO4 = l3 - l A1A2 ; when -2π / 3 < θ2 < -1.878, point A takes tangent point A2, corresponding to Figure 3 (c), at this time AO4 = l A1A2 - l3;
[0083] The said intersection point A1 is only related to θ2, and the tangent point A2 is only related to θ1 and θ2. When θ2 remains unchanged, the possible positions of the tangent point A2 are a ring on the surface of sphere O2. The distance from each point on this ring to the intersection point A1 is the same. The tangent point A2 can be obtained by setting θ1 = 0, and then l can be obtained A1A2 .
[0084] S42. From Figure 1 、 Figure 2 It can be known that when the link angle θ2 of the anthropomorphic arm 2 joint is a constant, the spatial position of the origin o4 of the axis joint coordinate system is a circle with the link angle θ1 of the 1 joint as the only variable; the homogeneous transformation matrix is obtained through the forward kinematics in step S2
[0085]
[0086] Wherein, t 11 ~t 33 represent terms that can be ignored. Arbitrarily assign 3 different angular values to the link angle θ1 of the 1 joint, and substitute them into formula (2) respectively to obtain the spatial positions o 41 、o 42 、o 43 of the origin o4 of the 3 axis joint coordinate systems. The center o a of the circle of the spatial position of the origin o4 of the axis joint coordinate system and the radius r can be obtained by the three-point circle method;
[0087] Transform the coordinate origin of the base coordinate system o0 to the center o a and rotate it around the x-axis by to obtain a new coordinate system with the center o a as the origin. The homogeneous transformation matrix is The representation of the position of the origin of the 7 coordinate systems in the new coordinate system is:
[0088]
[0089] According to Figure 4 shown, given the center coordinates, radius, and position of the known circle o a , the position point o′7, and the connection length l4 with the circle o a , through geometric analysis in space, the positions p1 and p2 of the origin o4 of the axis joint coordinate system can be determined:
[0090]
[0091] Among them,
[0092] δ1 = atan2(o′ 7y , o′ 7x )
[0093]
[0094] Then, according to formula (2), substitute the positions p1 and p2 respectively to obtain the link angles θ 11 , θ 12 of the first joint:
[0095] θ 11 = acos(p 1x / (a3cθ2 - d3sθ2))
[0096] θ 12 = acos(p 2x / (α3cθ2 - d3sθ2)).
[0097] S5. Solve for the link angle θ3 of the third joint; specifically:
[0098] According to formula (1), the joint link angles that affect the origin position of the seventh coordinate system are θ1, θ2, θ3, and θ4. Substitute the constant joint link angle θ2 and the previously obtained variable joint link angles θ1 and θ4 to obtain the link angles θ 31 , θ 32 , θ 33 , θ 34 , corresponding to θ 11 , θ 41 , θ 11 , θ 42 , θ 12 , θ 41 and θ 12 , θ 42 . Thus, four sets of joint link angles are obtained.
[0099] S6. Solve for the link angles θ5, θ6, and θ7 of the three joints of the humanoid arm wrist, namely the fifth, sixth, and seventh joints; specifically:
[0100] According to formula (1), the joint link angles θ5, θ6, and θ7 do not affect the position of the origin of the 7 - coordinate system. It is only necessary to perform attitude calculation on θ5, θ6, and θ7. Denote the attitude of the 7 - coordinate system as R p :
[0101]
[0102] The rotation transformation of the joint link angles θ5, θ6, and θ7 is as follows:
[0103]
[0104] From forward kinematics, we can obtain:
[0105]
[0106] By transposing the above formula, we can get:
[0107]
[0108] Combining formula (5) and (7), we can obtain two sets of joint link angles:
[0109] θ 51 = atan2(r23, r13)
[0110]
[0111] θ 71 = atan2(r32, -r31) (8)
[0112] θ 52 = atan2(r23, r13)+π
[0113]
[0114] θ 72 = atan2(r32, -r31)+π (9)
[0115] So far, the 8 - group inverse solutions of the humanoid arm can be obtained:
[0116]
[0117] The object of the present invention is to provide an inverse solution method of geometric-algebra method for a seven-degree-of-freedom humanoid arm with shoulder joint offset, combining the geometric method and the algebraic method, aiming at the deficiencies of the existing technology. Based on the existing algebraic solution method, a set of geometric-algebra inverse solution methods for this special configuration of a seven-degree-of-freedom humanoid arm with shoulder joint offset is extended through the arm angles and the basic geometric structure relationships in space. This set of methods combines the geometric method and the algebraic method, and has the advantages of small computational amount, high efficiency, reliable calculation accuracy, and easy implementation method, thus supplementing the inverse solution method for the seven-degree-of-freedom manipulator with shoulder joint offset of this configuration.
Claims
1. A geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset, characterized in that Based on a seven-degree-of-freedom humanoid arm, the shoulder joint of the humanoid arm is offset, and the three axes of the wrist joint of the humanoid arm are orthogonal to one point; the origin position of the 0 coordinate system of the humanoid arm is the intersection point of the joint axes of the left and right arms 1. The inverse kinematic method of the humanoid arm includes the following steps: S1. Establish the DH coordinate system of the seven-degree-of-freedom humanoid arm and calibrate its DH parameters; S2. Solve the forward kinematics of the humanoid arm according to the DH parameters set in step S1; S3. According to the joint limits of the humanoid arm, preset the link angle θ2 of the 2nd joint of the humanoid arm as a constant within the value range to degrade the degrees of freedom; S4. Solve the link angle θ4 of the 4th joint of the shaft part and the link angle θ1 of the 1st joint by the geometric method; S5. Solve the link angle θ2 of the 3rd joint; S6. Solve the link angles θ5, θ6, and θ7 of the three joints of the humanoid arm wrist, namely the 5th joint, the 6th joint, and the 7th joint.
2. The geometric inverse solution method of a seven-degree-of-freedom humanoid arm with shoulder joint offset according to claim 1, characterized in that, in In step S1, specifically: Establish the DH coordinate system of the seven-degree-of-freedom humanoid arm and calibrate its DH parameters: α i-1 , a i-1 , θ i , d i , that is, the connecting rod rotation angle α i-1 , the connecting rod length a i-1 , the connecting rod angle θ i , the connecting rod offset d i ; Among them, the coordinate system \(i = 1\sim7\), \(\alpha\) i-1 represents the angle between \(z\) i-1 and \(z\) i-1 seen from the direction of \(x\), i \(a\) i-1 represents the distance between \(z\) i-1 and \(z\) i-1 along the direction of \(x\), i \(\theta\) i represents the angle between \(x\) i and \(x\) i-1 seen from the direction of \(z\), positive for clockwise and negative for counterclockwise, i \(d\) i represents the distance between \(x\) i and \(x\) i-1 along the direction of \(z\). i 3. The geometric inverse solution method of a seven-degree-of-freedom humanoid arm with a shoulder joint offset according to claim 2, characterized in that, in In step S2, specifically: Solve the forward kinematics of the robotic arm according to the DH parameters set in step S1, and the description of coordinate system i in coordinate system i-1 Where, c represents cos, and s represents sin, The homogeneous transformation matrix of forward kinematics is: Where, nx, ny, and nz are the components of the unit vector of the x-axis of the 7th coordinate system in the 0th coordinate system, sx, sy, and sz are the components of the unit vector of the y-axis of the 7th coordinate system in the 0th coordinate system, ax, ay, and az are the components of the unit vector of the z-axis of the 7th coordinate system in the 0th coordinate system, and px, py, and pz are the coordinates of the origin of the 7th coordinate system in the 0th coordinate system.
4. A geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset according to claim 1 or 2 or 3, characterized in that, in In step S3, if the link angle θ2 of the 2nd joint needs to move, first change the link angle θ2, and then perform steps S4 to S6 to solve the inverse kinematics.
5. A geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset according to claim 3, characterized in that, in In step S4, the specific steps are as follows: S41. The intersection points of the upper arm l3 of the humanoid arm and the rotation axis z1 of joint 1 are always on the same straight line and are always tangent to the sphere O2, which is centered at the origin o2 of the 2 - coordinate system with a radius of a2. According to the above geometric relationships, the intersection point A1 of the extension line of the upper arm l3 of the humanoid arm and the rotation axis z1 of joint 1 and the tangent point A2 with the sphere O2 are obtained. In triangle Ao4o5, two solutions θ 41 and θ 42 of the joint angle θ4 can be obtained through the cosine theorem; S42. When the link angle θ2 of the anthropomorphic arm 2 joint is a constant, the spatial position of the origin o4 of the axis joint coordinate system is a circle with the 1 joint angle θ1 as the only variable; obtain the homogeneous transformation matrix through the forward kinematics obtained in step S2 Among them, t11 to t33 represent terms that can be ignored. Arbitrarily take three different angular values and assign them to the first joint angle θ1, and substitute them into formula (2) respectively to obtain the spatial positions o 41 , o 42 , o 43 of the origin o4 of the shaft joint coordinate system. Through the three-point circle determination method, the center o a of the circle of the spatial position of the origin o4 of the shaft joint coordinate system and the radius r can be obtained; Transform the origin of the coordinate system of the base coordinate system o0 to the center of the circle o a And rotate it around the x-axis to obtain a new coordinate system with the center of the circle o a as the origin. The homogeneous transformation matrix is The representation of the position of the origin of the 7 coordinate system in the new coordinate system is: Known circle o a The center coordinates, radius, position point o', and the connection length l4 with circle o a Through geometric analysis in space, the positions p1 and p2 of the origin o4 of the axis joint coordinate system can be determined. Then, according to formula (2), substitute the positions p1 and p2 respectively to obtain the 1-joint angles θ 11 、θ 12 .
6. The geometric inverse solution method of a seven-degree-of-freedom humanoid arm with a shoulder joint offset according to claim 5, characterized in that, in In step S5, specifically: According to formula (1), the joint angles that affect the origin position of the 7 - coordinate system are θ1, θ2, θ3, θ4. Substituting the constant joint angle θ2 and the obtained variable joint angles θ1, θ4, we can get the 3 joint angles θ 31 , θ 32 , θ 33 , θ 34 , which respectively correspond to θ 11 , θ 41 , θ 11 , θ 42 , θ 12 , θ 41 and θ 12 , θ 42 . Thus, 4 groups of joint angles are obtained.
7. A geometric inverse solution method for a seven-degree-of-freedom humanoid arm with a shoulder joint offset according to claim 6, characterized in that, in In step S6, specifically: According to Equation (1), the joint angles θ5, θ6, and θ7 do not affect the position of the origin of the 7 - coordinate system. It is only necessary to perform attitude calculation on θ5, θ6, and θ7. Denote the attitude of the 7 - coordinate system as R p : The rotation transformation of the joint angles θ5, θ6, and θ7 is: From forward kinematics, we can get: By transposing the above formula, we can get: Combining formulas (5) and (7), we can get two sets of joint angles: So far, the 8 sets of inverse solutions of the humanoid arm can be obtained: 1: θ 11 , θ2, θ 31 , θ 41 , θ 51 , θ 61 , θ 71 2: θ 11 , θ2, θ 31 , θ 41 , θ 52 , θ 62 , θ 72 3: θ 11 , θ2, θ 32 , θ 42 , θ 51 , θ 61 , θ 71 4: θ 11 , θ2, θ 32 , θ 42 , θ 52 , θ 62 , θ 72 5: θ 12 , θ2, θ 33 , θ 41 , θ 51 , θ 61 , θ 71 6: θ 12 , θ2, θ 33 , θ 41 , θ 52 , θ 62 , θ 72 7: θ 12 , θ2, θ 34 , θ 42 , θ 51 , θ 61 , θ 71 8: θ 12 , θ2, θ 34 , θ 42 , θ 52 , θ 62 , θ 72 (10).