A kinematics solving method and device of a dexterous finger parallel mechanism and an electronic device

Abstract

The present disclosure provides a kinematics solving method and device for a dexterous finger parallel mechanism and an electronic device, which can realize kinematics forward solution for the parallel mechanism configuration after replacing the spherical hinge with a cross hinge with two intersecting axes, has good configuration adaptability, and has good solving success rate and calculation stability, can meet high-precision motion control requirements, and has micron-level calculation accuracy and good real-time performance, thereby being beneficial to improving the control accuracy and response efficiency of the robot dexterous finger.

Description

Technical Field

[0001] This disclosure relates to the field of robot dexterous hand control technology, and more specifically, to a kinematic calculation method, apparatus and electronic device for a dexterous finger parallel mechanism. Background Technology

[0002] With the continuous development of robotics technology, dexterous hands, due to their high operational flexibility and humanoid grasping ability, have been widely used in precision assembly, service robots, medical assistance, and human-robot collaboration. As a key actuator in dexterous hands, the motion performance, control precision, and real-time response capability of the finger mechanism directly affect the overall grasping stability and operational accuracy of the robot. Among various finger mechanism solutions, parallel mechanisms have become an important configuration in the design of the index finger of a robot dexterous hand due to their advantages such as compact structure, high rigidity, strong load-bearing capacity, and fast motion response.

[0003] For the classic parallel mechanism configuration of the index finger of a robot dexterous hand, existing technologies typically employ analytical methods to solve for the forward kinematics. These methods usually rely on an idealized geometric model of the mechanism, resulting in a strong coupling between the method itself and the mechanism configuration. In other words, once the local structure of the mechanism changes, the original analytical model is often difficult to directly apply.

[0004] However, in practical engineering design, due to considerations such as processing costs, range of motion, structural stiffness, assembly convenience, or reliability, the local connection form of the parallel mechanism of the robot's dexterous hand index finger often needs to be adjusted. For example, replacing the ball hinge in the classic configuration with a cross hinge structure with two non-intersecting axes can provide certain advantages at the structural implementation level, but the geometric constraints of the mechanism also change. In the above situations, if the traditional analytical solution approach is still attempted, it is often necessary to re-derive complex mathematical equations, which presents problems such as difficult modeling, cumbersome derivation, and poor adaptability. At the same time, the analytical derivation process is quite sensitive to the geometric form of the mechanism, which is not conducive to subsequent structural iteration and parameter adjustment. Summary of the Invention

[0005] This disclosure provides at least one kinematic solution method, apparatus, and electronic device for a dexterous finger parallel mechanism. It can solve the forward kinematics of a parallel mechanism configuration after replacing a ball hinge with a cross hinge with two non-intersecting axes, and has good configuration adaptability. At the same time, the method has a good solution success rate and computational stability, which can meet the requirements of high-precision motion control. Its computational accuracy can reach the micrometer level, and it has good real-time performance, which is beneficial to improving the control accuracy and response efficiency of the index finger of the robot's dexterous hand.

[0006] This disclosure provides a kinematic solution method for a dexterous finger parallel mechanism, applicable to parallel mechanism configurations that use two non-intersecting cross hinges instead of ball hinges. The method includes: Obtain the target drive rod length of the parallel mechanism, preprocess the target drive rod length according to the structural symmetry of the parallel mechanism, and determine the target length parameter; Initialize the joint angle guess value, and initialize the current drive rod length based on the joint angle guess value. Perform inverse kinematics calculation based on the current joint angle to determine the current drive rod length corresponding to the current joint angle. An error vector is constructed based on the difference between the current drive rod length and the target length parameter, and it is determined whether the error vector satisfies the preset convergence condition. When the error vector does not meet the preset convergence condition, the Jacobian matrix at the current joint angle is calculated based on the finite difference method, and the guessed value of the joint angle is iteratively updated according to the Jacobian matrix and the error vector. When the error vector satisfies the preset convergence condition, the joint angles obtained by iteration are recovered according to the structural symmetry, and the forward kinematic solution of the parallel mechanism is output.

[0007] In one optional implementation, the target drive rod length of the parallel mechanism is obtained, and the target drive rod length is preprocessed according to the structural symmetry of the parallel mechanism, specifically including: Determine the lengths of the first target drive rod and the second target drive rod in the parallel mechanism; When the length of the first target drive rod is greater than the length of the second target drive rod, the lengths of the first target drive rod and the second target drive rod are swapped, and a symmetry flag is set. When the length of the first target drive rod is not greater than the length of the second target drive rod, the original target drive rod length remains unchanged.

[0008] In one optional implementation, inverse kinematics calculations are performed based on the current joint angle to determine the current drive rod length corresponding to the current joint angle, specifically including: Construct the joint rotation matrix corresponding to the current joint angle; Based on the joint rotation matrix, base-side connection point parameters, moving platform-side connection point parameters, and joint height parameters, calculate at least two sets of link vector positions. Calculate the corresponding link length constraint based on the cross hinge offset length and the initial link length; The current drive rod length is calculated based on the link vector position and the link length constraint.

[0009] In one optional implementation, an error vector is constructed based on the difference between the current drive rod length and the target length parameter, and it is determined whether the error vector satisfies a preset convergence condition, specifically including: Calculate the length difference between the current drive rod length and the target length parameter; An error vector is constructed based on the length differences described above; Determine whether the absolute value of each component in the error vector is less than a preset convergence accuracy threshold; If yes, then the preset convergence condition is satisfied; if no, then the preset convergence condition is not satisfied.

[0010] In one optional implementation, the Jacobian matrix at the current joint angle is calculated based on a finite difference method, specifically including: Positive and negative disturbances are applied to the first joint angle in the lateral direction and the second joint angle in the longitudinal direction of the target drive rod in the parallel mechanism, respectively. Inverse kinematics calculations were performed under each disturbance condition to obtain the length of the driving rod after disturbance. Based on the change in drive rod length before and after the disturbance and the disturbance step size, calculate each element of the Jacobian matrix. For any joint angle variable, take the calculated drive rod length when the joint angle variable is increased by a preset difference step size and the calculated drive rod length when the preset difference step size is decreased. Determine the corresponding partial derivative based on the ratio of the difference between the two to the preset difference step size.

[0011] In one optional implementation, the joint angle guess value is iteratively updated based on the Jacobian matrix and the error vector, specifically including: The joint angle correction is obtained based on the Jacobian matrix and the error vector. The joint angle correction amount is multiplied by a preset step size factor and used as the actual update amount for this iteration. The current joint angle guess value is corrected using the actual update amount to obtain the joint angle guess value for the next iteration.

[0012] In one optional implementation, the joint angles obtained through iteration are recovered based on the structural symmetry, and the forward kinematic solution of the parallel mechanism is output, specifically including: With the symmetry flag set, the sign of at least one joint angle obtained iteratively is restored. Without setting the symmetry flag, the joint angles obtained through iteration are directly output as the forward kinematics solution.

[0013] This disclosure also provides a kinematic calculation device for a dexterous finger parallel mechanism, comprising: The data preprocessing module is used to obtain the target drive rod length of the parallel mechanism, preprocess the target drive rod length according to the structural symmetry of the parallel mechanism, and determine the target length parameter. The data initialization module is used to initialize the joint angle guess value, initialize the current drive rod length based on the joint angle guess value, perform inverse kinematics calculation based on the current joint angle, and determine the current drive rod length corresponding to the current joint angle. The Newton iteration loop module is used to construct an error vector based on the difference between the current drive rod length and the target length parameter, and to determine whether the error vector satisfies the preset convergence condition. The Jacobian matrix construction module is used to calculate the Jacobian matrix at the current joint angle based on the finite difference method when the error vector does not meet the preset convergence condition, and to iteratively update the guessed value of the joint angle according to the Jacobian matrix and the error vector. The solution module is used to recover the joint angles obtained by iteration based on the structural symmetry when the error vector satisfies the preset convergence condition, and output the forward kinematic solution of the parallel mechanism.

[0014] This disclosure also provides an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the kinematic calculation method of the above-described dexterous finger parallel mechanism, or any possible implementation of the kinematic calculation method of the above-described dexterous finger parallel mechanism.

[0015] This disclosure also provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the kinematic calculation method for the above-described dexterous finger parallel mechanism, or any possible implementation of the kinematic calculation method for the above-described dexterous finger parallel mechanism.

[0016] This disclosure also provides a computer program product, including a computer program / instructions, which, when executed by a processor, implements the kinematic calculation method of the above-described dexterous finger parallel mechanism, or the steps in any possible implementation of the kinematic calculation method of the above-described dexterous finger parallel mechanism.

[0017] This disclosure provides a kinematic solution method, apparatus, and electronic device for a dexterous finger parallel mechanism. It enables forward kinematics solutions for parallel mechanism configurations where two non-intersecting cross hinges replace ball hinges, exhibiting good configuration adaptability. Furthermore, the method boasts a high success rate and computational stability, meeting the demands of high-precision motion control. Its computational accuracy reaches the micrometer level, and it possesses good real-time performance, thereby improving the control accuracy and response efficiency of the robot's dexterous hand index finger.

[0018] To make the above-mentioned objects, features and advantages of this disclosure more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings used in the embodiments will be briefly described below. These drawings are incorporated in and constitute a part of this specification. They illustrate embodiments conforming to this disclosure and, together with the specification, serve to explain the technical solutions of this disclosure. It should be understood that the following drawings only show some embodiments of this disclosure and should not be considered as limiting the scope. Those skilled in the art can obtain other related drawings based on these drawings without creative effort.

[0020] Figure 1 A schematic diagram of a parallel mechanism configuration provided by an embodiment of this disclosure, which uses two non-intersecting cross hinges instead of ball hinges; Figure 2 A flowchart is shown below illustrating a kinematic calculation method for a dexterous finger parallel mechanism provided in an embodiment of this disclosure; Figure 3 A schematic diagram of a kinematic calculation device for a dexterous finger parallel mechanism provided in an embodiment of this disclosure is shown; Figure 4 A schematic diagram of an electronic device provided in an embodiment of the present disclosure is shown. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. The components of the embodiments of this disclosure described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed disclosure, but merely represents selected embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0022] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0023] In this document, the term "and / or" merely describes a relationship, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0024] Research has revealed that in practical engineering design, the local connection forms of the parallel mechanism of the index finger of a robot's dexterous hand often need to be adjusted due to considerations such as processing costs, range of motion, structural stiffness, assembly convenience, and reliability. For example, replacing the ball hinge in the classic configuration with a cross hinge structure with two non-intersecting axes can provide certain advantages in terms of structural implementation, but the geometric constraints of the mechanism also change. In such cases, if the traditional analytical solution approach is still used, it is often necessary to re-derive complex mathematical equations, which presents problems such as difficult modeling, cumbersome derivation, and poor adaptability. At the same time, the analytical derivation process is quite sensitive to the geometric form of the mechanism, which is not conducive to subsequent structural iteration and parameter adjustment.

[0025] Based on the above research, this disclosure provides a kinematic solution method, device, and electronic device for a dexterous finger parallel mechanism. It can solve the forward kinematics of the parallel mechanism configuration after replacing the ball hinge with a cross hinge with two non-intersecting axes, and has good configuration adaptability. At the same time, the method has a good solution success rate and computational stability, which can meet the requirements of high-precision motion control. Its computational accuracy can reach the micrometer level, and it has good real-time performance, which is beneficial to improving the control accuracy and response efficiency of the index finger of the robot's dexterous hand.

[0026] To facilitate understanding of this embodiment, a detailed description of the kinematic calculation method for a dexterous finger parallel mechanism disclosed in this disclosure is provided first. The execution entity of the kinematic calculation method for the dexterous finger parallel mechanism provided in this disclosure is generally a computer device with certain computing capabilities. This computer device may include, for example, a terminal device, a server, or other processing devices. The terminal device may be a user equipment (UE), mobile device, user terminal, terminal, cellular phone, cordless phone, personal digital assistant (PDA), handheld device, computing device, in-vehicle device, wearable device, etc. In some possible implementations, the kinematic calculation method for the dexterous finger parallel mechanism can be implemented by a processor calling computer-readable instructions stored in memory.

[0027] In specific implementations, the kinematic calculation method for a dexterous finger parallel mechanism disclosed in this disclosure is applied to parallel mechanism configurations that use two non-intersecting cross hinges instead of ball hinges. See [link to relevant documentation]. Figure 1 The diagram shows a parallel mechanism configuration that uses two non-intersecting cross hinges instead of ball hinges.

[0028] like Figure 1 As shown, the parallel mechanism of the robot's dexterous hand index finger in this embodiment is a type of parallel mechanism composed of a base-side mounting point, a moving platform-side connection point, and an intermediate constraint branch. This parallel mechanism has two parallel branches, corresponding to the first branch and the second branch, respectively. Each branch is composed of a base-side connecting section, an intermediate link section, and a moving platform-side connecting section connected sequentially, and all connected to the end-effector moving platform.

[0029] Compared to the traditional ball joint configuration, this solution replaces the ball joint with a cross joint structure with two non-intersecting axes. This allows the spatial constraints between each branch and the end-effector to be achieved through a combination of cross joints. This replacement method preserves the predetermined motion capability of the end-effector relative to the base while also facilitating the engineering design of the mechanism to meet specific manufacturing processes and structural requirements.

[0030] Specifically, the end-effector moving platform of the parallel mechanism is located in the upper region, and the base mounting area is located in the lower region. The first branch and the second branch connect the base and the end-effector moving platform respectively to form a closed-loop parallel constraint. The two branches are connected to different mounting points on the base side and the moving platform side respectively, thus forming a dual-branch parallel drive structure.

[0031] In the diagram, x and z represent the directions of the coordinate axes in the base coordinate system, and u, v, and w represent the directions of the three coordinate axes in the moving platform coordinate system. Point P mcp Let p represent the reference point of the end effector platform, and p represent the distance from the origin of the base coordinate system to the reference point P of the end effector platform. mcp The position vectors are: A1 and A2, representing two connection points located on the base side, where A1 is the base-side connection point of the first branch and A2 is the base-side connection point of the second branch. Correspondingly, a1 and a2 represent the base-side position vectors pointing from the origin of the base coordinate system to A1 and A2, respectively. B1 and B2 represent two connection points located on the end moving platform side, where B1 is the connection point of the first branch on the moving platform side and B2 is the connection point of the second branch on the moving platform side. Correspondingly, b1′ and b2′ represent the reference point P of the driven platform. mcp Position vectors pointing to the moving platform side of B1 and B2. d1 and d2 represent the drive segments or drive rod segments corresponding to the first and second branches, respectively. m1 and m2 represent the intermediate connecting rod segments located in the first and second branches, respectively. n1′ and n2′ represent the upper connecting segments or end constraint segments located near the moving platform side, respectively.

[0032] See Figure 2 The diagram shows a flowchart of a kinematic calculation method for a dexterous finger parallel mechanism provided in an embodiment of this disclosure. The method includes steps S101 to S105, wherein: S101. Obtain the target drive rod length of the parallel mechanism, preprocess the target drive rod length according to the structural symmetry of the parallel mechanism, and determine the target length parameter.

[0033] In practical implementation, the kinematic solution method for the parallel mechanism of the index finger of a robot dexterous hand provided in this embodiment is applied to the forward kinematics solution of the joint angles of the parallel mechanism based on the target drive rod length. First, the target drive rod length of the parallel mechanism is obtained. The target drive rod length is an input parameter of the parallel mechanism in the current state to be solved, used to characterize the target length value of the corresponding drive rod in the two parallel branches. For the dual-branch parallel mechanism in this embodiment, the target drive rod length includes at least the target length d1 of the first drive rod and the target length d2 of the second drive rod. The subsequent forward kinematics solution process is based on this target drive rod length to solve for the corresponding joint angles.

[0034] Here, because the parallel mechanism of the robot's dexterous hand index finger in this embodiment has a left-right symmetrical structural feature, the two branches have corresponding mirror relationships in geometric arrangement and motion constraints. For example, the base-side connection points A1 and A2 are symmetrically arranged about the mechanism's symmetry plane, and the moving platform-side connection points B1 and B2 are also arranged about the corresponding symmetry. In terms of parameter expression, a1 and a2, as well as b1 and b2, satisfy the symmetrical arrangement relationship, thus giving the entire parallel mechanism usable structural symmetry in the solution process.

[0035] Based on the above structural symmetry, after obtaining the target drive rod length, the target drive rod length can be preprocessed to convert the input target length parameter into a unified standard solution form.

[0036] Specifically, the lengths of the first target drive rod d1 and the second target drive rod d2 can be compared. When d1 is greater than d2, it indicates that the current input state corresponds to the mirror image of the other side of the symmetrical configuration of the mechanism. In this case, the lengths of the two target drive rods are swapped, and the symmetry flag flag_q2=true is set to record that symmetry transformation was used in this solution. When d1 is less than or equal to d2, the original input order remains unchanged, and it can be considered that no symmetry transformation needs to be triggered.

[0037] In this way, different input scenarios with respect to the symmetric plane distribution can be normalized to the same solution interval.

[0038] In this embodiment, the target length parameters determined after the above preprocessing can be denoted as d_target1 and d_target2. d_target1 and d_target2 are the target values ​​that actually participate in the calculation in subsequent error calculation and iterative correction. That is, in the subsequent numerical iteration process, the current drive rod length corresponding to the current joint angle will be compared with d_target1 and d_target2 respectively to construct a length error vector.

[0039] Furthermore, the aforementioned preprocessing method can also improve the uniqueness and stability of the forward kinematics solution process. This is because the parallel mechanism has a symmetrical structural feature. If the length of the input target driving rod is not symmetrically normalized, the same physical configuration may correspond to two types of mirror inputs in the numerical solution, easily leading to inconsistent joint angle sign judgments, thus increasing the complexity of initial value selection and result discrimination.

[0040] S102. Initialize the joint angle guess value, and initialize the current drive rod length based on the joint angle guess value. Perform inverse kinematics calculation based on the current joint angle to determine the current drive rod length corresponding to the current joint angle.

[0041] In specific implementation, after completing the preprocessing of the target drive rod length and determining the target length parameter, this embodiment further initializes the joint angle guess values. Specifically, for the two joint variables of the parallel mechanism, the initial guess value q1=q1_init for the first joint angle and the initial guess value q2=q2_init for the second joint angle are set respectively.

[0042] Here, the joint angle guesses serve as the starting point for subsequent numerical iterations, providing an initial estimate of the current mechanism's attitude before the Newton iterations begin. Simultaneously, based on the joint angle guesses, the current drive link lengths are initialized, yielding the first current drive link length d1_current=d1_init and the second current drive link length d2_current=d2_init. This initialization process establishes the initial state for iteration, ensuring a usable initial correspondence between the joint angle variables and the drive link length variables before entering the inverse kinematics calculation.

[0043] In this embodiment, the joint angle guess value can be determined based on the mechanism's common working range, empirical initial value, the solution result of the previous moment, or a preset calibration value. Using the joint angle guess value as the iteration starting point helps the numerical solution process to approach the target solution from a position close to the true solution, thereby improving the convergence speed and solution stability of the forward kinematics solution.

[0044] After initialization, inverse kinematics calculations are performed based on the current joint angles to determine the current drive rod length corresponding to the current joint angles. Specifically, in each iteration, the inverse kinematics function inverseKinematic(q1, q2, d1_current, d2_current) is called to calculate the corresponding drive rod length based on the current joint angles q1 and q2, and this result is used as the current drive rod length in subsequent error calculations.

[0045] In other words, although the overall solution of this scheme is to solve the forward kinematics problem of inversely finding the joint angle from the target driving rod length, in the numerical iteration process, the theoretical current driving rod length is first calculated by substituting the current joint angle into the inverse kinematics model, and then compared with the target length parameter. This process continuously corrects the guessed joint angle value until the convergence condition is met.

[0046] Furthermore, the inverse kinematics calculation first constructs a joint rotation matrix R. This rotation matrix is ​​jointly determined by the current first joint angle q1 and the second joint angle q2, and is used to characterize the attitude change relationship of the end effector platform relative to the base coordinate system. By transforming the local vectors defined in the moving platform coordinate system to the base coordinate system through the rotation matrix, the spatial geometric correspondence between the end effector connection point and the base connection point can be established.

[0047] Here, the joint rotation matrix R can be represented by the following equation, which is composed of a combination of cos(q1), sin(q1), cos(q2), and sin(q2).

[0048]

[0049] After obtaining the rotation matrix R, the link vector positions corresponding to the two branches are further calculated. Specifically, the link vector position of the first branch is denoted as k1, and the link vector position of the second branch is denoted as k2, where k1 = [0, 0, p]. +R×b1-a1,k2=[0,0,p] +R×b2-a2.

[0050] Here, [0, 0, p] The position offset corresponding to the joint height parameter is represented by a1 and a2, which are the position vectors of the base side connection points A1 and A2 in the base coordinate system, respectively, and b1 and b2 are the position vectors of the moving platform side connection points B1 and B2 in the moving platform local coordinate system, respectively.

[0051] In this way, through the above calculations, the end pose corresponding to the current joint angle can be combined with the mechanism's geometric parameters to obtain the spatial link position relationship between the two branches in the current pose.

[0052] After determining the link vector positions, the link length constraints for the two branches are calculated by further considering the geometric constraints of the cross-hinge replacement structure. Specifically, the first branch satisfies l1²=l 10 ²+l5²+2l5 (l 10 The second branch satisfies l2² = l² - k1x². 20 ²+l5²+2l5 (l 20 (²-k2x²).

[0053] Among them, l 10 l 20 l1 represents the initial length of the link, and l5 represents the cross-axis offset length. By introducing the cross-axis offset length and the initial length of the link, the structural effects of replacing the ball joint with a cross hinge whose two axes do not intersect can be incorporated into the inverse kinematics model, thus enabling the calculation of the current drive rod length to accurately reflect the actual geometric constraints under this improved configuration.

[0054] After obtaining the above length constraints, the corresponding current drive rod length is further calculated. Specifically, the first current drive rod length d1 is calculated using the formula d1=k1z- (l1²-k1x²-k1y²) is determined, and the second current drive rod length d2 is obtained through the formula d2=k2z- (l2²-k2x²-k2y²) is determined.

[0055] Where k1x, k1y, and k1z represent the components of link vector k1 in the x, y, and z directions, respectively, and k2x, k2y, and k2z represent the components of link vector k2 in the x, y, and z directions, respectively. Therefore, the current drive rod lengths d1_current and d2_current can be uniquely determined based on the current joint angles q1 and q2.

[0056] Therefore, the essence of this step is as follows: First, set initial guess values ​​for the two joint variables and establish the corresponding initial state of the current driving rod length; then, substitute the current joint angle into the inverse kinematics model, and obtain the theoretical driving rod length at the current joint angle through rotation matrix construction, link vector position calculation, length constraint calculation, and driving rod elongation calculation. Subsequently, the current driving rod length can be compared with the aforementioned target length parameter to construct an error vector, and on this basis, Jacobian matrix calculation and Newton iteration update can continue to be performed.

[0057] In this way, by first initializing the joint angle guess values ​​and then calculating the current drive rod length in real time based on the inverse kinematics model, the complex forward kinematics problem can be transformed into a numerical iterative problem based on error approximation, avoiding the direct construction of complex analytical forward kinematics expressions. At the same time, combining the improved parallel mechanism configuration parameters for inverse kinematics solution can also improve the method's adaptability to changes in mechanism parameters and the overall solution robustness.

[0058] S103. Construct an error vector based on the difference between the current drive rod length and the target length parameter, and determine whether the error vector satisfies the preset convergence condition.

[0059] In specific implementation, after performing inverse kinematics calculations based on the current joint angle and determining the current drive rod length, this embodiment further constructs an error vector based on the difference between the current drive rod length and the target length parameter.

[0060] Specifically, the difference between the first current drive rod length and the first target length parameter, and the difference between the second current drive rod length and the second target length parameter are calculated respectively to obtain the first length error and the second length error.

[0061] The first length error can be represented as e1 = d1_current - d_target1, and the second length error can be represented as e2 = d2_current - d_target2. Further, the first length error e1 and the second length error e2 are combined to construct an error vector e, which characterizes the overall deviation between the theoretical drive rod length corresponding to the current joint angle and the target drive rod length.

[0062] In this embodiment, each component of the error vector corresponds to the degree of deviation of the current driving rod length of each branch from the target length parameter. If the absolute value of the first length error e1 is large, it indicates that there is a large deviation between the driving rod length calculated by the first branch at the current joint angle and the target length parameter; if the absolute value of the second length error e2 is large, it indicates that the second branch has not yet reached the target state. By incorporating the length errors of the two branches into the same error vector, the forward kinematics problem of the parallel mechanism can be transformed into a multivariate error approximation problem, thereby providing an error input basis for subsequent iterative correction based on the Jacobian matrix.

[0063] Furthermore, after constructing the error vector, it is necessary to determine whether the error vector satisfies the preset convergence condition. Specifically, it can be determined whether the absolute value of the first length error e1 and the absolute value of the second length error e2 are both less than the preset convergence accuracy threshold ε.

[0064] Here, when |e1|<ε and |e2|<ε, the error vector is determined to satisfy the preset convergence condition, indicating that the current drive rod length corresponding to the current joint angle is close enough to the target length parameter, and the current joint angle can be used as the result of the desired forward kinematics solution; when |e1|≥ε or |e2|≥ε, the error vector is determined not to satisfy the preset convergence condition, and the subsequent iterative update process needs to be continued. The convergence judgment form given in the document embodiment is: if |e1|<ε and |e2|<ε, then exit the loop, where ε can be 1e-10.

[0065] It should be understood that the preset convergence condition is essentially used to measure the closeness between the current numerical solution and the target solution. Since the forward kinematics solution of the parallel mechanism in this scheme is achieved through numerical iteration, it is usually impossible to obtain an absolutely accurate analytical solution directly within a finite number of steps. Instead, the current solution gradually approaches the true solution by continuously reducing the error vector. By setting a preset convergence accuracy threshold ε, a balance can be achieved between solution accuracy and computational efficiency: a smaller ε improves solution accuracy; a more relaxed ε helps shorten the iteration time and improve real-time performance. Therefore, in different application scenarios, the preset convergence accuracy threshold can be set according to control accuracy requirements, computational resource conditions, and real-time requirements.

[0066] In this embodiment, by constructing the error vector and performing convergence judgment in the above manner, the deviation between the target drive rod length and the current drive rod length can be expressed in an explicit form, thereby transforming the forward kinematics solution process from directly solving the nonlinear equation system into an iterative solution process with gradually decreasing error.

[0067] This approach not only facilitates subsequent correction of joint angles using the Jacobian matrix, but also enhances the algorithm's feasibility and engineering adaptability. Especially after replacing ball joints with cross joints whose two axes do not intersect, the geometric relationship of the mechanism becomes more complex than the traditional configuration. Using the error vector as the iteration criterion more directly reflects the degree of matching between the current solution and the target solution under the improved configuration, thereby improving the stability and accuracy of the overall solution process.

[0068] In other words, the purpose of this step is to first construct an error vector based on the difference between the current drive rod length and the target length parameter, and then use a preset convergence condition to determine whether the current joint angle has met the requirements of the forward kinematics solution. If it does, the iteration can be terminated and the result can be output; if it does not, the error can be gradually reduced through subsequent Jacobian matrix calculations and joint angle updates. Thus, a clear, stable, and quantifiable basis for determining the numerical iterative solution of the entire forward kinematics solution can be established.

[0069] S104. When the error vector does not meet the preset convergence condition, calculate the Jacobian matrix at the current joint angle based on the finite difference method, and iteratively update the joint angle guess value according to the Jacobian matrix and the error vector.

[0070] In practical implementation, when the error vector does not meet the preset convergence condition, it indicates that there is still a large deviation between the current drive rod length obtained from the current joint angle guess and the target length parameter, and the current joint angle has not yet converged to the required forward kinematics solution. Therefore, this embodiment further calculates the Jacobian matrix at the current joint angle based on the finite difference method, and iteratively updates the joint angle guess value according to the Jacobian matrix and the error vector, so that the current drive rod length in subsequent iterations gradually approaches the target length parameter.

[0071] In this embodiment, the Jacobian matrix is ​​used to characterize the sensitivity of the drive rod length error to changes in the joint angle variables. Since the parallel mechanism configuration, after replacing the ball joint with two non-intersecting cross hinges, has complex nonlinear geometric constraints, directly deriving its analytical form of the Jacobian matrix is ​​cumbersome. Therefore, this embodiment uses a finite difference method to numerically approximate the Jacobian matrix at the current joint angle. This method eliminates the need for explicit derivation of complex partial derivative expressions; it only requires applying a small perturbation near the current joint angle and observing the change in the corresponding drive rod length error to obtain the numerical results of each element of the Jacobian matrix, thereby improving the engineering implementation convenience of the method.

[0072] Specifically, the difference step size can be set to δq, for example, δq can be 1e-5. Based on the current first joint angle q1 and second joint angle q2, positive and negative perturbations are applied to q1 and q2 respectively, and the inverse kinematics calculation process is called under each perturbation condition to obtain the length of the drive rod after perturbation.

[0073] Subsequently, based on the changes in the drive rod length error before and after the disturbance, the elements of the Jacobian matrix are calculated. The Jacobian matrix is ​​calculated as follows: J 11 = [(d1(q1-δq,q2) - d_target1) - (d1(q1+δq,q2) - d_target1)] / (-2δq) J 12 = [(d1(q1,q2-δq) - d_target2) - (d1(q1,q2+δq) - d_target2)] / (-2δq) J 21 = [(d2(q1-δq,q2) - d_target1) - (d2(q1+δq,q2) - d_target1)] / (-2δq) J 22 = [(d2(q1,q2-δq) - d_target2) - (d2(q1,q2+δq) - d_target2)] / (-2δq) This forms a two-dimensional Jacobian matrix J = [J 11 J 12 J 21 J 22 ].

[0074] Here, after obtaining the Jacobian matrix, the guessed joint angle value is further iteratively updated based on the Jacobian matrix and the error vector. Specifically, the joint angle correction Δq can be calculated first based on the Jacobian matrix J and the error vector e. A Newton-Raphson iterative update method is used, i.e., according to Δq=J... - The joint angle correction is calculated as ¹×e×0.5, where 0.5 is the step size factor. Then, this correction is subtracted from the current joint angle prediction to obtain the updated joint angles: q1 = q1 - Δq1, q2 = q2 - Δq2. The updated q1 and q2 will serve as inputs for the next round of inverse kinematics calculations, continuing to participate in subsequent error calculations and convergence determination.

[0075] Furthermore, the step size factor is used to control the actual applied magnitude of the joint angle correction in each iteration, so as to avoid iteration divergence or oscillation due to excessive update step size in cases of strong nonlinearity or large initial error.

[0076] For example, the step size factor can be 0.5, and can be between 0.2 and 0.6. That is to say, the step size factor can be adapted to different mechanism parameter configurations, initial value conditions, or real-time control scenarios according to the numerical stability requirements.

[0077] It should be understood that the core of this step lies in utilizing the local linear approximation relationship near the current joint angle to solve for the joint angle correction direction and magnitude corresponding to the current error vector. In other words, the Jacobian matrix reflects the influence of small changes in the joint angle on the drive rod length error, while the error vector reflects the magnitude of the deviation between the current state and the target state. By combining the two, a joint angle adjustment amount that reduces the error can be obtained in each iteration, thereby gradually approximating the current joint angle guess value to the true kinematic forward solution.

[0078] Thus, this embodiment uses the finite difference method to calculate the Jacobian matrix and combines it with Newton's iteration to update the guessed joint angle values. This avoids the modeling burden caused by directly deriving the complex analytical Jacobian matrix, and is especially suitable for complex parallel mechanism configurations after replacing ball hinges with cross hinges with two non-intersecting axes. At the same time, this method has a good solution success rate and computational stability, and can ensure solution accuracy while taking into account real-time requirements. This is beneficial for meeting the kinematic forward solution requirements in the high-precision motion control scenario of the robot's dexterous hand index finger.

[0079] S105. When the error vector satisfies the preset convergence condition, the joint angles obtained by iteration are recovered according to the structural symmetry, and the forward kinematic solution of the parallel mechanism is output.

[0080] In specific implementation, when the error vector satisfies the preset convergence condition, it indicates that the length of the driving rod corresponding to the joint angle obtained in the current iteration is basically consistent with the target length parameter. At this time, it can be considered that the numerical iteration has converged, and the current joint angle is a candidate result of the kinematic forward solution. Correspondingly, in this embodiment, when both the first length error e1 and the second length error e2 meet the preset accuracy threshold requirements, the current iteration process ends, and the joint angle obtained by the iteration is subjected to result restoration processing.

[0081] Here, since the input target drive rod length has been preprocessed based on the structural symmetry of the parallel mechanism at the beginning of the solution process in this embodiment, the actual problem solved during the iteration is the standard problem after symmetry normalization. That is, when the input first target drive rod length is greater than the second target drive rod length, the system first swaps the two target length parameters and sets the symmetry flag_q2=true to map the original input to a unified standard solution range.

[0082] While this simplifies subsequent error calculations and iterative solutions, the joint angle results obtained at the end of the iteration still correspond to the normalized symmetrical configuration, and may not directly correspond to the actual mechanism posture under the original input state. Therefore, after the error vector satisfies the preset convergence condition, it is still necessary to recover the iteration results based on the aforementioned structural symmetry.

[0083] Specifically, in this embodiment, the need for result restoration processing can be determined based on the symmetry flag. When the symmetry flag_q2=true, it indicates that the target drive rod length has been swapped during the current solution process, and the second joint angle q2 obtained in the current iteration corresponds to the result after symmetry transformation. Therefore, a sign restoration operation needs to be performed on the second joint angle, i.e., q2=-q2, to map the result obtained under the standard solution interval back to the actual mechanism configuration corresponding to the original input state. That is, according to the symmetry restoration result, if flag_q2=true, then q2=-q2.

[0084] Correspondingly, when the symmetry flag is not set (flag_q2=false), it indicates that the input target drive rod length is already in the standard solution order. No normalization processing using symmetry transformation is needed during iteration. Therefore, the converged joint angle result can be directly output as the forward kinematic solution of the parallel mechanism without further sign restoration or order adjustment. In other words, only when an input transformation based on structural symmetry occurs in the preprocessing stage is it necessary to perform the corresponding inverse restoration in the result output stage to ensure that the output result is consistent with the original input parameters. This output result is the successfully solved joint angle (q1, q2).

[0085] Thus, by employing the aforementioned result recovery method, the uniformity and engineering feasibility of the entire forward kinematics solution process can be improved. On the one hand, by unifying different mirror inputs into the same solution process through structural symmetry before solving, branch judgments can be reduced, simplifying the numerical solution model. On the other hand, by performing result recovery through symmetry flags after solving, it can be ensured that the output results accurately correspond to the original input conditions. Therefore, this embodiment utilizes the structural symmetry of the mechanism to reduce solution complexity, and ensures the correctness and completeness of the forward kinematics solution output through result recovery.

[0086] This disclosure provides a kinematic solution method for a parallel dexterous finger mechanism. This method can solve the forward kinematics of a parallel mechanism configuration after replacing a ball joint with two non-intersecting cross joints, exhibiting good configuration adaptability. Furthermore, this method has a high success rate and computational stability, meeting the requirements of high-precision motion control. Its computational accuracy can reach the micrometer level, and it has good real-time performance, thus improving the control accuracy and response efficiency of the robot's dexterous hand index finger.

[0087] Those skilled in the art will understand that, in the above-described method of the specific implementation, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0088] Based on the same inventive concept, this disclosure also provides a kinematic calculation device for a dexterous finger parallel mechanism corresponding to the kinematic calculation method of the dexterous finger parallel mechanism. Since the principle of the device in this disclosure for solving the problem is similar to the kinematic calculation method of the dexterous finger parallel mechanism described above in this disclosure, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be described again.

[0089] Please see Figure 3 , Figure 3 This is a schematic diagram of a kinematic calculation device for a dexterous finger parallel mechanism provided in an embodiment of this disclosure. Figure 3 As shown in the embodiments of this disclosure, the kinematic calculation device 300 for the dexterous finger parallel mechanism includes: The data preprocessing module 310 is used to obtain the target drive rod length of the parallel mechanism, preprocess the target drive rod length according to the structural symmetry of the parallel mechanism, and determine the target length parameter.

[0090] The data initialization module 320 is used to initialize the joint angle guess value, initialize the current drive rod length based on the joint angle guess value, perform inverse kinematics calculation based on the current joint angle, and determine the current drive rod length corresponding to the current joint angle.

[0091] The Newton iteration loop module 330 is used to construct an error vector based on the difference between the current drive rod length and the target length parameter, and to determine whether the error vector satisfies the preset convergence condition.

[0092] The Jacobian matrix construction module 340 is used to calculate the Jacobian matrix at the current joint angle based on the finite difference method when the error vector does not meet the preset convergence condition, and to iteratively update the joint angle guess value according to the Jacobian matrix and the error vector.

[0093] The solution module 350 is used to recover the joint angle obtained by iteration based on the structural symmetry when the error vector satisfies the preset convergence condition, and output the forward kinematic solution of the parallel mechanism.

[0094] The processing flow of each module in the device and the interaction flow between each module can be referred to the relevant descriptions in the above method embodiments, and will not be detailed here.

[0095] This disclosure provides a kinematics calculation device for a parallel dexterous finger mechanism, which can solve the forward kinematics of the parallel mechanism configuration after replacing the ball hinge with a cross hinge with two non-intersecting axes. It has good configuration adaptability. At the same time, the method has a good solution success rate and computational stability, which can meet the requirements of high-precision motion control. Its computational accuracy can reach the micrometer level, and it has good real-time performance, which is beneficial to improving the control accuracy and response efficiency of the index finger of the robot's dexterous hand.

[0096] Corresponding to Figure 2 The kinematic calculation method for the dexterous finger parallel mechanism in the present disclosure also provides an electronic device 400, such as... Figure 4 The diagram shown is a structural schematic of an electronic device 400 provided in an embodiment of this disclosure, including: Processor 41, memory 42, and bus 43; memory 42 is used to store execution instructions, including main memory 421 and external memory 422; the main memory 421, also called internal memory, is used to temporarily store the computational data in processor 41, as well as the data exchanged with external memory 422 such as hard disk. Processor 41 exchanges data with external memory 422 through main memory 421. When the electronic device 400 is running, processor 41 and memory 42 communicate through bus 43, enabling processor 41 to execute... Figure 2 The steps of the kinematic solution method for the dexterous finger parallel mechanism.

[0097] This disclosure also provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the kinematic calculation method for the dexterous finger parallel mechanism described in the above-described method embodiments. The storage medium can be either volatile or non-volatile computer-readable storage.

[0098] This disclosure also provides a computer program product, which includes computer instructions. When the computer instructions are executed by a processor, they can perform the steps of the kinematic calculation method for the dexterous finger parallel mechanism described in the above method embodiments. For details, please refer to the above method embodiments, which will not be repeated here.

[0099] The aforementioned computer program product can be implemented through hardware, software, or a combination thereof. In one optional embodiment, the computer program product is specifically embodied in a computer storage medium; in another optional embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0100] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this disclosure, it should be understood that the disclosed device and method can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection may be through some communication interfaces; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms.

[0101] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0102] In addition, the functional units in the various embodiments of this disclosure can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0103] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0104] Finally, it should be noted that the above-described embodiments are merely specific implementations of this disclosure, used to illustrate the technical solutions of this disclosure, and not to limit it. The protection scope of this disclosure is not limited thereto. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this disclosure. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure, and should all be covered within the protection scope of this disclosure. Therefore, the protection scope of this disclosure should be determined by the protection scope of the claims.

Claims

1. A kinematic solution method for a dexterous finger parallel mechanism, characterized in that, The method, applied to parallel mechanism configurations that use two non-intersecting cross hinges instead of ball hinges, comprises: Obtain the target drive rod length of the parallel mechanism, preprocess the target drive rod length according to the structural symmetry of the parallel mechanism, and determine the target length parameter; Initialize the joint angle guess value, and initialize the current drive rod length based on the joint angle guess value. Perform inverse kinematics calculation based on the current joint angle to determine the current drive rod length corresponding to the current joint angle. An error vector is constructed based on the difference between the current drive rod length and the target length parameter, and it is determined whether the error vector satisfies the preset convergence condition. When the error vector does not meet the preset convergence condition, the Jacobian matrix at the current joint angle is calculated based on the finite difference method, and the guessed value of the joint angle is iteratively updated according to the Jacobian matrix and the error vector. When the error vector satisfies the preset convergence condition, the joint angles obtained by iteration are recovered according to the structural symmetry, and the forward kinematic solution of the parallel mechanism is output.

2. The method according to claim 1, characterized in that, Obtain the target drive rod length of the parallel mechanism, and preprocess the target drive rod length according to the structural symmetry of the parallel mechanism, specifically including: Determine the lengths of the first target drive rod and the second target drive rod in the parallel mechanism; When the length of the first target drive rod is greater than the length of the second target drive rod, the lengths of the first target drive rod and the second target drive rod are swapped, and a symmetry flag is set. When the length of the first target drive rod is not greater than the length of the second target drive rod, the original target drive rod length remains unchanged.

3. The method according to claim 1, characterized in that, Perform inverse kinematics calculations based on the current joint angle to determine the current drive rod length corresponding to the current joint angle, specifically including: Construct the joint rotation matrix corresponding to the current joint angle; Based on the joint rotation matrix, base-side connection point parameters, moving platform-side connection point parameters, and joint height parameters, calculate at least two sets of link vector positions. Calculate the corresponding link length constraint based on the cross hinge offset length and the initial link length; The current drive rod length is calculated based on the link vector position and the link length constraint.

4. The method according to claim 1, characterized in that, An error vector is constructed based on the difference between the current drive rod length and the target length parameter, and it is determined whether the error vector satisfies a preset convergence condition, specifically including: Calculate the length difference between the current drive rod length and the target length parameter; An error vector is constructed based on the length differences described above; Determine whether the absolute value of each component in the error vector is less than a preset convergence accuracy threshold; If yes, then the preset convergence condition is satisfied; if no, then the preset convergence condition is not satisfied.

5. The method according to claim 1, characterized in that, The Jacobian matrix at the current joint angle is calculated using the finite difference method, specifically including: Positive and negative disturbances are applied to the first joint angle in the lateral direction and the second joint angle in the longitudinal direction of the target drive rod in the parallel mechanism, respectively. Inverse kinematics calculations were performed under each disturbance condition to obtain the length of the driving rod after disturbance. Based on the change in drive rod length before and after the disturbance and the disturbance step size, calculate each element of the Jacobian matrix. For any joint angle variable, take the calculated drive rod length when the joint angle variable is increased by a preset difference step size and the calculated drive rod length when the preset difference step size is decreased. Determine the corresponding partial derivative based on the ratio of the difference between the two to the preset difference step size.

6. The method according to claim 1, characterized in that, The joint angle guess value is iteratively updated based on the Jacobian matrix and the error vector, specifically including: The joint angle correction is obtained based on the Jacobian matrix and the error vector. The joint angle correction amount is multiplied by a preset step size factor and used as the actual update amount for this iteration. The current joint angle guess value is corrected using the actual update amount to obtain the joint angle guess value for the next iteration.

7. The method according to claim 2, characterized in that, Based on the structural symmetry, the joint angles obtained through iteration are recovered, and the forward kinematic solution of the parallel mechanism is output, specifically including: With the symmetry flag set, the sign of at least one joint angle obtained iteratively is restored. Without setting the symmetry flag, the joint angles obtained through iteration are directly output as the forward kinematics solution.

8. A kinematic calculation device for a dexterous finger parallel mechanism, characterized in that, include: The data preprocessing module is used to obtain the target drive rod length of the parallel mechanism, preprocess the target drive rod length according to the structural symmetry of the parallel mechanism, and determine the target length parameter. The data initialization module is used to initialize the joint angle guess value, initialize the current drive rod length based on the joint angle guess value, perform inverse kinematics calculation based on the current joint angle, and determine the current drive rod length corresponding to the current joint angle. The Newton iteration loop module is used to construct an error vector based on the difference between the current drive rod length and the target length parameter, and to determine whether the error vector satisfies the preset convergence condition. The Jacobian matrix construction module is used to calculate the Jacobian matrix at the current joint angle based on the finite difference method when the error vector does not meet the preset convergence condition, and to iteratively update the guessed value of the joint angle according to the Jacobian matrix and the error vector. The solution module is used to recover the joint angles obtained by iteration based on the structural symmetry when the error vector satisfies the preset convergence condition, and output the forward kinematic solution of the parallel mechanism.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the kinematic calculation method for the dexterous finger parallel mechanism as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the kinematic calculation method for the dexterous finger parallel mechanism as described in any one of claims 1 to 7.

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