A search parameter angle-based full-joint bias redundant space robot arm inverse kinematics solving method

Abstract

The application relates to a search parameter angle-based inverse kinematics solving method for a full-joint-biased redundant space manipulator, and relates to the technical field of space robots. In view of the problem that a full-joint-biased redundant space manipulator cannot satisfy the Pieper criterion and cannot adopt a traditional arm-type angle parameterization method to solve inverse kinematics, an included angle between a shoulder-wrist vector and a shoulder-elbow vector is introduced as a search parameter angle, joint angle analytical solving logic of arm-type angle parameterization is constructed, and the solving of the search parameter angle is completed in combination with a parity pruning adaptive recursion algorithm, so that semi-analytical inverse kinematics calculation is realized. By introducing the search parameter angle as a redundant parameter and combining the semi-analytical solving strategy of the parity pruning adaptive recursion, the problem that the full-joint-biased redundant space manipulator cannot adopt the traditional arm-type angle parameterization method to solve inverse kinematics is solved, the solving efficiency, success rate and reliability are improved, and the application requirements of on-orbit tasks are met.

Description

Technical Field

[0001] This invention relates to the field of space robot technology, specifically a method for solving the inverse kinematics of a fully jointed offset redundant space manipulator based on search parameter angles. Background Technology

[0002] With the continuous development of space technology, the demand for on-orbit services is becoming increasingly urgent, making the development of reusable and maintainable space systems an inevitable trend. Redundant space robotic arms, as core equipment for on-orbit services, have been widely used in various on-orbit missions. The S2 dual-arm system designed by NASA's GITAI has completed on-orbit validation on the International Space Station. Its fully articulated offset redundant space robotic arm, compared to typical non-offset or partially offset robotic arms, offers a larger workspace, a smaller folding volume, and superior precision operation capabilities, enabling it to handle complex and varied on-orbit missions and diverse space environments with varying operational scales.

[0003] Inverse kinematics is a fundamental core problem in realizing motion planning and control of space robotic arms. For redundant space robotic arms, the parameterized inverse kinematics solution method for arm shape angle introduces the arm shape angle as a redundant parameter, which has a clear geometric meaning and can be effectively applied to the configuration control of robotic arms to achieve obstacle avoidance.

[0004] However, existing parametric inverse kinematics methods for arm angles are mostly designed for redundant manipulators that meet specific structural conditions, such as the unbiased SRS configuration or the partially biased traditional SSRMS configuration. For fully jointed biased redundant space manipulators, since their overall structure does not satisfy the Pieper criterion, analytical inverse kinematics solutions cannot be obtained. Furthermore, unlike the traditional SSRMS configuration, the three joints in the middle of the fully jointed biased redundant space manipulator are mutually perpendicular, meaning the long arm section has additional rotary joints. This makes the spatial projection relationship of the arm-arm angles more complex, making it impossible to pre-solve the elbow joint angles using traditional methods, significantly increasing the difficulty of solving the parametric inverse kinematics of the arm angles.

[0005] In summary, current inverse kinematics solutions for fully articulated biased redundant space manipulators do not incorporate analytical analysis of the manipulator configuration. Existing methods are all purely numerical, which typically suffer from sensitivity to initial conditions, low computational efficiency, and limited success rate and stability, making it difficult to meet the real-time, reliability, and configuration controllability requirements of on-orbit missions. Therefore, there is an urgent need to propose an efficient parametric inverse kinematics solution method for fully articulated biased redundant space manipulators to improve the efficiency and reliability of solving such manipulators in complex on-orbit missions. Summary of the Invention

[0006] To address the shortcomings of the existing technology, this invention provides a method for solving the inverse kinematics of a fully jointed offset redundant space manipulator based on search parameter angles. By introducing search parameter angles as redundant parameters and combining them with a semi-analytical solution strategy of odd-even pruning adaptive recursion, this method solves the problem that the inverse kinematics of a fully jointed offset redundant space manipulator cannot be solved using traditional arm angle parameterization methods. This improves the solution efficiency, success rate, and reliability, and meets the application requirements of on-orbit missions.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for solving the inverse kinematics of a fully jointed offset redundant space manipulator based on search parameter angles, comprising the following steps:

[0008] Step 1: Establish the kinematic model of the fully jointed offset redundant spatial manipulator;

[0009] The MDH parameter method was used to perform kinematic modeling on a 7-DOF fully articulated offset redundant space manipulator, defining the link sequence. The coordinate system corresponding to the link and MDH parameters, coordinate system The x, y, and z axes are denoted as follows: , , MDH parameters include link offset. and joint angle and the length of the connecting rod and connecting rod torsion angle Calculate the homogeneous transformation matrix between the coordinate systems of adjacent links. Construct the forward kinematic equations of the robotic arm , , and Coordinate systems Relative to the reference coordinate system The homogeneous transformation matrix, rotation matrix, and position vector;

[0010] Step 2: Define the redundant parameter arm angle and the search parameter angle;

[0011] Select the axis of joint 1. and joint 2 axis The intersection point is Points, joints, and three axes and joint 4 axis The intersection is Points, joints, and axes and joint 7 axis The intersection point is Point, pass The arm plane is defined by three points, based on the shoulder-wrist vector. Shoulder-elbow vector and elbow-wrist vector Define arm angle shoulder-wrist vector Shoulder-elbow vector The included angle is used as the search parameter angle. The search parameter angle is determined by constraining it using the law of cosines. The valid range of values;

[0012] Step 3: Derive the parametric analytical solution of the joint angle by introducing the search parameter angle for the arm-shaped angle;

[0013] Preset search parameter angle Analytical solution of joint angles based on the equivalent relationship of elbow-wrist vector magnitudes Based on coordinate system The elbow-wrist geometric relationship is obtained by solving the problem. Analytical solution of joint angles for known quantities and Based on coordinate system The shoulder-elbow geometric relationship is obtained by solving for it. to Analytical solution of joint angles for known quantities and The search error value is determined based on the constraint relationship of the shoulder-elbow vector, and then the obtained solution is used. to Analytical solution of joint angles for known quantities and This yields eight sets of joint angle solutions corresponding to the end pose;

[0014] Step 4: Solve for the search parameter angle using the odd-even pruning adaptive recursive inverse kinematics algorithm;

[0015] The search parameter angle is solved using an adaptive recursive inverse kinematics algorithm with parity pruning, given the desired pose. Arm-shaped angle Based on the valid intervals determined in step two, and the search configuration parameters, the intervals are recursively traversed with a caching mechanism. The unsolvable intervals are pruned by combining the characteristic that the solvable intervals of the odd and even channels are the same. The roots of the solvable intervals are obtained by numerical methods. Finally, the joint angles are obtained by analytical solution in step three, and the inverse kinematics solution is completed.

[0016] Furthermore, in step two, the search parameter angle The valid range of values ​​is:

[0017]

[0018] In the formula, These are the link offsets of the corresponding links of the robotic arm.

[0019] Furthermore, in step three, the joint angle The solution expression is:

[0020]

[0021] In the formula, Preset search parameters angle The corresponding elbow-wrist vector, These are the link offsets of the corresponding links of the robotic arm.

[0022] Furthermore, in step three, the joint angle and The solution method is as follows: take ,make ,in and Each refers to and Solving for , .

[0023] Furthermore, in step three, the joint angle and The solution method is as follows: take First, solve for... Then solve for the result. ,in These are the link offsets of the corresponding links of the robotic arm.

[0024] Furthermore, in step three, the search error value is determined based on the equation... The (3,3) element of the matrix on the right-hand side of the equation is taken as the error value, expressed as: .

[0025] Furthermore, in step four, the specific method of odd-even pruning is as follows: only the unsolvable flag of odd channels is judged. If the left endpoint and midpoint of the interval of all odd channels are unsolvable, the maximum allowable recursion depth of the left segment of the interval is adjusted to the maximum recursion depth of the unsolvable interval; if the midpoint and right endpoint of the interval of all odd channels are unsolvable, the maximum allowable recursion depth of the right segment of the interval is adjusted to the maximum recursion depth of the unsolvable interval.

[0026] Furthermore, in step four, the interval recursive traversal with caching mechanism specifically involves: constructing a cache mapping to retain 12 significant digits. The value serves as the key, and the array consisting of the error values ​​corresponding to the 8 channels and the unsolved flag serves as the value. The cache is called or updated via the ProbeCache function. If the passed-in... If the value is not cached, then perform step three to analyze and solve for the corresponding error value and the no-solution flag. If the value is already cached, then directly read the cached result.

[0027] Furthermore, in step one, the MDH parameters of the fully articulated biased redundant space robot are as follows:

[0028] Link 1: Link torsion angle 0°, link length 0m, link offset 0.31m;

[0029] Link 2: Link torsion angle -90°, link length 0m, link offset 0.2225m;

[0030] Link 3: Link twist angle 90°, link length 0m, link offset 2.071m;

[0031] Link 4: Link torsion angle -90°, link length 0m, link offset 0.2225m;

[0032] Link 5: Link twist angle 90°, link length 0m, link offset 2.071m;

[0033] Link 6: Link torsion angle -90°, link length 0m, link offset 0.2225m;

[0034] Link 7: Link torsion angle 90°, link length 0m, link offset 0.31m.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] 1. The present invention proposes a new inverse kinematics solution scheme for a fully jointed offset redundant space robot arm. By introducing a search parameter angle as a redundant parameter, and based on the vector relationship of different reference coordinate systems, it solves the problem that the arm angle parameterized inverse kinematics solution method cannot be introduced for this special configuration. When performing tasks, the arm angle can be effectively adjusted to achieve obstacle avoidance operation.

[0037] 2. The method of this invention adopts a semi-analytical inverse kinematics solution strategy of odd-even pruning adaptive recursion. By limiting the range of search parameter angle values ​​through geometric relationships, it eliminates the need for initial iteration values. Different iteration depths are set for the solvable interval and the suspected unsolvable interval during the error iteration process, which reduces a large number of analytical solutions compared to traversal algorithms. At the same time, the feature that the solvable intervals of odd and even channels are the same is introduced into the unsolvable judgment process, reducing the judgment logic of each channel by half. Compared with existing pure numerical iteration methods, it has higher computational efficiency and solution success rate, and can effectively ensure the real-time performance and reliability of inverse kinematics solution for this type of robot arm in complex on-orbit tasks. Attached Figure Description

[0038] Figure 1This is a schematic diagram of the MDH coordinate system for a fully articulated offset redundant space robot arm;

[0039] Figure 2 This is a schematic diagram of the arm-shaped angle and the search parameter angle in this invention;

[0040] Figure 3 This is a flowchart of the odd-even pruning adaptive recursive inverse kinematics algorithm in this invention. Detailed Implementation

[0041] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0042] like Figures 1-3 As shown, a method for solving the inverse kinematics of a fully jointed biased redundant space manipulator based on search parameter angles includes the following steps:

[0043] Step 1: Establish the kinematic model of the fully jointed offset redundant spatial manipulator;

[0044] The fully articulated offset redundant space robot arm is a 7-DOF robot arm, and its MDH coordinate system is combined with... Figure 1 As shown, the MDH parameter method is used to perform kinematic modeling of the robotic arm.

[0045] definition Link number, , Link The corresponding coordinate system coordinate system x-axis, coordinate system The y-axis, coordinate system The z-axis defines the link offset. and joint angle respectively along Shaft from Move to The distance and angle define the link length. and connecting rod torsion angle respectively along Shaft from Move to The distance and angle, where the MDH parameters of the fully articulated offset redundant space manipulator are shown in the table below:

[0046]

[0047] adjacent link coordinate system of robotic arm and Homogeneous transformation matrix between Calculated by the following formula:

[0048]

[0049] The forward kinematics equation of the robotic arm is expressed as:

[0050]

[0051] In the formula, , and Coordinate systems Relative to the reference coordinate system The homogeneous transformation matrix, rotation matrix, and position vector.

[0052] Step 2: Define the redundant parameter arm angle and the search parameter angle;

[0053] S2.1 Definition of arm angle:

[0054] Geometric definition of arm angle combined Figure 2 As shown, select the axis of joint 1. and joint 2 axis The intersection point is Points, joints, and three axes and joint 4 axis The intersection is Points, joints, and axes and joint 7 axis The intersection point is Point, pass Define the arm plane using three points, then:

[0055] Shoulder-wrist vector Represented as ;

[0056] Shoulder-elbow vector Represented as ;

[0057] Elbow-wrist vector Represented as .

[0058] Definition point For point In vector The projection point on the vector is then the vector Represented as:

[0059]

[0060] In the formula, For vectors unit vector, It is an antisymmetric matrix operator.

[0061] Passing point Construct a vector perpendicular to the axis of joint 1. The unit vector is used as the reference vector. , represented as:

[0062]

[0063] In the formula, is the unit vector of the axis of joint 1.

[0064] unit vector and reference vector As a base plane, a reference plane is defined, passing through the point... Construct the unit normal vectors for the reference plane and the arm plane respectively. and ,in For vectors The unit vector, referring to the reference vector. unit vector As the rotation angle of the pivot The rotation matrix for the first part can be solved using the Rodriguez formula as follows:

[0065]

[0066] Define vector with vector The included angle or vector sum vector The included angle is an arm-shaped angle, that is... .

[0067] S2.2, Definition of search parameter angle:

[0068] To address the issues of fully articulated offset redundant space robotic arms failing to satisfy the Pieper criterion and lacking analytical inverse kinematics solutions, a semi-analytical inverse kinematics solution method based on one-dimensional search is proposed, combining... Figure 2 As shown, the vector sum vector The included angle As the search parameter angle, the vector It can be represented as ,vector It can be represented as .

[0069] Search parameters Its own search scope is Using the Law of Cosines The range of values ​​for is constrained, as shown below:

[0070]

[0071] From geometric relations, we can obtain , , The target pose is determined at that time, therefore The range of values ​​for is further restricted to:

[0072]

[0073] Step 3: Derive the parametric analytical solution of the joint angle by introducing the search parameter angle for the arm-shaped angle;

[0074] Preset search parameter angle Based on the vector relationships between different reference coordinate systems, the inverse kinematics is solved analytically. The specific process is as follows:

[0075] S3.1, Joint angle Solving for:

[0076] because Vectors The modulus should be related to the vector represented by the joint angle. The modulus lengths are equal, that is... Therefore, there is Solving for the given information yields the following results. .

[0077] S3.2, Joint angle and Solving for:

[0078] In coordinate system Based on the elbow-wrist geometry, the following relationship can be derived:

[0079]

[0080] Pick The above formula can be expressed as:

[0081]

[0082] In the formula and Each refers to and .

[0083] By simplifying the system of equations, we can obtain:

[0084]

[0085] make Solving the system of equations yields:

[0086]

[0087] Ultimately, for each The solutions can be obtained separately. and Two sets of solutions, , .

[0088] S3.3, Joint angle and Solving for:

[0089] In coordinate system Based on the shoulder-elbow geometry, the following relationship can be derived:

[0090]

[0091] because , and It is known, therefore Given a known quantity, take Then the above formula can be expressed as:

[0092]

[0093] For each group , and Two solutions can be obtained. By simplifying the system of equations, we can obtain:

[0094]

[0095] Solving the system of equations yields:

[0096]

[0097] For each group , , and achievable .

[0098] S3.4 Determination of search error:

[0099] Given search parameter angle The shoulder-elbow vector can be determined directly. And vector This should be... and Therefore, given This actually implies a and Constraints. End-effector attitude. The association with the remaining joint angles introduces additional nonlinear coupling. Therefore, errors exist. Expanding the left side of the equation yields Since its (3,3) element is 0, the (3,3) element corresponding to the matrix on the right side of the equation is taken as the error value and expressed as: .

[0100] S3.5, joint angle and Solving for:

[0101] based on The left side of the equation is expanded to obtain Similarly, the following system of equations can be derived:

[0102]

[0103] Finally, an analytical solution can be obtained. , .

[0104] Through the above solution process, given the desired end pose, arm angle, and root search of the search parameter angles, the solutions for the eight joint angles corresponding to the end pose can be calculated.

[0105] Step 4: Solve for the search parameter angle using the odd-even pruning adaptive recursive inverse kinematics algorithm;

[0106] For search parameter angles where the solvable interval constitutes a small proportion of the effective interval, or even some solvable intervals are extremely narrow, and the error function cannot be directly listed analytically, numerical methods must be used in conjunction with... Figure 3 As shown, an adaptive recursive inverse kinematics algorithm with odd-even pruning is used to implement variable step-size traversal, in order to balance the availability of solutions in narrow intervals with solution efficiency. The specific algorithm flow is as follows:

[0107] STEP1: Input the desired pose Arm-shaped angle And search configuration parameters, including convergence tolerance. Maximum recursion depth Maximum recursion depth of unsolvable intervals and the number of function calls to solve for the maximum error ;

[0108] STEP 2: Based on the derivation in step two, calculate the search parameter angle. effective range .

[0109] STEP3: Initialize the cache mapping, assigning each search parameter angle Corresponding error value The value is cached, and the cache container uses 12 significant digits. The value is used as the key, and the value corresponding to the key is one of the 8 channels in that key. Error value under value and the unsolvable flag The array is composed of elements, where the unsolvable flag is... It is a Boolean value. This indicates that the channel is currently... There is no solution for the value. This indicates that a solution exists;

[0110] STEP4: and These will serve as the initial left and right endpoints, respectively. and The ProbeCache function is used to calculate the error values ​​and no-solution flags corresponding to the left and right endpoints, respectively. The ProbeCache function is a function that inserts or calls key-value pairs in the cache container. If the passed-in... If the value is not cached, then perform step three to solve the analytical inverse kinematics to obtain the corresponding error value and no-solution flag. If the value already exists in the cache, retrieve the cached result directly.

[0111] STEP 5: [The sentence is incomplete and requires more context to be translated.] left and right interval endpoints and and the corresponding error value and Unsolvable flag and and the current iteration depth of that interval. (Initially 0) and maximum allowable depth (Initially) Encapsulate the data as a stack node and push it onto the stack to initialize the search stack;

[0112] STEP 6: Enter the while loop that checks if the stack is empty. If the stack is empty, exit the loop. If the stack is not empty, pop the last element pushed onto the stack node, and simultaneously check if the cache length has reached the maximum error calculation function call count. If so, the interval will not be refined further; the current endpoint information will be used for coarse judgment and recorded to ensure the upper limit of the algorithm's time consumption. Otherwise, the subsequent steps will be executed.

[0113] STEP 7: Find the midpoint of the input interval The midpoint is solved using the ProbeCache function. Corresponding error value With no solution flag Considering the characteristic that the solvable intervals of odd and even channels are the same, the unsolvable intervals are shared to improve the solution efficiency. The algorithm's time consumption mainly lies in finding the solvable intervals. Therefore, the following efficient method for judging unsolvable intervals is designed to allocate less computational resources to unsolvable intervals. Specifically, only the unsolvable indicator of odd channels is judged: if the left endpoint of all odd channels is... and midpoint There is no solution. and If the left interval is considered to have no solution, then the maximum allowable depth of the left interval is set. From the maximum recursion depth Adjusted to the maximum recursion depth of the unsolvable interval If the midpoint of all odd-numbered channels and right endpoint There is no solution. and If the right interval is considered to have no solution, then the maximum allowable depth of the right interval is set. From the maximum recursion depth Adjusted to the maximum recursion depth of the unsolvable interval ;

[0114] STEP8: Determine the current iteration depth of the interval Has the maximum allowable depth been reached? If so, try to find the root using the interval endpoints and midpoint. The root-finding function FindRoot uses the Brent method. If a solution is found, store it in a tuple. And continue the while loop; if the maximum allowed depth has not been reached... Then the endpoints and midpoint of the current interval will be... , and and the corresponding error value , and Unsolvable flag , and Iteration depth and the maximum allowable depth of the left and right intervals and Each node is encapsulated as a stack node, and the while loop continues after the node is pushed onto the stack.

[0115] STEP 9: During the root-finding process, simultaneously determine the unsolvable intervals of adjacent endpoints of the odd-numbered channels corresponding to each channel, and remove those with the maximum allowable depth. The solution is found in the intervals with no solution at both ends, and the root is found only when the signs of the adjacent two endpoints are opposite, to ensure the effectiveness of the root finding.

[0116] STEP 10: End the while loop and perform post-processing, removing duplicates and merging the solved approximate duplicate terms. The criteria for determining duplicate terms are two. The difference in values ​​is less than the convergence tolerance. ;

[0117] STEP 11: Solve the results for each channel The value is then used to perform the analytical inverse kinematics solution in step three to obtain the joint angle. ~ Complete the inverse kinematics solution.

[0118] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0119] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles, characterized in that: Includes the following steps: Step 1: Establish the kinematic model of the fully jointed offset redundant spatial manipulator; The MDH parameter method was used to perform kinematic modeling on a 7-DOF fully articulated offset redundant space manipulator, defining the link sequence. The coordinate system corresponding to the link and MDH parameters, coordinate system The x, y, and z axes are denoted as follows: , , MDH parameters include link offset. and joint angle and the length of the connecting rod and connecting rod torsion angle Calculate the homogeneous transformation matrix between the coordinate systems of adjacent links. Construct the forward kinematic equations of the robotic arm , , and Coordinate systems Relative to the reference coordinate system The homogeneous transformation matrix, rotation matrix, and position vector; Step 2: Define the redundant parameter arm angle and the search parameter angle; Select the axis of joint 1. and joint 2 axis The intersection point is Points, joints, and three axes and joint 4 axis The intersection is Points, joints, and axes and joint 7 axis The intersection point is Point, pass The arm plane is defined by three points, based on the shoulder-wrist vector. Shoulder-elbow vector and elbow-wrist vector Define arm angle shoulder-wrist vector Shoulder-elbow vector The included angle is used as the search parameter angle. The search parameter angle is determined by constraining it using the law of cosines. The valid range of values; Step 3: Derive the parametric analytical solution of the joint angle by introducing the search parameter angle for the arm-shaped angle; Preset search parameter angle Analytical solution of joint angles based on the equivalent relationship of elbow-wrist vector magnitudes Based on coordinate system The elbow-wrist geometric relationship is obtained by solving the problem. Analytical solution of joint angles for known quantities and Based on coordinate system The shoulder-elbow geometric relationship is obtained by solving for it. to Analytical solution of joint angles for known quantities and The search error value is determined based on the constraint relationship of the shoulder-elbow vector, and then the obtained solution is used. to Analytical solution of joint angles for known quantities and This yields eight sets of joint angle solutions corresponding to the end pose; Step 4: Solve for the search parameter angle using the odd-even pruning adaptive recursive inverse kinematics algorithm; The search parameter angle is solved using an adaptive recursive inverse kinematics algorithm with parity pruning, given the desired pose. Arm-shaped angle Based on the valid intervals determined in step two, and the search configuration parameters, the intervals are recursively traversed with a caching mechanism. The unsolvable intervals are pruned by combining the characteristic that the solvable intervals of the odd and even channels are the same. The roots of the solvable intervals are obtained by numerical methods. Finally, the joint angles are obtained by analytical solution in step three, and the inverse kinematics solution is completed.

2. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 1, characterized in that: In step two, the search parameter angle The valid range of values ​​is: In the formula, These are the link offsets of the corresponding links of the robotic arm.

3. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 1, characterized in that: In step three, the joint angle The solution expression is: In the formula, Preset search parameters angle The corresponding elbow-wrist vector, These are the link offsets of the corresponding links of the robotic arm.

4. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 3, characterized in that: In step three, the joint angle and The solution method is as follows: take ,make ,in and Each refers to and Solving for , .

5. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 4, characterized in that: In step three, the joint angle and The solution method is as follows: take First, solve for... Then solve for the result. ,in These are the link offsets of the corresponding links of the robotic arm.

6. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 5, characterized in that: In step three, the search error value is determined based on the equation. The (3,3) element of the matrix on the right-hand side of the equation is taken as the error value, expressed as: .

7. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 1, characterized in that: In step four, the specific method of odd-even pruning is as follows: only the unsolvable flag of odd channels is judged. If the left endpoint and midpoint of the interval of all odd channels are unsolvable, the maximum allowable recursion depth of the left segment of the interval is adjusted to the maximum recursion depth of the unsolvable interval. If the midpoint and right endpoint of the interval of all odd channels are unsolvable, the maximum allowable recursion depth of the right segment of the interval is adjusted to the maximum recursion depth of the unsolvable interval.

8. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 7, characterized in that: In step four, the interval recursive traversal with caching mechanism specifically involves: constructing a cache mapping to retain 12 significant digits. The value serves as the key, and the array consisting of the error values ​​corresponding to the 8 channels and the unsolvable flag serves as the value. The cache is called or updated via the ProbeCache function. If the passed-in... If the value is not cached, then perform step three to analyze and solve for the corresponding error value and the no-solution flag. If the value is already cached, then directly read the cached result.

9. The method for solving the inverse kinematics of a fully jointed offset redundant spatial manipulator based on search parameter angles according to claim 1, characterized in that: In step one, the MDH parameters of the fully articulated biased redundant space robot are as follows: Link 1: Link torsion angle 0°, link length 0m, link offset 0.31m; Link 2: Link torsion angle -90°, link length 0m, link offset 0.2225m; Link 3: Link twist angle 90°, link length 0m, link offset 2.071m; Link 4: Link torsion angle -90°, link length 0m, link offset 0.2225m; Link 5: Link twist angle 90°, link length 0m, link offset 2.071m; Link 6: Link torsion angle -90°, link length 0m, link offset 0.2225m; Link 7: Link torsion angle 90°, link length 0m, link offset 0.31m.

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