Parameter optimization method and bionic control system based on orthogonal axis parallel device

Abstract

The application provides a parameter optimization method and a bionic control system based on an orthogonal axis parallel device, and belongs to the technical field of robot joints and bionic motion mechanisms, and the method comprises the following steps: establishing an orthogonal axis parallel mechanism mathematical model; taking the human hip joint motion range as the reference, a multi-objective optimization model of the orthogonal axis parallel mechanism mathematical model is established; the multi-objective optimization model is solved to obtain the optimal solution of the to-be-optimized parameters of the orthogonal axis parallel mechanism mathematical model; the optimal solution is used to generate positive kinematics training data; the positive kinematics training data is used to train the pulse neural network of a pulse neural network positive kinematics controller; and the trained pulse neural network is deployed in the pulse neural network positive kinematics controller. The system of the application is controlled by using the pulse neural network positive kinematics controller. The method of the application overcomes the limitation of single-objective optimization, and the system of the application improves the load and motion capacity.

Description

Technical Field

[0001] This invention belongs to the technical field of robot joints and bionic motion mechanisms, specifically relating to a parameter optimization method and a bionic control system based on an orthogonal axis parallel device. Background Technology

[0002] The biomimetic design of humanoid robot lower limbs is typically based on the human hip joint. The human hip joint is a ball-and-socket joint with three rotational degrees of freedom (flexion / extension, abduction / inversion, and rotation). Its movement is driven by multiple muscles working together, exhibiting high load-bearing capacity, high flexibility, and high stability. Traditional robot hip joints often employ a tandem configuration. While this simplifies kinematics, it suffers from low stiffness, poor dynamic performance, torque concentration on a single actuator, and error accumulation.

[0003] Spherical parallel mechanisms (SPMs) are widely used in robot joint design due to their advantages such as compact structure, high stiffness, strong load-bearing capacity, and low error accumulation. In particular, the three-degree-of-freedom orthogonal-axis spherical parallel mechanism (3-RRR Orthogonal-axis SPM, OSPM), with its orthogonal arrangement of drive axes, facilitates compactness and lightweight design. However, existing coaxial SPM mechanisms still have shortcomings in terms of workspace, dexterity, and singularity avoidance, making it difficult to fully meet the motion requirements of humanoid hip joints.

[0004] While existing research has explored the kinematics, workspace, and optimization design of SPMs to some extent, systematic parameter optimization methods for OSPMs, which are asymmetric, orthogonal-axis, and need to adapt to the movement characteristics of the human hip joint, are still lacking. In particular, a complete and efficient design system has not yet been formed for the synergistic optimization among multiple objectives (such as workspace coverage, dexterity, and torque requirements).

[0005] Furthermore, solving the forward kinematics of parallel mechanisms is a core challenge in real-time control. Unlike inverse kinematics, which can directly yield analytical solutions, forward kinematics requires solving multiple nonlinear constraint equations simultaneously, resulting in an octet equation after elimination. According to existing theories, there is no universal root-finding formula for algebraic equations of degree five and above, thus making analytical solutions impossible and requiring iterative numerical methods. The commonly used Newton-Raphson iterative method suffers from initial value sensitivity and lack of convergence guarantee, typically requiring 5 to 100 iterations to converge, with a single solution time of 0.5 to 10 ms, and each iteration involves highly complex operations such as inverting the Jacobian matrix. For high-dynamic motion control of the hip joint of humanoid robots, the control cycle is typically required to be 1 to 5 ms. The solution time and uncertainty of traditional numerical methods are insufficient to meet real-time requirements, and excessive iterations lead to high CPU (Central Processing Unit) utilization, high power consumption, and increased control latency, which in turn causes a decline in closed-loop control performance and reduced system stability. Therefore, there is an urgent need for a method for solving forward kinematics that is computationally efficient, has strong real-time performance, and low power consumption. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a parameter optimization method and a biomimetic control system based on an orthogonal axis parallel device. This method maximizes the workspace, optimizes dexterity, and minimizes driving torque while satisfying the range of motion of the human hip joint. Simultaneously, it achieves efficient forward kinematic control through a spiking neural network, thereby improving the motion performance and load-bearing capacity of the humanoid robot's lower limbs.

[0007] In a first aspect, the present invention provides a parameter optimization method based on an orthogonal axis parallel device, comprising:

[0008] A mathematical model of an orthogonal axis parallel mechanism is established, with the joint axes of the first active link, the second active link, and the third active link as the axes of the proximal joints, the joint axis of the first passive link connected by a revolute joint as the axis of the intermediate joints, and the axis of the revolute joint connected to the first passive link and the moving platform as the axis of the end joints.

[0009] A multi-objective optimization model for the mathematical model of the orthogonal axis parallel mechanism is established with reference to the range of motion of the human hip joint.

[0010] Solve the multi-objective optimization model to obtain the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism;

[0011] Generate forward kinematics training data using the optimal solution;

[0012] The spiking neural network of the positive kinematics controller is trained using positive kinematics training data.

[0013] The trained spiking neural network is deployed in the spiking neural network forward kinematics controller.

[0014] The multi-objective optimization model includes: an objective function for workspace coverage, an objective function for mechanism dexterity index, and an objective function for maximum driving torque.

[0015] The objective function for workspace coverage is constructed as follows:

[0016] Discretize the range of motion of the human hip joint to obtain Discretized joint space points;

[0017] The hip joint pose is calculated for each joint space point, and the inverse kinematics solution (OSPM) is performed using the hip joint pose to obtain the number of discrete points in the inverse kinematics solution. ;

[0018] Based on the number of discrete points in the inverse kinematics solution The ratio of the workspace coverage to the joint space points yields the objective function for workspace coverage.

[0019] The objective function for the mechanism dexterity index is constructed as follows:

[0020] Based on the mathematical model of the orthogonal axis parallel mechanism, the Jacobian matrix is ​​obtained;

[0021] The dexterity is obtained by taking the reciprocal of the condition number of the Jacobian matrix;

[0022] The average of the minimum and maximum values ​​of dexterity within the workspace is taken to characterize the dexterity of the orthogonal axis parallel mechanism body, thus obtaining the objective function of the mechanism dexterity index.

[0023] The objective function for the maximum driving torque is constructed as follows:

[0024] The input shaft torque is obtained based on the Jacobian matrix and the load torque.

[0025] Construct the objective function for the maximum driving torque based on the maximum value of the torque of all input axes within the workspace.

[0026] The parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism are: the structural angle of the driving link. Structural angle of the follower linkage The semi-cone angle of the static platform and the distribution angles of each branch after projection Among them, the structural angle of the drive link , representing the joint axis vectors of the first, second, and third active links. The joint axis vector connected to the first passive link via a revolute joint The included angle; the structural angle of the follower link. , representing the joint axis vector of the first passive link connected by a revolute joint. The axis of the rotary joint connected to the first passive link and the moving platform is the axis vector of the end joint. The included angle; the semi-cone angle of the static platform , representing the joint axis vector of the first passive link connected by a revolute joint. and The included angle; the distribution angle of each branch after projection. This represents the angle of distribution of each branch after projecting the static platform onto a horizontal plane. , Each branch includes: the first branch is composed of a first active link, a first passive link and a moving platform; the second branch is composed of two active links, a second passive link and a moving platform; and the third branch is composed of a third active link, a third passive link and a moving platform.

[0027] The solution to the multi-objective optimization model, which yields the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism, includes:

[0028] The workspace coverage, mechanism dexterity, and maximum driving torque were normalized to obtain positive and negative indicators.

[0029] Based on the design requirements of the humanoid robot's hip joint, the weights of workspace coverage, mechanism dexterity index, and maximum driving torque are determined respectively.

[0030] A weighted decision matrix is ​​constructed based on the weights of positive indicators, negative indicators, workspace coverage, mechanism dexterity indicators, and maximum driving torque.

[0031] Based on the weighted decision matrix, determine the positive ideal solution and the negative ideal solution in each solution set;

[0032] Determine the distance between the positive and negative ideal solutions based on the positive and negative ideal solutions.

[0033] Based on the positive and negative ideal solution distances, the relative closeness of each angle optimization scheme to the ideal solution is determined, where each solution set corresponds to one angle optimization scheme.

[0034] The NSGA-III algorithm (Non-dominated Sorting Genetic Algorithm III) was used to solve the multi-objective optimization model. After multiple iterations, the Pareto optimal solution set was obtained.

[0035] In the Pareto optimal solution set, all relative proximity degrees are calculated and sorted from highest to lowest. The second sorted result is selected as the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism.

[0036] The step of generating positive kinematics training data using the optimal solution includes: uniformly sampling motor angles based on the optimal solution, combining the uniformly sampled motor angles, and using numerical methods to solve the positive kinematics using the combined motor angles to obtain the corresponding end pose, thereby constructing the positive kinematics training data.

[0037] The spiking neural network employs a multi-layer feedforward structure, including:

[0038] The input layer includes three groups of neurons, each corresponding to an angle signal of a motor encoder. The angle signal of the motor encoder is converted into a pulse sequence by using a time encoding method, and the pulse sequence is used as the angle signal of the motor encoder. Each group of neurons contains multiple encoding neurons.

[0039] First hidden layer: includes a 2M leak-integrated triggering neuron model;

[0040] The second hidden layer consists of M leak-integrated triggering neuron models.

[0041] Output layer: consists of 3 neurons, each corresponding to the terminal pose in one direction;

[0042] The spiking neural network is trained using a backpropagation method with alternative gradients. In this method, the gradient function is replaced by the arctan function, and the loss function of the spiking neural network is a total loss function constructed by combining mean squared error loss and pulse sparsity regularization.

[0043] Secondly, the present invention provides a biomimetic control system based on an orthogonal axis parallel device, comprising:

[0044] The orthogonal axis parallel mechanism body includes: a first active link, a second active link, a third active link, a first passive link, a second passive link, a third passive link, and a moving platform;

[0045] The motor encoder is used to collect the joint angles of the first active link, the second active link, and the third active link in real time.

[0046] The spiking neural network positive kinematics controller deploys a spiking neural network trained in the first aspect to calculate the real-time end-effector pose based on the joint angles of the first, second, and third active links; and controls the body of the orthogonal axis parallel mechanism based on the real-time end-effector pose.

[0047] The end-effector pose output interface is used to transmit real-time end-effector pose to the upper-level control system.

[0048] Beneficial effects:

[0049] This application proposes a parameter optimization method and a biomimetic control system based on orthogonal axis parallel devices. Systematic optimization: For the first time, a multi-objective collaborative optimization method covering workspace, dexterity, and torque is proposed for asymmetric orthogonal axis 3-RRR parallel mechanisms, overcoming the limitations of single-objective optimization. High biomimetic fit: Based on the range of motion of the human hip joint, the optimized mechanism better conforms to human kinematics, improving the naturalness and adaptability of robot movement. Balanced and superior performance: Through Pareto front and multi-attribute decision-making, parameter combinations that perform excellently on multiple key indicators are obtained, achieving overall performance improvement. Brain-like control: A spiking neural network is used to solve the forward kinematics, simulating the information processing mode of the biological nervous system, achieving efficient event-driven computation. Ultra-low power consumption: The SNN controller operates on neuromorphic hardware with extremely low power consumption, suitable for portable exoskeletons and long-endurance robots. Strong real-time performance: The parallel computing characteristics of the spiking neural network result in a forward kinematics inference latency of less than 1ms, meeting the requirements of high-dynamic motion control. Highly practical for engineering applications: The optimization method combines evolutionary algorithms and decision theory, with a clear process and strong operability, making it suitable for the design and improvement of actual robot joints. Significantly improves load-bearing and motion capabilities: The optimized mechanism, while maintaining a compact structure, achieves a large workspace, high dexterity, and low torque requirements, significantly improving the walking stability, load-bearing capacity, and dynamic performance of humanoid robots' lower limbs. Attached Figure Description

[0050] Figure 1 Flowchart of a parameter optimization method based on an orthogonal axis parallel device according to an embodiment of the present invention;

[0051] Figure 2 A schematic flowchart of a parameter optimization method based on an orthogonal axis parallel device according to an embodiment of the present invention;

[0052] Figure 3 A schematic diagram of the biomimetic control process of the SNN-based 3-RRR orthogonal axis parallel device according to an embodiment of the present invention;

[0053] Figure 4 The TOPSIS multi-objective decision-making with custom weights in this embodiment of the invention obtains a score ranking graph;

[0054] Figure 5 A schematic diagram of the Pareto optimal solution set in an embodiment of the present invention;

[0055] Figure 6A simplified model diagram of the 3-RRR orthogonal axis parallel mechanism according to an embodiment of the present invention;

[0056] Figure 7 Overall optimized diagram of the 3-RRR orthogonal axis parallel mechanism according to an embodiment of the present invention;

[0057] Figure 8 A schematic diagram of a humanoid robot hip joint model with optimized parameters according to an embodiment of the present invention;

[0058] Among them, 1-first active link, 2-first passive link, 3-moving platform, 4-second passive link, 5-second active link, 6-third active link, and 7-third passive link. Detailed Implementation

[0059] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0060] Example 1:

[0061] This embodiment provides a parameter optimization method based on an orthogonal axis parallel device, such as... Figure 1 , Figure 2 , Figure 3 As shown, it includes:

[0062] Step S1: Establish a mathematical model of the orthogonal axis parallel mechanism by taking the joint axes of the first active link, the second active link and the third active link as the axis of the proximal joint, the joint axis of the first passive link connected by the revolute joint as the axis of the intermediate joint, and the revolute joint axis of the first passive link and the moving platform as the axis of the end joint.

[0063] In this embodiment, a mathematical model of the orthogonal axis parallel mechanism is first established, specifically a mathematical model of the 3-RRR orthogonal axis parallel mechanism:

[0064] (1) Define the names and symbols of each variable: The joint axis vectors of the first active link, the second active link, and the third active link are defined as follows: ( ), called the proximal joint axis, the other end of which is connected to the first passive rod (bending radius is The joint axis vector of the connection is defined as follows: These are called intermediate joint axes, and together they form a branch. The rotational joint axis vector connecting the first passive link and the moving platform is defined as... This is called the end joint axis, the structural angle of the drive link. , representing a unit vector and The included angle; the structural angle of the follower link. , representing a unit vector and The included angle; the semi-cone angle of the static platform , representing a unit vector and The included angle; projecting the static platform onto the horizontal plane, the distribution angles of each branch after projection are represented by parameters. ( )express, This refers to the rotation angle of the moving platform in all directions.

[0065] (2) Establish the inverse kinematics model:

[0066] Unit vector ( () represents the vector of the intermediate joint axis, which can be obtained from the input angle. have to:

[0067] (1);

[0068] in, Indicates about the axis Rotation angle The rotation transformation matrix. Unit vector. ( The axis () represents the axis of the rotary joint connected to the moving platform, and its orientation is related to the moving platform's attitude. Euler angles are used. Rotation transformation matrix of the sequence To describe the attitude of the moving platform:

[0069] (2);

[0070] (3);

[0071] in, ( () represents the unit vector along the axis of the rotational joint connected to the moving platform when the moving platform is in its initial pose.

[0072] (4);

[0073] ( The projection on the moving platform is denoted as ,in for:

[0074] (5);

[0075] Rotation axis unit vector , To satisfy the institutional closed-chain constraint:

[0076] , (6);

[0077] in, It can be obtained using the Law of Cosines of the Spherical Surface:

[0078] (7);

[0079] Taking the first link as an example, in equation (1) Substituting (6), we get:

[0080] (8);

[0081] (8) Expanding the left side, we get:

[0082] (9);

[0083] To obtain the motor angle ,make:

[0084] (10);

[0085] in, This refers to the motor angle data of motor encoder 1 for motor 1. The unknown variable is assumed (a half-width formula is used here, transforming sin and cos into an unknown variable). It is understood that in this embodiment, each active link requires a motor for control, and each motor includes a motor encoder to obtain the motor angle of the corresponding active link.

[0086] Substituting equation (10) into equation (9), we obtain the equation describing the reverse motion of the first branch of the mechanism. The quadratic equation of :

[0087] (11);

[0088] in:

[0089] (12);

[0090] in, As the first intermediate parameter, As the second intermediate parameter, This is the third intermediate parameter.

[0091] Solving equation (11) yields the input angle:

[0092] (13);

[0093] Similarly, for other branches, their quadratic equations can be obtained, and the corresponding solutions can be found. The overall solution can be expressed as:

[0094] , (14);

[0095] (3) Singularity analysis:

[0096] Since this mechanism has eight configurations, when the mechanism changes from one configuration to another, there must be a chain that passes through a position where the driving link and the driven link are collinear. , , The three vectors are coplanar, where, The joint axis vector of the i-th active link. Let be the axis vector of the i-th rotary joint connecting the first passive link and the moving platform. Let be the axis vector of the i-th joint connected by the first passive link through a revolute joint. At this point, the mechanism reaches a singular configuration. Therefore, within the workspace (which is the attitude angles in the three directions reachable by the orthogonal parallel axis device), it is necessary to limit... The sign remains unchanged, thus confining the mechanism to the same configuration. The specific formula is as follows:

[0097] (15);

[0098] At the same time, the study found that when , and When the connecting rod is coplanar, its input shaft reaches the middle position. Due to errors in assembly and machining accuracy, the moving platform will also exhibit a singular shape at this point, which is called an error singularity point and needs to be controlled. Greater than or equal to 0.05. Therefore, the following must be ensured within the workspace:

[0099] (16);

[0100] in, for ( () represents the projection onto the moving platform. for Projection on the moving platform for Projection on the moving platform for Projection on the moving platform As the first control rule, This is the second control rule. This is the third control rule. This is the fourth control rule. This is the fifth control rule. This is the sixth control rule.

[0101] (4) Constructing the Jacobian matrix:

[0102] The velocity Jacobian matrix of the mechanism can be obtained by differentiating both sides of the first equation (6):

[0103] , (17);

[0104] in, for The derivative of for The derivative of .

[0105] , (18);

[0106] , (19);

[0107] in: Indicates the angular velocity of the moving platform. To represent the driving angular velocity at a specific input angle, equation (17) can be further written as:

[0108] , (20);

[0109] After rearranging the above formula, we get:

[0110] (twenty one);

[0111] in:

[0112] (twenty two);

[0113] in, It is represented as a diagonal matrix, where T is the transpose of the corresponding matrix. For process matrix, Diagonal matrix.

[0114] Jacobian matrix It can be represented as:

[0115] (twenty three);

[0116] The dexterity analysis of parallel mechanisms is directly related to their kinematic Jacobian matrix. Dexterity is defined as the ability of the SPM (Short-range Partition Machine) to provide a wide range of orientations for its end effector. It is defined as follows: using the reciprocal of the condition number of the Jacobian matrix—a local performance index—as the LDI (Local Dexterity Index), it measures the mechanism's flexible and precise motion capability within a small space. It is a more "advanced" dynamic performance index than workspace volume in the optimization design of parallel mechanisms. An operability index reflecting the dexterity motion capability of the OSPM can be defined, namely:

[0117] (twenty four);

[0118] in, The Euclidean norm of a matrix. For Jacobian matrices, The condition number of the Jacobian matrix is ​​closer to zero, indicating that the mechanism is closer to a singular configuration. LDI is the local dexterity index.

[0119] Step S2: Using the range of motion of the human hip joint as a reference, establish a multi-objective optimization model for the mathematical model of the orthogonal axis parallel mechanism;

[0120] In this embodiment, taking the range of motion of the human hip joint as a reference, as shown in Table 1, a multi-objective optimization model for the mathematical model of the orthogonal axis parallel mechanism is established, including: the objective function of workspace coverage, the objective function of mechanism dexterity index, and the objective function of maximum driving torque.

[0121] Table 1: Common Range of Motion of the Human Hip Joint;

[0122] ;

[0123] The objective function for workspace coverage is constructed as follows:

[0124] Step S2.1.1: Discretize the range of motion of the human hip joint to obtain... Discretized joint space points;

[0125] Step S2.1.2: Calculate the hip joint pose for each joint space point, and use the hip joint pose to perform inverse kinematics on the OSPM to obtain the number of discrete points in the inverse kinematics solution. ;

[0126] Step S2.1.3: Based on the number of discrete points in the inverse kinematics solution The ratio of the workspace coverage to the joint space points yields the objective function for workspace coverage.

[0127] In this embodiment, the first objective function is the workspace coverage, which is appropriately larger for the functional range of motion of the human hip joint, calculated by step length. Discretize it to obtain The system uses discrete joint space points. For each discrete point, the hip joint pose is calculated, and the inverse kinematics of the OSPM is derived using this pose. Due to the characteristics of parallel mechanisms, only a finite number of discrete points can yield the inverse kinematics of the mechanism; therefore, the number of discrete points for the inverse kinematics solution is limited. This represents the extent to which the organization's workspace covers the human shoulder joint's workspace. Therefore, the following workspace coverage index is defined to measure the size of the organization's workspace relative to the human shoulder joint's workspace:

[0128] (25);

[0129] in, This represents the number of points in the discretized joint space. The number of discrete points in the inverse kinematics solution. The objective function is the workspace coverage rate.

[0130] The objective function for the mechanism dexterity index is constructed as follows:

[0131] Step S2.2.1: Obtain the Jacobian matrix based on the mathematical model of the orthogonal axis parallel mechanism;

[0132] Step S2.2.2: Obtain the dexterity based on the reciprocal of the condition number of the Jacobian matrix;

[0133] Step S2.2.3: Take the average of the minimum and maximum values ​​of dexterity within the workspace to characterize the dexterity of the orthogonal axis parallel mechanism body, and obtain the objective function of the mechanism dexterity index.

[0134] In this embodiment, the second objective function is the dexterity of the mechanism, which is defined using LDI in equation (37). To describe the dexterity of the mechanism throughout the workspace, the average of the minimum and maximum operability indices within the workspace is selected to represent the overall dexterity of the mechanism. The larger the minimum value, the better the overall dexterity within the workspace.

[0135] (25);

[0136] in, Let be the objective function for the mechanism dexterity index. Let be the number of discrete points in the inverse kinematics solution, where each inverse kinematics solution corresponds to an LDI. The dexterity of the entire mechanism is represented by the average of the minimum and maximum values ​​of the operability index within the workspace.

[0137] The objective function for the maximum driving torque is constructed as follows:

[0138] Step S2.3.1: Obtain the input shaft torque based on the Jacobian matrix and the load torque;

[0139] In this embodiment, under the same end load, the input torque requirements for different mechanism parameters are different. Therefore, it is necessary to estimate the maximum torque requirement of the input shaft of the shoulder joint mechanism. Under static equilibrium conditions, the torque of the input shaft can be obtained by the following formula:

[0140] (26);

[0141] in, The load torque can be determined by applying a certain load force in the sagittal plane from the zero position. It is a Leyakubi matrix. The input shaft torque is .

[0142] Step S2.3.2: Based on the maximum value of the torque of all input axes within the workspace, construct the objective function for the maximum driving torque. The third objective function can be expressed as:

[0143] (27);

[0144] in, The objective function is the maximum driving torque. For the first The first motor Input axial torque at discrete points Represents three motors. Indicates the first motor. The discrete point numbers representing the inverse kinematics solution, up to... .

[0145] Finally, the constraints of the multi-objective optimization model of the orthogonal axis parallel mechanism are set:

[0146] When performing multi-objective optimization, it is necessary to restrict... The sign remains unchanged, thus confining the mechanism to the same configuration. The specific constraints are as follows:

[0147] (28);

[0148] It is also necessary to control Greater than or equal to 0.05. Therefore, another constraint is:

[0149] (29);

[0150] To make the motion space of this mechanism closer to the human leg hip joint, the posture angle of the working space platform of this mechanism is constrained. The angle must be greater than or equal to 45 degrees.

[0151] (30);

[0152] Step S3: Solve the multi-objective optimization model to obtain the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism;

[0153] In this embodiment, the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism are: the structural angle of the driving link. Structural angle of the follower linkage The semi-cone angle of the static platform and the distribution angles of each branch after projection Among them, the structural angle of the drive link , representing the joint axis vectors of the first, second, and third active links. The joint axis vector connected to the first passive link via a revolute joint The included angle; the structural angle of the follower link. , representing the joint axis vector of the first passive link connected by a revolute joint. The axis of the rotary joint connected to the first passive link and the moving platform is the axis vector of the end joint. The included angle; the semi-cone angle of the static platform , representing the joint axis vector of the first passive link connected by a revolute joint. and The included angle; the distribution angle of each branch after projection. This represents the angle of distribution of each branch after projecting the static platform onto a horizontal plane. , .

[0154] The solution to the multi-objective optimization model, which yields the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism, includes:

[0155] Step S3.1: Normalize the workspace coverage, mechanism dexterity index, and maximum driving torque respectively to obtain positive and negative indices;

[0156] In this embodiment, the TOPSIS algorithm with custom weights is used to analyze the above-mentioned multi-objective decision problem.

[0157] First, the three target values ​​(workspace, maximum torque, and local dexterity) are normalized. The positive index is:

[0158] (31);

[0159] Negative indicators are:

[0160] (32);

[0161] in: For the first The solution is the first The normalized target sequence values ​​of each optimization objective; For the first The solution is the first Unprocessed target sequence values ​​for each optimization objective; The minimum value in the target sequence; is the maximum value of the target sequence, where , The number of solutions, , To optimize the number of targets.

[0162] Step S3.2: Based on the design requirements of the humanoid robot's hip joint, determine the weights of the workspace coverage, mechanism dexterity index, and maximum driving torque, respectively;

[0163] In this embodiment, the weights of each evaluation index are determined. According to the design requirements of the humanoid robot's hip joint, the size of the workspace determines the range of motion of the humanoid robot's hip joint, which is more important than the maximum joint torque, while the operability index is generally important. The weight design is shown in Table 2.

[0164] Table 2: Weights of each evaluation indicator;

[0165] ;

[0166] Step S3.3: Construct a weighted decision matrix based on the weights of positive indicators, negative indicators, workspace coverage, mechanism dexterity indicators, and maximum driving torque;

[0167] In this embodiment, a weighted decision matrix is ​​constructed, and the formula for calculating the weighted decision matrix is ​​as follows:

[0168] (33);

[0169] in, The first in the weighted matrix Line 1 Column elements, For the first The weights of workspace coverage, mechanism dexterity, or maximum driving torque for each optimization objective.

[0170] Step S3.4: Determine the positive ideal solution and the negative ideal solution based on the weighted decision matrix;

[0171] In this embodiment, positive and negative ideal solutions are determined:

[0172] (34);

[0173] in, and These represent the positive ideal solution set and the negative ideal solution set, respectively.

[0174] Step S3.5: Determine the distance between the positive ideal solution and the negative ideal solution based on the positive ideal solution and the negative ideal solution;

[0175] In this embodiment, the ideal solution distance is determined, where positive ideal refers to the optimal value of each index (maximum working space, maximum operability index), and negative ideal refers to the worst value of each index.

[0176] Distance to the ideal solution:

[0177] (35);

[0178] Distance to the negative ideal solution:

[0179] (36);

[0180] in, and The first The distance between the optimized solution from each angle and the positive and negative ideal solutions.

[0181] Step S3.6: Based on the positive ideal solution distance and the negative ideal solution distance, determine the relative closeness of each angle optimization scheme to the ideal solution, wherein each solution set corresponds to one angle optimization scheme;

[0182] In this embodiment, it can be understood that: because the result obtained from multi-objective optimization is as follows Figure 5 As shown, there are multiple solution sets, each corresponding to a different angle of optimization. The relative closeness of each optimization scheme to the ideal solution is determined.

[0183] (37);

[0184] in, For the first The closer the optimization scheme is to the value of 1, the better the evaluation effect of the scheme.

[0185] Step S3.7: Use the NSGA-III algorithm to solve the multi-objective optimization model. After multiple iterations, obtain the Pareto optimal solution set.

[0186] The design variables for the new OSPM are The multi-objective optimization problem can be described as follows:

[0187] (38);

[0188] (39);

[0189] The range of values ​​for the designed variables is shown in Table 3.

[0190] Table 3. Range of values ​​for multi-objective optimization design variables;

[0191] ;

[0192] Step S3.8: In the Pareto optimal solution set, calculate all relative proximity degrees and sort all relative proximity degrees from highest to lowest. Select the second sorted result as the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism.

[0193] In this embodiment, after multiple iterations, a set of Pareto optimal solutions is obtained as follows: Figure 5 As shown, each point represents three optimization objective values ​​corresponding to a set of solutions, and these solutions form the Pareto front.

[0194] Workspace metrics The theoretical optimal value is −1, the dexterity index and maximum joint torque The smaller the better. It's clear from the Pareto chart that it's impossible to find a point that simultaneously satisfies the requirements of maximum workspace, maximum operability index, and minimum maximum joint torque. To find the optimal solution, a score ranking chart is obtained through TOPSIS multi-objective decision-making with custom weights, as shown below. Figure 4 As shown. The Pareto solution set corresponding to the highest score is the optimal decision solution. However, due to the size constraints of the parallel mechanism and the rationality of the mechanism, the second-ranked solution set is selected and verified as the optimal decision solution. The three optimization objective function values ​​of this solution are... The mechanism constructed using this parameter exceeds the range of motion of the human hip joint corresponding to Table 1. The workspace of this parameter can reach 50% of the ideal workspace. The average of the maximum and minimum values ​​of the operability index within the selected working point is at least 1.33, and the maximum output shaft torque is... The optimized mechanism parameters are shown in Table 4. The humanoid robot hip joint model designed based on these parameters is as follows. Figure 8As shown, where, Let be the rotation angle of the moving platform in the x-direction. The rotation angle of the moving platform in the z-direction is shown. The diagram illustrates the workspace for the Pitch and Roll rotation directions, where blue dots represent reachable attitude angles, red dots represent singular points, and green dots represent unreachable attitude angles. The first branch consists of a first active link, a first passive link, and the moving platform; the second branch consists of two active links, a second passive link, and the moving platform; and the third branch consists of a third active link, a third passive link, and the moving platform.

[0195] Table 4. Optimization results of OSPM mechanism parameters;

[0196] ;

[0197] Step S4: Generate forward kinematics training data using the optimal solution;

[0198] The step of generating positive kinematics training data using the optimal solution includes: uniformly sampling motor angles based on the optimal solution, combining the uniformly sampled motor angles, and using numerical methods to solve the positive kinematics using the combined motor angles to obtain the corresponding end pose, thereby constructing the positive kinematics training data.

[0199] In this embodiment, uniform sampling means assuming the motor angle is between -90° and 90°, sampling at 0.05° intervals. Due to the parallel mechanism, there are three motors, corresponding to three motor angles. These three uniformly sampled angle values ​​are combined. The numerical method is a numerical solution using Newton-Raphson iteration and pseudo-inverse matrices, which is existing technology and will not be elaborated further in this application. The motor in this embodiment includes a motor encoder.

[0200] Step S5: Use positive kinematics training data to train the spiking neural network of the positive kinematics controller;

[0201] Step S6: Deploy the trained spiking neural network in the spiking neural network forward kinematics controller;

[0202] In this embodiment, the optimal solution obtained in step S3 is used to generate forward kinematics training data. The forward kinematics training data is then used to train the spiking neural network of the forward kinematics controller. The trained spiking neural network is then deployed in the spiking neural network forward kinematics controller. Finally, the spiking neural network forward kinematics controller is used to control the orthogonal axis parallel mechanism body. The specific implementation process is as follows:

[0203] 1. Construction of a spiking neural network:

[0204] (1) System input layer design:

[0205] The control system receives angle signals from three motor encoders. As input, continuous angle values ​​are converted into a pulse sequence using time encoding:

[0206] (40);

[0207] in, The timing of the encoder pulse delivery for the motor. Let be the actual angle value of the i-th motor encoder (where is the actual angle value of the i-th motor encoder). There is a one-to-one correspondence between the encoder of the i-th motor and the encoder of the i-th motor. This is the minimum value of the encoding time window, which corresponds to the minimum angle of the motor. The pulse firing time of the time, This is the maximum value of the encoding time window, which corresponds to the maximum angle of the motor. The pulse firing time of the time, This is the minimum range value of the motor angle sensor (i.e., the lower limit of angle measurement). This is the maximum range value of the motor angle sensor (i.e., the upper limit of angle measurement).

[0208] (2) The Leaky Integrate-and-Fire neuron model (LIF, Leakage Integration Triggered Neuron Model) was adopted:

[0209] (41);

[0210] in, Membrane time constant, the characteristic time of membrane potential decay; Membrane potential, which is the physical difference between the inside and outside of the neuron's cell membrane, reflects the activation state of the neuron; This is the resting potential, the steady-state membrane potential of a neuron when there is no input. Membrane resistance is the equivalent resistance of the cell membrane, which affects the strength of the effect of the input current on the membrane potential. The input current is the weighted sum of input currents from the presynaptic neuron; when the membrane potential... Exceeding the threshold of membrane potential At that time, the neuron fires a pulse and resets: if , ;in, The target value for resetting the membrane potential after pulse delivery is used to reset the potential.

[0211] (3) Network structure design:

[0212] The SNN controller employs a multi-layer feedforward structure: Input layer: 3 groups of neurons (corresponding to three motor angles), each group containing N_enc encoding neurons; First hidden layer: 2M LIF neurons; Second hidden layer: M LIF neurons; Output layer: 3 neurons (corresponding to the 3 parameters of the end pose: In this embodiment, M is 64.

[0213] (4) Synaptic plasticity and learning rules:

[0214] Training is performed using an alternative gradient method based on backpropagation:

[0215] (42);

[0216] in, The loss function is the measure of error between the network output and the target value. Synaptic weights, from neurons To neurons The connection strength; For pulse output, neurons At any moment The pulse delivery status (0 or 1); For membrane potential, neuron At any moment The membrane potential value.

[0217] Due to the real pulse firing function The derivative of is a Dirac delta function, which cannot be used for gradient descent optimization. Therefore, a backpropagation method based on the surrogate gradient is used for training.

[0218] The arctan function is used as an alternative gradient:

[0219] (43);

[0220] 2. Training data generation and preprocessing:

[0221] (1) Generation of positive kinematic samples:

[0222] Based on the optimized mechanism parameters, motor angle combinations are uniformly sampled within the workspace, and the corresponding end-effector pose is obtained by solving the forward kinematics using numerical methods, thus constructing a training dataset.

[0223] (44);

[0224] in, For positive kinematic training data, This represents the total number of training samples. The sample index number, with values ​​ranging from 1, 2, 3… . For the first The end effector corresponding to each sample is in Pose components in direction (e.g.) Direction, position, coordinates, or orbit The orientation angle of the axis depends specifically on the mechanism's output parameters. For the first The end effector corresponding to each sample is in Pose components in the direction, For the first The end effector corresponding to each sample is in Pose components in the direction.

[0225] (2) Data normalization:

[0226] For input angle and end pose Perform Min-Max normalization:

[0227] (45);

[0228] in, This is one data point from the positive kinematic training data. This is the minimum value among the positive kinematic training data. This represents the maximum value in the positive kinematic training data. This is the normalized data.

[0229] The SNN controller outputs the normalized pose prediction value. It needs to be inversely normalized (inverse transform) to restore it to the actual physical quantity:

[0230] (46);

[0231] in, This represents the normalized pose prediction value output by the SNN controller. The pose prediction value is the result of inverse normalization. No. Each pose component ( Corresponding to The maximum value in the training dataset is used as the upper bound for scaling during denormalization. No. The minimum value of each pose component in the training dataset is used as the scaling lower bound during inverse normalization.

[0232] 3. Using positive kinematics training data, train the spiking neural network (SNN model training) of the positive kinematics controller:

[0233] (1) Definition of loss function:

[0234] Mean squared error loss combined with impulse sparsity regularization:

[0235] (47);

[0236] Where N is the number of samples, which is the number of samples in the current training batch; Predicting pose, the SNN controller for the first Normalized pose prediction output vector for each sample; True pose, number The normalized pose true value vector of each sample; Mean squared error, the squared Euclidean distance between the predicted pose and the true pose; The sparsity coefficient is... The average distribution rate of the l-th layer. This is the loss function.

[0237] (2) Training parameter settings:

[0238] Time step: T = 100; Learning rate: η = 0.001; Batch size: batch_size = 64; Number of training epochs: 500; Membrane potential time constant: = 10ms; Threshold voltage: = 1.0.

[0239] (3) Hardware deployment

[0240] After training, the SNN model is deployed to a neuromorphic chip or FPGA to achieve low-power real-time inference.

[0241] 4. A pulse neural network positive kinematics controller is used to control the body of the orthogonal axis parallel mechanism (i.e., real-time control and closed-loop feedback):

[0242] (1) Control Flow:

[0243] (a) The motor encoder collects the angles of the three joints in real time. ;

[0244] (b) The angle values ​​are converted into a pulse sequence via time encoding;

[0245] (c) Pulse sequence input spiking neural network positive kinematics controller;

[0246] (d) The output layer of the spiking neural network forward kinematics controller uses a pulse decoding module to convert the pulse sequence into continuous pose values ​​to obtain the end-effector pose output. In this embodiment, the position accuracy is <0.5mm and the pose accuracy is <0.1mm. The delay is less than 1ms.

[0247] (f) The end-effector pose output interface transmits pose information to the upper-level motion planning module.

[0248] (2) Real-time performance metrics:

[0249] Inference latency: < 1ms (neuromorphic hardware); Power consumption: < 100mW; Position accuracy: < 0.5mm; Attitude accuracy: < 0.1°.

[0250] Example 2:

[0251] This embodiment provides a biomimetic control system based on an orthogonal axis parallel device, such as Figure 6 , Figure 7 As shown, it includes:

[0252] The orthogonal axis parallel mechanism body includes: a first active link 1, a second active link 5, a third active link 6, a first passive link 2, a second passive link 4, a third passive link 7, and a moving platform 3;

[0253] The motor encoder is used to collect the joint angles of the first active link 1, the second active link 5, and the third active link 6 in real time.

[0254] A pulsed neural network positive kinematics controller is used to calculate the real-time end pose based on the joint angles of the first active link 1, the second active link 5, and the third active link 6.

[0255] The end-effector pose output interface is used to transmit real-time end-effector pose to the upper-level control system.

[0256] In this embodiment, the existing 3-RRR orthogonal axis parallel device is improved by adding a motor encoder, a spiking neural network positive kinematics controller, and an end-effector pose output interface. Specifically, the motor encoder collects the joint angles of the first active link 1, the second active link 5, and the third active link 6 in real time. The spiking neural network positive kinematics controller calculates the real-time end-effector pose based on the joint angles of these three links. The end-effector pose output interface transmits the real-time end-effector pose to the upper-level control system. The spiking neural network positive kinematics controller is a biomimetic control system design based on a spiking neural network (SNN). Specifically, based on biomimetic principles and using the range of motion of the human hip joint as a reference, a multi-objective optimization model is established, encompassing workspace coverage, mechanism dexterity, and driving torque requirements. An evolutionary algorithm and multi-attribute decision-making method are used to solve this model, resulting in a balanced and superior combination of mechanism parameters across multiple performance indicators—the optimal solution for the parameters to be optimized. The optimal solution is used to generate forward kinematics training data. This data is then used to train the spiking neural network (SNN) of the forward kinematics controller. The trained SNN is then deployed within the SNN forward kinematics controller. The SNN forward kinematics controller is used to control the orthogonal axis parallel mechanism, achieving efficient, low-power, and brain-like motion control. This embodiment aims to maximize the mechanism's workspace, optimize dexterity, and minimize driving torque while satisfying the range of motion of the human hip joint. Simultaneously, efficient forward kinematic control is achieved through the SNN, thereby improving the motion performance and load-bearing capacity of the humanoid robot's lower limbs.

[0257] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0258] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of equivalent technology of this disclosure, then the intent of this disclosure also includes such modifications and variations.

Claims

1. A parameter optimization method based on an orthogonal axis parallel device, characterized in that, include: A mathematical model of an orthogonal axis parallel mechanism is established, with the joint axes of the first active link, the second active link, and the third active link as the axes of the proximal joints, the joint axis of the first passive link connected by a revolute joint as the axis of the intermediate joints, and the axis of the revolute joint connected to the first passive link and the moving platform as the axis of the end joints. A multi-objective optimization model for the mathematical model of the orthogonal axis parallel mechanism is established with reference to the range of motion of the human hip joint. Solve the multi-objective optimization model to obtain the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism; The optimal solution is used to generate forward kinematics training data; The spiking neural network of the positive kinematics controller is trained using positive kinematics training data. The trained spiking neural network is deployed in the spiking neural network forward kinematics controller.

2. The parameter optimization method based on an orthogonal axis parallel device according to claim 1, characterized in that, The multi-objective optimization model includes: an objective function for workspace coverage, an objective function for mechanism dexterity index, and an objective function for maximum driving torque.

3. The parameter optimization method based on an orthogonal axis parallel device according to claim 2, characterized in that, The objective function for workspace coverage is constructed as follows: Discretize the range of motion of the human hip joint to obtain Discretized joint space points; The hip joint pose is calculated for each joint space point, and the inverse kinematics solution (OSPM) is performed using the hip joint pose to obtain the number of discrete points in the inverse kinematics solution. ; Based on the number of discrete points in the inverse kinematics solution The ratio of the workspace coverage to the joint space points yields the objective function for workspace coverage.

4. The parameter optimization method based on an orthogonal axis parallel device according to claim 2, characterized in that, The objective function for the mechanism dexterity index is constructed as follows: Based on the mathematical model of the orthogonal axis parallel mechanism, the Jacobian matrix is ​​obtained; The dexterity is obtained by taking the reciprocal of the condition number of the Jacobian matrix; The average of the minimum and maximum values ​​of dexterity within the workspace is taken to characterize the dexterity of the orthogonal axis parallel mechanism body, thus obtaining the objective function of the mechanism dexterity index.

5. The parameter optimization method based on an orthogonal axis parallel device according to claim 2, characterized in that, The objective function for the maximum driving torque is constructed as follows: The input shaft torque is obtained based on the Jacobian matrix and the load torque. Construct the objective function for the maximum driving torque based on the maximum value of the torque of all input axes within the workspace.

6. The parameter optimization method based on an orthogonal axis parallel device according to claim 1, characterized in that, The parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism are: the structural angle of the driving link, the structural angle of the follower link, the half-cone angle of the stationary platform, and the distribution angles of each branch after projection; where, the structural angle of the driving link represents the angle between the joint axis vectors of the first, second, and third driving links and the joint axis vector of the first driven link connected by a revolute joint; the structural angle of the follower link represents the angle between the joint axis vector of the first driven link connected by a revolute joint and the axis vector of the revolute joint connecting the first driven link and the moving platform (which is the end joint); the half-cone angle of the stationary platform represents the angle between the joint axis vector of the first driven link connected by a revolute joint and the joint axis vector of the first driven link connected by a revolute joint. The included angle; the distribution angle of each branch after projection, representing the distribution angle of each branch after the static platform is projected onto the horizontal plane. Each branch includes: the first branch is composed of the first active link, the first passive link and the moving platform; the second branch is composed of the second active link, the second passive link and the moving platform; and the third branch is composed of the third active link, the third passive link and the moving platform.

7. The parameter optimization method based on an orthogonal axis parallel device according to claim 1, characterized in that, The solution to the multi-objective optimization model, which yields the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism, includes: The workspace coverage, mechanism dexterity, and maximum driving torque were normalized to obtain positive and negative indicators. Based on the design requirements of the humanoid robot's hip joint, the weights of workspace coverage, mechanism dexterity index, and maximum driving torque are determined respectively. A weighted decision matrix is ​​constructed based on the weights of positive indicators, negative indicators, workspace coverage, mechanism dexterity indicators, and maximum driving torque. Based on the weighted decision matrix, determine the positive ideal solution and the negative ideal solution in each solution set; Determine the distance between the positive and negative ideal solutions based on the positive and negative ideal solutions. Based on the positive and negative ideal solution distances, the relative closeness of each angle optimization scheme to the ideal solution is determined, where each solution set corresponds to one angle optimization scheme. The NSGA-III algorithm was used to solve the multi-objective optimization model, and after multiple iterations, the Pareto optimal solution set was obtained. In the Pareto optimal solution set, all relative proximity degrees are calculated and sorted from highest to lowest. The second sorted result is selected as the optimal solution for the parameters to be optimized in the mathematical model of the orthogonal axis parallel mechanism.

8. The parameter optimization method based on an orthogonal axis parallel device according to claim 1, characterized in that, The step of generating positive kinematics training data using the optimal solution includes: uniformly sampling motor angles based on the optimal solution, combining the uniformly sampled motor angles, and using numerical methods to solve the positive kinematics using the combined motor angles to obtain the corresponding end pose, thereby constructing the positive kinematics training data.

9. The parameter optimization method based on an orthogonal axis parallel device according to claim 1, characterized in that, The spiking neural network employs a multi-layer feedforward structure, including: The input layer includes three groups of neurons, each corresponding to an angle signal of a motor encoder. The angle signal of the motor encoder is converted into a pulse sequence by using a time encoding method, and the pulse sequence is used as the angle signal of the motor encoder. Each group of neurons contains multiple encoding neurons. First hidden layer: includes a 2M leak-integrated triggering neuron model; The second hidden layer includes M leak-integrated triggering neuron models; Output layer: consists of 3 neurons, each corresponding to the terminal pose in one direction; The spiking neural network is trained using a backpropagation method that replaces the gradient. In this method, the gradient function in the backpropagation is replaced by the arctan function, and the loss function of the spiking neural network is a total loss function constructed by combining the mean squared error loss and the pulse sparsity regularization.

10. A biomimetic control system based on an orthogonal axis parallel device, wherein the parameter optimization method based on an orthogonal axis parallel device as described in any one of claims 1 to 9 is used for control, characterized in that, include: The orthogonal axis parallel mechanism body includes: a first active link, a second active link, a third active link, a first passive link, a second passive link, a third passive link, and a moving platform; The motor encoder is used to collect the joint angles of the first active link, the second active link, and the third active link in real time. The spiking neural network positive kinematics controller deploys a spiking neural network trained in the first aspect to calculate the real-time end-effector pose based on the joint angles of the first, second, and third active links; and controls the body of the orthogonal axis parallel mechanism based on the real-time end-effector pose. The end-effector pose output interface is used to transmit real-time end-effector pose to the upper-level control system.

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