A method for solving inverse kinematics of a serpentine redundant robotic arm

Abstract

This invention discloses an inverse kinematics solution method for a serpentine redundant robotic arm, comprising: setting m target points of the end joints of the robotic arm according to the target to be detected; constructing an objective function with the condition of minimizing the offset of each joint relative to the Y-axis; the objective function being a1 to a... n‑1 The weighted sum of squares of the offsets relative to the Y-axis, and a n‑1 The weights of a1 and a1 increase sequentially. The objective function is constrained by the physical rotation limits of each joint, the length of each link, the initial joint always moving along the Y-axis, the end joint reaching the target point in a set posture, and the motion smoothness index. A constrained nonlinear optimization problem-solving algorithm is used to find the coordinates of each joint when the objective function is minimized. This invention fully utilizes the redundant degrees of freedom of the snake-like robotic arm, achieving automatic optimization of the robotic arm's configuration given the target point of the end joint.

Description

Technical Field

[0001] This invention relates to the field of inverse kinematics solving for redundant robotic arms, and more particularly to a method for solving the inverse kinematics of a serpentine redundant robotic arm. Background Technology

[0002] When a serpentine redundant robotic arm approaches a target, it uses actuators at its end effector, such as industrial cameras or high-pressure water nozzles, to maintain and inspect the target. To perform multi-directional and multi-angle maintenance and observation of the target, several joints near the end effector need to work together to maintain a certain posture as the arm moves near the target. This problem of determining the joint space of the robotic arm given its end effector path is an inverse kinematics problem. Considering the finite length of the serpentine redundant robotic arm and its need to pass through the arm's compartment door during operation, achieving an optimal configuration under various constraints can fully utilize the redundant degrees of freedom of the serpentine robotic arm, allowing it to reach its maximum operating range within the constraints. Currently, common methods for solving the inverse kinematics of serpentine redundant robotic arms include inverse kinematics methods based on the pseudo-inverse of the Jacobian matrix and heuristic inverse kinematics methods. Since the inverse kinematics problem of a serpentine redundant robot arm has no unique solution, inverse kinematics solutions based on the pseudo-inverse of the Jacobian matrix cannot achieve the optimal configuration of the robot arm. Currently common heuristic inverse kinematics algorithms calculate a new configuration based on the previous configuration, with joints moving sequentially. Joints that have already moved cannot return to their zero position in subsequent movements; that is, the links will only continuously lift, failing to automatically optimize the configuration based on a given path. In this situation, the robot arm may not be able to reach its intended target position. Therefore, a method for solving the inverse kinematics of a serpentine redundant robot arm is needed, enabling the robot arm to achieve its optimal configuration under various constraints, thereby fully utilizing the redundant degrees of freedom of the serpentine robot arm. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes an inverse kinematics solution method for serpentine redundant robotic arms.

[0004] The specific technical solution is as follows:

[0005] A method for solving the inverse kinematics of a serpentine redundant robotic arm includes the following steps:

[0006] S1: Set the target points of the end effector joints of the robotic arm according to the target to be detected. There are m target points. The robotic arm includes a base, n links, and n joints. Adjacent links are connected by joints. a1 is the initial joint of the robotic arm, connecting the base and link 1. n For the distal joint, a n+1 For end effector; a i Let G be the i-th joint, i = 1, 2, ..., n; jLet j be the j-th target point, j = 1, 2, ..., m; the robotic arm is initially positioned along the Y-axis of the base coordinate system;

[0007] S2: Construct an objective function based on minimizing the offset of each joint relative to the Y-axis. The objective function is from a1 to a... n-1 The weighted sum of squares of the offsets relative to the Y-axis, and a n-1 The weights of a1 increase sequentially.

[0008] S3: Based on the physical rotation limits of each joint of the robotic arm, the length of each link, the initial joint always moving along the Y-axis, and the end joint reaching the target point G in a set posture. j Motion smoothness index is used as a constraint on the objective function;

[0009] S4: Use a constrained nonlinear optimization problem-solving algorithm to find the coordinates of each joint when the objective function is minimized.

[0010] Furthermore, the expression for the objective function is:

[0011]

[0012] In the formula, Let X be the X coordinate of the i-th joint. Let be the Z-coordinate of the i-th joint. It represents the square of the vertical distance from the i-th joint to the horizontal slide rail.

[0013] Furthermore, the physical rotation limit constraint expressions for each joint of the robotic arm in the constraints of the objective function are as follows:

[0014] q i ≤q max i = 1, ..., n

[0015]

[0016] In the formula, q i Let q represent the rotation angle of the i-th joint. max This indicates the physical rotation limit of the joint.

[0017] Furthermore, the expressions for the length constraints of each link of the robotic arm in the constraints of the objective function are as follows:

[0018] |a i -a i+1 |=L i i = 1, ..., n

[0019] In the formula, L i This represents the length of the i-th link.

[0020] Furthermore, the expression for the initial joint motion constraint in the objective function is as follows:

[0021]

[0022] In the formula, Let X be the initial X-coordinate of the joint. The initial Z-coordinate of the joint.

[0023] Furthermore, the expression for the end-joint attitude constraint in the objective function is as follows:

[0024] a n =G j

[0025] a n+1 =a n +k j ·L n

[0026] In the formula, k j This indicates that the distal joint has reached the target point G. j The direction vector of the end link, L n This represents the length of the nth link.

[0027] Furthermore, the expression for the motion smoothness constraint in the objective function is as follows:

[0028]

[0029] In the formula, a represents the sum of motion of the remaining n-1 joints of the robotic arm, excluding the end joint. i This indicates that the distal joint is located at the target point G. j The i-th joint point at time a i ′ indicates that the distal joint is located at the target point G. j-1 The i-th joint point at time.

[0030] Furthermore, in S4, the algorithm for solving the constrained nonlinear optimization problem is the sequential quadratic programming method.

[0031] The beneficial effects of this invention are:

[0032] The proposed inverse kinematics algorithm uses minimizing joint deviation as the optimization objective, while also considering factors such as joint limits, motion smoothness, and end-effector pose. By setting a motion smoothness index, the optimization objective is transformed into constraints, achieving collaborative optimization for multiple objectives. This invention features high computational efficiency and strong versatility. The robotic arm configuration obtained using the inverse kinematics algorithm of this invention is superior to that obtained by conventional inverse kinematics algorithms. In practical applications, the objective function and constraints can be configured according to requirements, and the optimal inverse kinematics solution under multiple objectives and constraints can be obtained using this invention. This invention can serve as a general method for solving the inverse kinematics problem of ultra-redundant robotic arms. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the macroscopic geometric features and path target points of the snake-shaped robotic arm in an embodiment of the present invention.

[0034] Figure 2 This is a schematic diagram of the configuration of the snake-shaped robotic arm in an embodiment of the present invention, which performs "end-effector translation" near the target while keeping the end-effector horizontal.

[0035] Figure 3 This is a schematic diagram of the configuration of the snake-shaped robotic arm under different adjacent solution steps in an embodiment of the present invention.

[0036] Figure 4 This is a schematic diagram of the configuration of the snake-shaped robotic arm in an embodiment of the present invention, where all links except the end link are located in a straight line.

[0037] Figure 5 This is a schematic diagram of the joint rotation angle of the snake-shaped robotic arm in an embodiment of the present invention.

[0038] Figure 6 This is a schematic diagram of the snake-shaped robotic arm configuration when the wrist joint is located at different target points in an embodiment of the present invention.

[0039] Figure 7 This is a schematic diagram of the configuration of the snake-shaped robotic arm wrist joint in an embodiment of the present invention, which begins to observe the target from multiple angles after reaching the target point. Detailed Implementation

[0040] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0041] For a multi-joint serpentine redundant robotic arm where adjacent links are connected by universal joints, to describe the inverse kinematics problem and simplify the robotic arm configuration, the universal joint connecting the two links is considered as a point, called a joint. The link is then simplified to a line segment, and the entire serpentine robotic arm can be simplified to a broken line segment. For example... Figure 1 As shown, assume the snake-like robotic arm has n links and n joints, i.e., a1 to a2 in the diagram. n+1 This describes the macroscopic geometric features of the snake-like robotic arm, where a1 is the initial joint of the robotic arm, connecting the base and link 1; joint a2 connects link 1 and link 2, and so on. n The end joint of a robotic arm, also known as the wrist joint, a n+1 For the end effector of a robotic arm, a i Let i be the i-th joint, where i = 1, 2, ..., n.

[0042] The inverse kinematics problem of a snake-like robotic arm can be described as the following process: the snake-like robotic arm in its initial state (i.e., Figure 1 In the state shown, all joints are at zero position, and the links remain horizontal. During operation, the robotic arm moves gradually from the end joint to the initial joint, and each link of the robotic arm gradually lifts. As the robotic arm gradually delves deeper into the work area, once all links have left their initial positions, the robotic arm will reach its limit of motion, and the end joints will be unable to reach any further. The inverse kinematics problem is the process of solving the problem from the robotic arm's task space to its joint space. The pose of the robotic arm in the task space is the wrist joint 'a'. n Position and end link (can be denoted as a) n -a n+1 After the wrist joint reaches the target position, the end effector adjusts its attitude by using several joints near the end effector to observe the target from multiple angles. The target path of the serpentine robotic arm's wrist joint in the task space is described by multiple discrete points. Assuming the target path consists of a total of m target points, the entire inverse kinematics solution process is divided into m steps. In the j-th step (j = 1, 2, ..., m) of the inverse kinematics solution, the end effector of the robotic arm reaches the j-th target point G in a specified attitude. j And among them, wrist joint a n Location and target point G j The positions coincide. Therefore, in each step of the inverse kinematics solution process, the wrist joint a n With actuator a n+1 The positions are all determined, and then a1 to a2 are solved with the specified optimization objective. n-1 Position in the base coordinate system.

[0043] Based on the operational requirements of a serpentine inspection robotic arm cleaning and inspecting cutting tools inside a tunnel boring machine (TBM), and considering the limited space within the TBM's sealed chamber and the robotic arm's inherent angular limits, this invention focuses on solving inverse kinematics problems by specifying the wrist joint position and end-effector posture under multiple constraints to determine the robotic arm's joint spatial parameters. For example... Figure 2 As shown, the operator controls the snake-like robotic arm to perform "end-effector translation" near the target while keeping the end-effector horizontal. Unlike the snake-following path planning method, the inverse kinematics of the snake-like robotic arm only provides the pose of the end-effector joints. The paths of the remaining joints of the robotic arm are generated by the inverse kinematics algorithm. The inverse kinematics problem of the redundant snake-like robotic arm has no unique solution. Therefore, how to make full use of the redundant degrees of freedom of the snake-like robotic arm is the key issue of this invention.

[0044] Based on the above architecture, this invention proposes an inverse kinematics solution method for a serpentine redundant robotic arm. This method considers factors such as the quality of the robotic arm configuration, solution efficiency, motion smoothness, joint rotation limits, and posture accuracy. Specifically, it includes the following steps:

[0045] S1: Set m target points for the end joint of the robotic arm according to the target to be detected; the robotic arm is initially arranged along the Y-axis of the base coordinate system.

[0046] S2: Construct an objective function based on minimizing the offset of each joint relative to the Y-axis. The objective function is from a1 to a... n-1 The weighted sum of squares of the offsets relative to the Y-axis, and a n-1 The weights of a1 increase sequentially.

[0047] Specifically, since the configuration of the serpentine robotic arm is determined by the positions of its joints, these joints are treated as system variables in the optimization problem modeling. The inverse kinematics solution is performed with the principle of minimizing the number of joints involved in the motion. In the algorithm implementation, this principle can be transformed into minimizing the deviation of each joint from the horizontal linear guide rail, thus modeling the optimization problem. Since the initial joint a1 must be on the Y-axis, and the wrist joint a... n The position is given and equal to the target point G. j Therefore, excluding the initial joint point a1 and the wrist joint a n The sum of the vertical distances from all other joints to the Y-axis can be used to describe the extent to which the robotic arm as a whole has moved away from its initial position.

[0048] like Figure 3 As shown, the deviation of each joint of the snake-like robotic arm from the horizontal linear guide rail is the vertical distance from each joint to the Y-axis. The sum of the squares of the vertical distances from all joints except the wrist joint to the Y-axis is used as the objective function, as expressed below:

[0049]

[0050] In the formula, Let X be the X coordinate of the i-th joint. Let be the Z-coordinate of the i-th joint. It represents the square of the vertical distance from the i-th joint to the horizontal slide rail.

[0051] Considering that during the movement of the snake-like robotic arm, the joints near the wrist joint are usually farther from the Y-axis than the joints near the initial joint, if the sum of the vertical distances of each joint point to the Y-axis is directly used as the objective function, the deviation of the initial few joints will only have a small impact on the objective function, which will lead to the optimization result being biased towards the joints near the wrist joint, failing to meet the optimization objective of minimizing the number of joints in the robotic arm's movement. Therefore, it is necessary to gradually increase the weight coefficients in the objective function in the order from the wrist joint to the initial joint, increasing the impact of the deviation of the joints near the base on the objective function.

[0052] For ease of calculation, the snake-like robotic arm is positioned as follows: Figure 4 In the shown posture, the weighting coefficients for each joint offset are set so that the offset from joint 2 to joint n-1 has the same impact on the objective function. Then, according to the principle of similar triangles, we can obtain:

[0053]

[0054] In the formula, l2 represents the vertical distance from joint point a2 to the Y-axis, and so on. i This represents the vertical distance from joint point i to the y-axis.

[0055] Therefore, we get:

[0056]

[0057] Therefore, we can see that multiplying the distance from the i-th joint to the Y-axis by a coefficient... Then the distance from the i-th joint to the Y-axis can be converted into joint a. n-1 Distance to the Y-axis.

[0058] This allows us to obtain the vertical distance l from the i-th joint to the Y-axis. i The expression is as follows:

[0059]

[0060] The perpendicular distance from the (n-1)th joint to the Y-axis is used as the metric, and the perpendicular distances of the remaining joints to the Y-axis are multiplied by a coefficient. The effect of the vertical distance from the remaining joints to the Y-axis on the objective function will be the same as that of the (n-1)th joint. The optimized objective function expression with weight coefficients is as follows:

[0061]

[0062] S3: When performing inverse kinematics solutions on a serpentine robotic arm mounted on a horizontal linear slide, the following conditions must be met: ensuring smooth motion in two consecutive solution steps while minimizing the number of joints involved; all joint angles must be within their limits; the lengths of all links must be fixed; the initial joints must always move along the Y-axis; and the robotic arm's wrist joint must reach the target point in a specified posture. Therefore, the constraints of the objective function are constructed based on the above conditions, as follows:

[0063] (1) Physical rotation limit constraints of each joint of the robotic arm: The serpentine redundant robotic arm itself has physical rotation limits. Therefore, in the process of finding the inverse kinematics solution, it is necessary to ensure that the rotation angles of all joints are within the physical rotation limits. According to the universal joint structure between the links of the robotic arm, each joint has a yaw angle and a pitch angle corresponding to the two physical rotation angles of the universal joint. Through the verification action of the yaw angle and pitch angle, the angle formed between two adjacent links becomes the equivalent rotation angle. The equivalent rotation angle is used to measure whether the joint rotation angle of the robotic arm is within the physical rotation limit. The equivalent rotation angle q of the i-th joint of the robotic arm i Let be the angle formed by the (i-1)th link and the ith link, especially when i = 1. The cross product with the unit vector of the Y-axis should be used. The physical rotation angle limit constraint expression is as follows:

[0064] q i ≤q max i = 1, ..., n

[0065]

[0066] In the formula, q i Let q represent the rotation angle of the i-th joint. max This indicates the physical rotation limit of the joint.

[0067] In solving optimization problems, to simplify calculations, the expression for the physical rotation limit constraint is simplified as follows:

[0068]

[0069] (2) Length constraints of each link of the robotic arm: The link length condition needs to be met during the inverse solution process, that is, joint a i With joint a i+1 The distance between them is equal to the length L of the i-th link. i The expression is as follows:

[0070] a i -a i+1 |=L i i = 1, ..., n

[0071] (3) Initial joint motion constraints: The initial joint always moves along the Y-axis, i.e. and

[0072] (4) Wrist joint posture constraint: In each step of the inverse kinematics solution, the robotic arm wrist joint a n Reach the j-th target point G in the specified posture j The expression is as follows:

[0073] a n =G j

[0074] a n+1 =a n +k j ·L n

[0075] In the formula, k j This indicates that the wrist joint has reached the target point G. j The direction vector of the end link.

[0076] (5) Motion smoothness constraint: If the inverse kinematics solution method proposed in this invention considers both the optimal joint offset and the optimal running smoothness, the optimal inverse solution problem will become a multi-objective optimization problem. In solving the multi-objective optimization problem, it is impossible to find a solution that can simultaneously satisfy the optimal joint offset and the optimal running smoothness in every step. Therefore, multi-objective optimization will increase the complexity of the optimal inverse solution problem and lead to a decrease in solution efficiency. This invention analyzes the configuration of the snake-shaped robotic arm and adds the motion smoothness optimization objective as a constraint condition to the inverse kinematics solution problem to achieve multi-objective collaborative optimization.

[0077] The motion smoothness index specifically states that in each step of the inverse kinematics solution, the resulting new configuration must maintain continuity of motion relative to the configuration in the previous step. For example... Figure 6 As shown, assume the current configuration of the robotic arm is a1-a2-…-a n+1 The robotic arm starts from the (j-1)th target point G. j-1 Action to the j-th target point G j The new configuration to be solved is a1'-a2'-…-a n+1 Since the interval between target points varies under different paths, the interval between target points in each step determines the overall offset of the robotic arm relative to the previous step. Therefore, the amount of joint motion of the robotic arm in each step is related to the distance between the current target point and the target point in the previous step.

[0078] In each step of the inverse kinematics solution, the motion of each joint relative to the previous step should be less than the interval |G| between the target point and the previous step. j -G j-1|σ times, where σ is set manually, yields the following expression for the motion smoothness constraint:

[0079]

[0080] In the formula, Let a represent the sum of motion of the remaining n-1 joints of the robotic arm, excluding the wrist joint. i This indicates that the wrist joint is located at the target point G. j The i-th joint point at time a i ′ indicates that the wrist joint is located at the target point G. j-1 The i-th joint point at time; in this embodiment, the value of σ is 2.

[0081] Based on the above analysis, the expression for the inverse kinematics problem is:

[0082]

[0083] S4: Use a constrained nonlinear optimization problem-solving algorithm to calculate the inverse kinematics problem and obtain the coordinates of each joint when the objective function is minimized.

[0084] After the serpentine robotic arm's wrist joint reaches the target, it begins to inspect the target. However, some targets, such as tunnel boring machine cutters, require the serpentine robotic arm to observe different positions of the target from multiple angles. Manually controlling this multi-angle, precise observation of the target is quite difficult. By using the inverse kinematics solution method described above, the robotic arm can achieve precise multi-angle observation of the same target. Given the target T and the end joint a... n In this case, it is necessary to observe the target under test from a specific angle in the circumferential direction, determine the coordinates of the new end-joint target point (i.e., complete the setting of the m target points in S1), and the process of moving from the original end-joint to the new target point is as follows:

[0085] like Figure 7 As shown, the position of the robotic arm's wrist joint is G. j The target to be tested is T, and the end effector a of the robotic arm is... n+1 The distance to T is L T The direction vector of the end effector of the robotic arm is k, and the line of sight of the robotic arm must be at an angle θ with the original direction of the end effector. T The target T is observed from multiple angles. During this process, the position P of the robotic arm wrist joint moves at a distance of G. j With R as the center, T On a circle with radius k and normal vector k, the parametric equation of this circle can be obtained to get the position of the wrist joint in each step of the multi-angle observation process. Then, the direction vector of the end link can be calculated based on the position of the observed target T.

[0086] In the plane containing the circle, take a pair of orthogonal unit vectors u and v. To find u and v, choose any vector e that is not parallel to u, such as the basis vector i of the X-axis. If u is parallel to i, then we can choose the basis vector j of the Y-axis. The cross product of k and e must be perpendicular to k. Normalize it to get u. Then take the cross product of k and u, normalize the result to get v. The expression is as follows:

[0087]

[0088] Origin O and target point G j Constructing vectors G j A vector is formed with a point P on the circumference. If the angle between the vector and the unit vector u is α, then the vector... The expression is as follows:

[0089]

[0090] In the plane containing the circle, u and v can be considered as coordinate axes. Projecting onto the u-axis and v-axis, we obtain its expression as follows:

[0091]

[0092] In the formula, For vectors Projection onto u For vectors Projection onto v.

[0093] The parametric equation of a circle can be written as:

[0094] P(α)=G j +R·cos(α)·u+R·sin(α)·v

[0095] The inverse kinematics problem proposed in this invention is a planning problem in which the objective function and constraints contain nonlinear functions. Sequential Quadratic Programming (SQP) has the advantages of good convergence, high computational efficiency, and strong boundary search capability. Therefore, in this embodiment, SQP is selected as the algorithm for solving the nonlinear optimization problem with constraints to solve the inverse kinematics problem proposed in this invention. In each iteration of SQP, an approximate quadratic programming problem is constructed based on the current iteration point. Then, this quadratic programming problem is solved to update the iteration point. The above process is repeated until the termination condition is met. Therefore, SQP is divided into the following three processes: (1) approximation of the objective function and constraints, (2) solving the quadratic programming subproblem, and (3) line search and iteration point update. Finally, the optimal solution of the inverse kinematics is obtained, that is, the target point G is reached.j The coordinates a of each joint of the robotic arm at that time i .

[0096] This invention uses minimizing joint deviation as the optimization objective for inverse kinematics solution, while considering factors such as joint limits, motion smoothness, and end-effector pose. By setting a motion smoothness index, the optimization objective is transformed into constraints, achieving collaborative optimization for multiple objectives. Numerical optimization methods are then used to obtain the optimal inverse solution for the snake-like robotic arm under the aforementioned specific optimization objectives and constraints. The inverse kinematics solution method proposed in this invention is not limited to robotic arms of a specific configuration but is applicable to all serially redundant robotic arms. In practical applications, objective functions and constraints can be configured according to actual needs, and the method in this invention can be used to transform multiple optimization objectives into constraints. Finally, the optimal inverse solution under multiple objectives and constraints is obtained using the solution method in this invention.

[0097] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for solving the inverse kinematics of a serpentine redundant robotic arm, characterized in that, Includes the following steps: S1: Set the target points of the end effector joints of the robotic arm according to the target to be detected. There are m target points. The robotic arm includes a base, n links, and n joints. Adjacent links are connected by joints. a1 is the initial joint of the robotic arm, connecting the base and link 1. n For the distal joint, a n+1 For end effector; a i Let G be the i-th joint, i = 1, 2, ..., n; j Let j be the j-th target point, j = 1, 2, ..., m; the robotic arm is initially positioned along the Y-axis of the base coordinate system; S2: Construct an objective function based on minimizing the offset of each joint relative to the Y-axis. The objective function is from a1 to a... n-1 The weighted sum of squares of the offsets relative to the Y-axis, and a n-1 The weights of a1 increase sequentially. S3: Based on the physical rotation limits of each joint of the robotic arm, the length of each link, the initial joint always moving along the Y-axis, and the end joint reaching the target point G in a set posture. j Motion smoothness index is used as a constraint on the objective function; S4: Use a constrained nonlinear optimization problem-solving algorithm to find the coordinates of each key point when the objective function is minimized.

2. The inverse kinematics solution method for a serpentine redundant robotic arm according to claim 1, characterized in that, The expression for the objective function is: In the formula, Let X be the X coordinate of the i-th joint. Let be the Z-coordinate of the i-th joint. It represents the square of the vertical distance from the i-th joint to the horizontal slide rail.

3. The inverse kinematics solution method for a serpentine redundant robotic arm according to claim 1, characterized in that, The physical rotation limit constraint expressions for each joint of the robotic arm in the constraints of the objective function are as follows: q i ≤q max ,i=1,...,n In the formula, q i Let q represent the rotation angle of the i-th joint. max This indicates the physical rotation limit of the joint.

4. The inverse kinematics solution method for a serpentine redundant robotic arm according to claim 1, characterized in that, The expressions for the length constraints of each link of the robotic arm in the objective function are as follows: |a i -a i+1 |=L i ,i=1,...,n In the formula, L i This represents the length of the i-th link.

5. The inverse kinematics solution method for a serpentine redundant robotic arm according to claim 1, characterized in that, The expression for the initial joint motion constraint in the objective function is as follows: In the formula, Let X be the initial X-coordinate of the joint. The initial Z-coordinate of the joint.

6. The inverse kinematics solution method for a serpentine redundant robotic arm according to claim 1, characterized in that, The expression for the end-joint attitude constraint in the objective function is as follows: a n =G j a n+1 =a n +k j ·L n In the formula, k j This indicates that the distal joint has reached the target point G. j The direction vector of the end link, L n This represents the length of the nth link.

7. The inverse kinematics solution method for a serpentine redundant robotic arm according to claim 1, characterized in that, The expression for the motion smoothness constraint in the objective function is as follows: In the formula, a represents the sum of motion of the remaining n-1 joints of the robotic arm, excluding the end joint. i This indicates that the distal joint is located at the target point G. j The i-th joint point at time, a i ′ indicates that the distal joint is located at the target point G. j-1 The i-th joint point at time.

8. The inverse kinematics solution method for a serpentine redundant robotic arm according to claim 1, characterized in that, In S4, the algorithm for solving the constrained nonlinear optimization problem is the sequential quadratic programming method.

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