Two-legged robot form optimization method based on metric index identification of variable additive grouping
By identifying additive grouping structures using metrics and employing the K-Means clustering algorithm, the problem of unstable grouping in bipedal robot morphology optimization was solved, achieving efficient and reliable optimization results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV
- Filing Date
- 2026-03-23
- Publication Date
- 2026-06-05
AI Technical Summary
Existing Bayesian optimization methods based on additive grouping structures are inaccurate and inefficient in bipedal robot morphology optimization, especially under limited evaluation budgets, where grouping evaluation bias and joint sampling complexity are high, leading to unstable optimization results.
An additive grouping structure identification method based on metrics is adopted. By calculating the interaction strength of variables and converting it into a distance matrix, the K-Means clustering algorithm with capacity constraints is used to group the variables and construct an additive kernel GP surrogate model to obtain the next evaluation point.
Stable additive grouping of identification variables under limited samples improves the fitting efficiency of surrogate models, achieves high efficiency and reliability in bipedal robot morphology optimization, and simplifies the optimization process.
Smart Images
Figure CN122153654A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a bipedal robot morphology optimization method, particularly a bipedal robot morphology optimization method based on additive grouping of variables identified by metric indicators, and relates to the field of artificial intelligence technology. Background Technology
[0002] The bipedal robot morphology optimization task employed the parametric morphology of the MuJoCo Walker2d robot. Walker2d simulates a bipedal robot consisting of a central torso and two legs, each composed of a thigh, lower leg, and foot. The core objective of this task was to achieve walking and crawling in specific directions by adjusting the robot's morphological parameters, specifically the torques of its six joints. Bipedal robot morphology optimization technology has broad application prospects in the real world, especially in high-risk tasks such as search and rescue and terrain exploration, where optimized robots can demonstrate higher efficiency and better safety.
[0003] Bipedal robot morphology optimization involves complex system dynamics, and the impact of morphological parameters on walking performance is often difficult to predict accurately through intuitive judgment or simple calculation. Therefore, this type of optimization problem can be considered a black-box optimization problem (BBO), where the objective function lacks an analytical expression and can only be evaluated through actual inputs. In such problems, Bayesian optimization (BO) is widely used due to its high sample efficiency. BO constructs a surrogate model (usually a Gaussian process, GP) in each iteration to approximate the objective function and selects the next evaluation point by maximizing the obtained function. However, accurate evaluation of morphological parameters typically requires running hundreds of time steps in a simulator and performing numerous repeated experiments, making each evaluation costly. With limited evaluation budgets, traditional BO methods can only obtain a small number of observation points, resulting in insufficient accuracy of the surrogate model and consequently affecting the optimization effect. Therefore, traditional BO methods have significant limitations in handling high-cost bipedal robot morphology optimization problems.
[0004] To address the costly morphology optimization problem of bipedal robots, recent studies have attempted to improve Bayesian optimization (BO) by utilizing the additive grouping structure of variables. BO methods based on additive grouping assume that the objective function can be approximated as a sum of functions of multiple variable groups, with significant coupling relationships between variables within the same group and approximate independence between variables in different groups. By identifying the additive grouping structure of variables, the objective function can be represented as the sum of functions composed of low-dimensional subgroup variables. Compared to directly fitting generalized generalization (GP), this additive assumption eliminates the need for modeling cross-group interactions, enabling surrogate models to more stably and efficiently approximate the overall objective function with limited samples. The key to this type of method lies in accurately identifying the additive grouping structure of variables. Although existing algorithms based on additive grouping of variables have shown significant potential, they still have the following limitations: (1) Existing methods typically use marginal likelihood as an indicator to assess the quality of variable grouping. However, with limited assessment budgets and only a small amount of observation data, the likelihood value corresponding to the true additive grouping structure may not be the maximum, which may lead to bias in the grouping assessment.
[0005] (2) Existing methods typically calculate posterior probabilities based on likelihood and perform joint sampling of variable groups. Due to the high dimensionality of the joint distribution, the sampling process is complex and difficult to converge, which can easily lead to unstable grouping results. This can result in performance that is even worse than randomly generated grouping. Summary of the Invention
[0006] Objective: To address the inaccuracies and low efficiency of current Boolean (BO) methods based on additive grouping structure recognition in bipedal robot morphology optimization, this invention provides a bipedal robot morphology optimization method based on metric-based recognition of additive grouping structures.
[0007] Technical Solution: A bipedal robot morphology optimization method based on metric index for identifying additive grouping structures. This method mainly includes an additive structure grouping stage and a Bayesian optimization stage based on additive decomposition. In the additive structure grouping stage, the invention first calculates the pairwise interaction strength between variables using a designed interaction metric index and transforms the interaction strength into a distance matrix. Subsequently, using this distance matrix, a capacity-constrained K-Means clustering algorithm is employed to cluster the high-dimensional variables to obtain groups, thus yielding the additive grouping structure. In the Bayesian optimization stage based on additive decomposition, an additive kernel GP surrogate model is constructed using the obtained additive grouping structure, and the next evaluation point is obtained by maximizing the acquisition function.
[0008] The detailed process of the bipedal robot morphology optimization method based on metric identification of additive grouping structure is as follows: (101) The set of morphological parameters currently evaluated , represents the historical sample dataset that has been evaluated up to the t-th iteration. The total number of samples, This represents the robot's walking morphology parameters corresponding to the i-th sample. Let be the function value used to evaluate the robot's walking task performance under these morphological parameters; if the state parameter set If empty, generate randomly. Candidate morphological parameters An evaluation was conducted, and corresponding evaluation values were obtained. ,Will 1 data point as the initial dataset And set the maximum evaluation value in the dataset as the current optimal evaluation value. Set the morphological parameter corresponding to the maximum value as the current optimal morphological parameter. .
[0009] (102) Based on the currently evaluated set of morphological parameters The calculation variable is the interaction strength matrix between the robot's morphological parameters. .
[0010] (103) Convert the interaction strength matrix into a distance matrix .
[0011] (104) Using the distance matrix The K-Means clustering algorithm with capacity constraints is used to cluster the variables, namely the robot morphological parameters, to obtain groups. ,Right now Each subgroup The number of variables in the middle does not exceed the capacity limit. .
[0012] (105) Based on grouping Fit an additive kernel GP surrogate model.
[0013] (106) Maximize the function to obtain new candidate morphological parameters The function obtained is a function defined in the Bayesian optimization algorithm to measure the sampling value of sample points.
[0014] (107) Candidate morphological parameters An evaluation was conducted to obtain an evaluation value. And the assessment points Add to target task dataset In the middle. When At that time, a new optimal morphological parameter was found, and... Updated to ,Will Updated to .
[0015] Repeat steps (101)-(107) until the stopping criterion is met. The morphological parameters stored in the database serve as the initial morphological parameters for the final application of the bipedal robot.
[0016] Step (102) involves calculating the group identification metric, and the specific steps are as follows: (2101) Based on the currently evaluated set of morphological parameters Construct a multinomial regression model that includes linear and quadratic terms of the variables. Where d is the variable, i.e., the total number of morphological parameters. They represent the first The variables are the values of the morphological parameters. Let be the regression coefficients of the first-order term and the noise term as defined in the multinomial regression model, respectively.
[0017] (2102) Variable pairs in a multinomial regression model The absolute value of the coefficient of the corresponding interaction term is defined as the interaction strength between the variables. The interaction strengths among all variables constitute the interaction metric matrix. ,in And the diagonal elements are zero.
[0018] (2103) Interaction metric matrix The interaction strength matrix is obtained by performing min-max normalization. .
[0019] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the bipedal robot morphology optimization method based on metric index identification of additive grouping structures as described above.
[0020] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the bipedal robot morphology optimization method described above based on metric index identification of additive grouping structures.
[0021] Beneficial Effects: This invention provides an effective solution for efficient morphological optimization of quadruped robots by employing a metric-based method for identifying additive groupings. The invention achieves grouping identification by constructing an interaction index between variables and combining it with a capacity-constrained K-Means clustering algorithm. Compared to existing algorithms, this invention is simpler and more robust, and by limiting the maximum dimension of each subgroup, it balances optimization efficiency and grouping identification accuracy, thus achieving efficient optimization with limited evaluation samples. Attached Figure Description
[0022] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 The diagram shows the effect of an embodiment of the present invention, namely the average ranking and variance of each optimization algorithm in the Mujuco Walker2d environment. Detailed Implementation
[0023] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.
[0024] Additive grouping structure identification based on metrics, abbreviated as MBD, is a bipedal robot morphology optimization method that iteratively identifies additive grouping of variables. First, it calculates the interaction strength of each pair of variables using a designed interaction metric and transforms the interaction strength into a distance matrix. Then, it uses a capacity-constrained K-Means clustering algorithm to group high-dimensional variables, thus obtaining the additive grouping structure. This method can effectively characterize the coupling relationship between variables with limited samples, ensuring strong interaction among variables in the same group while controlling the subgroup dimensionality to avoid excessive complexity, thereby improving the fitting efficiency and optimization stability of the surrogate model. Constructing an additive kernel GP model based on the additive grouping structure identified by this method can improve the efficiency of bipedal robot morphological parameter search.
[0025] The purpose of this invention is to address the problem of low efficiency in bipedal robot morphology optimization. To implement a bipedal robot morphology optimization method based on metric-based additive grouping identification, this embodiment uses the MuJoCoWalker2d test environment, where the morphological parameters of the Walker2d bipedal robot consist of approximately 56 continuous parameters, including position, velocity, and angular velocity of each part. In many real-world scenarios, the number of evaluations is often limited. By identifying the additive grouping structure of variables, the objective function can be represented as the sum of functions composed of low-dimensional subgroup variables. Compared to directly fitting GP, this additive assumption eliminates the need for modeling cross-group interactions, enabling the surrogate model to more stably and efficiently approximate the overall objective function with limited samples. Existing algorithms for capturing additive grouping structures rely on unreliable metrics, and sampling-based methods are complex and difficult to converge, resulting in unstable and unreliable identified groups. The MBD method proposed in this invention directly quantifies variable coupling relationships through interaction metrics and uses a clustering method with capacity constraints for group identification. Even with limited samples, it can robustly construct low-dimensional subgroup functions, thereby significantly improving the efficiency and reliability of bipedal robot morphology optimization.
[0026] The main process of the method is based on the currently evaluated set of morphological parameters. Calculate the interaction matrix between variables Convert to a distance matrix The variables were clustered using the K-Means clustering algorithm with capacity constraints to obtain additive groupings. During the optimization phase, the additive grouping structure obtained by MBD is used to fit the additive kernel GP surrogate model, and the next morphological parameter point to be evaluated is obtained by maximizing the acquisition function.
[0027] After multiple iterations, once the algorithm reaches the stopping criterion, it will use the morphological parameters stored in best_x as the initial morphological parameters for the final bipedal robot application.
[0028] This algorithm has several significant advantages: (1) It can stably identify the additive grouping structure of variables under limited evaluation samples, providing a reliable low-dimensional subgroup function representation for the morphological optimization of bipedal robots, thereby improving the fitting efficiency of the surrogate model.
[0029] (2) By using the constrained K-Means clustering method to obtain the grouping structure based on the interaction index, it is possible to ensure that the variables in the same group have a strong coupling relationship, while the subgroup dimension is not too high, thereby achieving a balance between optimization efficiency and accuracy.
[0030] (3) The method is simple and easy to implement, and does not rely on high-dimensional joint sampling or complex posterior estimation, making the optimization process more robust and efficient.
[0031] The specific steps of the main process of the method are as follows.
[0032] (1) The set of morphological parameters currently evaluated If empty, a random number will be generated. Candidate morphological parameters An evaluation was conducted, and corresponding results were obtained. ,Will 1 data point as the initial dataset And set the maximum evaluation value in the dataset as the current optimal evaluation value. Set the shape parameter corresponding to the maximum value as the current optimal shape parameter. .
[0033] (2) Based on the currently evaluated set of morphological parameters Calculate the interaction strength matrix between variables .
[0034] (3) Convert the interaction intensity into a distance matrix .
[0035] (4) Using the distance matrix The high-dimensional variables were clustered using the capacity-constrained K-Means clustering algorithm to obtain groups. ,Right now There are several subgroups, and the number of variables in each subgroup does not exceed the capacity limit. .
[0036] (5) Based on grouping structure Fit an additive kernel GP surrogate model.
[0037] (6) Maximize the function to obtain new candidate morphological parameters .
[0038] (7) For candidate morphological parameters An evaluation was conducted, and the results were obtained. And the assessment points Add to target task dataset In the middle. When At that time, the algorithm found a new optimal morphological parameter and... Updated to ,Will Updated to .
[0039] Repeat steps (2)-(7) until the algorithm stops. The algorithm will use the morphological parameters stored in best_x as the initial morphological parameters for the final bipedal robot application.
[0040] Step (2) in the process involves calculating the group identification metric, and the specific steps are as follows: (1) Based on the currently evaluated set of morphological parameters Construct a multinomial regression model that includes linear and quadratic terms of the variables. .
[0041] (2) Variable pairs in a multinomial regression model The absolute value of the coefficient of the corresponding interaction term is defined as the interaction strength between the variables. The interaction strengths among all variables constitute the interaction metric matrix. ,in And the diagonal elements are zero.
[0042] (3) For the interaction metric matrix Mini-max normalization is obtained .
[0043] verify This invention provides a bipedal robot morphology optimization method based on a metric to identify additive grouping of variables. Bipedal robot morphology optimization is a complex black-box optimization task. To verify and demonstrate MBD's ability to effectively identify variable grouping structures in complex high-dimensional problems, this invention conducts experimental evaluations on two sets of robot morphology optimization problems. For a set of morphological parameters... The evaluation method adopted in this invention is to perform 1000 time steps in the Mujoco Walker2d simulator environment, repeat the experiment 5 times, and use the average return under this morphological parameter as the evaluation result.
[0044] This invention compares the following methods: (1) MBD-Turbo: The method of this invention.
[0045] (2) Non-additive grouping BO Turbo: A Bayesian optimization method based on adaptive trust regions, which improves optimization efficiency through trust region constraints and local modeling. This invention is a version that does not perform additive grouping of variables.
[0046] (3) Additive grouping algorithm RDUCB: A state-of-the-art additive grouping algorithm. It restricts the variable grouping structure to a tree structure and randomly generates the grouping structure under this constraint.
[0047] MBD-Random-Turbo: A version that randomly generates variable groupings under the same grouping constraints as this invention.
[0048] To ensure a fair comparison, all identical parameters in the algorithm are kept consistent. The experimental curves represent the mean and standard deviation of the algorithm's ranking results across all test problems, such as... Figure 2 As shown.
[0049] By comparing MBD-Turbo, MBD-Random-Turbo Bayesian optimization methods that randomly generate groups under the same grouping constraints as this invention, and Turbo Bayesian optimization methods based on adaptive trust regions, it is found that the Bayesian optimization method of this invention, which identifies additive grouping of variables to construct additive kernels through a metric, can significantly improve the optimization effect, proving the effectiveness of the metric in identifying additive grouping of variables. Under the same number of iterations, the optimization performance of MBD-Turbo surpasses existing additive grouping algorithms, demonstrating the significant advantage of this invention in handling complex tasks. This invention can identify better variable grouping structures based on metric indicators, thereby alleviating the problem that existing additive grouping algorithms are unable to effectively capture the optimal grouping, and achieving better additive grouping results.
[0050] This invention improves the optimization efficiency of high-dimensional optimization problems by identifying additive groupings of variables based on metric indicators to construct a Bayesian optimization model with additive kernels for grouping. Furthermore, this invention can dynamically determine the grouping structure based on the magnitude of the metric indicators between variables. Compared with existing methods, this invention can accurately identify key variable groups in complex high-dimensional optimization tasks, achieving superior performance. Moreover, the method is easy to implement and can be applied to various optimization algorithms, demonstrating significant practical application potential.
[0051] Obviously, those skilled in the art should understand that the steps of the bipedal robot morphology optimization method based on additive grouping of metric identification variables in the above embodiments of the present invention can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using device-executable program code, thereby storing them in a storage device for execution by the computing device. Furthermore, in some cases, the steps shown or described can be performed in a different order than presented here, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the embodiments of the present invention are not limited to any particular hardware and software combination.
Claims
1. A method for morphological optimization of bipedal robots based on metric index identification of additive grouping structures, characterized in that, The process includes an additive structure grouping stage and a Bayesian optimization stage based on additive decomposition. In the additive structure grouping stage, the interaction strength between each pair of variables is first calculated using the designed interaction metric, and the interaction strength is transformed into a distance matrix. Subsequently, using this distance matrix, a capacity-constrained K-Means clustering algorithm is used to cluster the high-dimensional variables to obtain groups, thus obtaining the additive grouping structure. In the Bayesian optimization stage based on additive decomposition, an additive kernel GP surrogate model is constructed using the obtained additive grouping structure. The next evaluation point is obtained by maximizing the acquisition function, and the morphological parameters of the evaluation point are used as the initial morphological parameters of the bipedal robot for the final application.
2. The bipedal robot morphology optimization method based on metric index identification of additive grouping structure according to claim 1, characterized in that, The interaction strength between each pair of variables is calculated using a designed interaction metric, and the interaction strength is then transformed into a distance matrix. The steps are as follows: (101) The set of morphological parameters currently evaluated , represents the historical sample dataset that has been evaluated up to the t-th iteration. The total number of samples, This represents the robot's walking morphology parameters corresponding to the i-th sample. This is a function value used to evaluate the robot's performance in walking tasks under these morphological parameters; If the morphological parameter set If empty, generate randomly. Candidate morphological parameters An evaluation was conducted, and corresponding evaluation values were obtained. ,Will 1 data point as the initial dataset And set the maximum evaluation value in the dataset as the current optimal evaluation value. Set the morphological parameter corresponding to the maximum value as the current optimal morphological parameter. ; (102) Based on the currently evaluated set of morphological parameters The calculation variable is the interaction strength matrix between the robot's morphological parameters. ; (103) Convert the interaction strength matrix into a distance matrix .
3. The bipedal robot morphology optimization method based on metric index identification of additive grouping structure according to claim 2, characterized in that, The capacity-constrained K-Means clustering algorithm is used to cluster high-dimensional variables to obtain groups, thus obtaining an additive grouping structure. Specifically, the distance matrix is used... The K-Means clustering algorithm with capacity constraints is used to cluster the variables, namely the robot morphological parameters, to obtain groups. ,Right now Each subgroup The number of variables in the middle does not exceed the capacity limit. .
4. The bipedal robot morphology optimization method based on metric index identification of additive grouping structure according to claim 3, characterized in that, In the Bayesian optimization stage based on additive decomposition, based on grouping Fit an additive kernel GP surrogate model; maximize the acquisition function to obtain new candidate morphological parameters. The obtained function is the function defined in the Bayesian optimization algorithm to measure the sampling value of sample points; for candidate morphological parameters An evaluation was conducted to obtain an evaluation value. And the assessment points Add to target task dataset In the middle; when At that time, a new optimal morphological parameter was found, and... Updated to ,Will Updated to ; Repeat the additive structure grouping phase and the Bayesian optimization phase based on additive decomposition until the stopping criterion is met; The morphological parameters stored in the database serve as the initial morphological parameters for the final application of the bipedal robot.
5. The bipedal robot morphology optimization method based on metric index identification of additive grouping structure according to claim 2, characterized in that, Step (102) involves calculating the group identification metric, and the specific steps are as follows: (2101) Based on the currently evaluated set of morphological parameters Construct a multinomial regression model that includes linear and quadratic terms of the variables. Where d is the variable, i.e., the total number of morphological parameters. They represent the first The variables are the values of the morphological parameters. Let be the regression coefficients of the first-order term and the noise term as defined in the multinomial regression model; (2102) Variable pairs in a multinomial regression model The absolute value of the coefficient of the corresponding interaction term is defined as the interaction strength between the variables. The interaction strengths among all variables constitute the interaction metric matrix. ,in And the diagonal elements are zero; (2103) For the interaction metric matrix The interaction strength matrix is obtained by performing min-max normalization. .
6. A computer device, characterized in that: The computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the bipedal robot morphology optimization method based on metric index identification of additive grouping structure as described in any one of claims 1-5.
7. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that: When the computer program / instruction is executed by the processor, it implements the steps of the bipedal robot morphology optimization method based on metric index identification of additive grouping structure as described in any one of claims 1-5.