A data-driven design method for legged robot systems

Abstract

This application relates to the field of legged robot technology, and more particularly to a data-driven legged robot system design method, comprising: obtaining the kinematic and weight parameters of the new configuration legged robot by combining the body speed and terrain-crossing capability of the new configuration legged robot proposed according to task requirements with the gait data, kinematic data, and weight data of the original configuration legged robot; obtaining the joint parameters of the new configuration legged robot by combining the kinematic data, weight data, and joint data of the original configuration legged robot with the kinematic and weight parameters of the new configuration legged robot; and obtaining the design input parameters of the power system of the new configuration legged robot by combining the joint parameters of the new configuration legged robot with the body speed and endurance of the new configuration legged robot proposed according to task requirements. This application can improve the utilization rate of historical data and enhance design efficiency and system integrity.

Description

Technical Field

[0001] This application relates to the field of legged robot technology, and in particular to a data-driven legged robot system design method. Background Technology

[0002] In recent years, the field of legged robots has made some progress in biomimetic structural design and motion control algorithms, but the following problems still exist: 1. Insufficient systematic design: Existing research and development relies heavily on experience iteration or imitation of open-source solutions, lacking a data-driven systematic design process, resulting in poor hardware adaptability and serious homogenization; 2. Independent optimization of subsystems: Although foreign research focuses on the synergy between algorithms and hardware (e.g., Boston Dynamics model predictive control, MIT Mini Cheetah direct drive motor), independent optimization of subsystems leads to limited improvement in overall robot performance and high hardware costs; 3. Low utilization of historical data: Existing methods do not fully utilize historical data of isomorphic robots (e.g., kinematic parameters, gait data), making it difficult to efficiently derive new configuration design parameters through scaled-down models.

[0003] The paper "Structure-Control Co-design of Quadruped Robot Based on Pre-training-Fine-tuning Framework" achieves the co-optimization of mechanical structure and control strategy through the "pre-training-fine-tuning" framework. However, this technology only focuses on "leg length optimization + control strategy adaptation" and does not cover the core subsystems of the legged robot, such as the body structure and power system (e.g., power matching and endurance design). It does not form a design process that is coordinated across the entire system. At the same time, it relies on "training generalization models with multi-structure data" and does not establish a quantitative derivation mechanism for parameters such as historical data and new configuration dimensions and power. Therefore, it still has shortcomings in design efficiency and system integrity.

[0004] Therefore, how to improve the utilization rate of historical data and enhance design efficiency and system integrity is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This application provides a data-driven method for designing legged robot systems to improve the utilization of historical data and enhance design efficiency and system integrity.

[0006] To solve the above-mentioned technical problems, this application provides the following technical solution: A data-driven legged robot system design method includes the following steps: Step S10: The body speed and terrain-crossing capability of the new legged robot, proposed according to task requirements, are combined with the gait data, kinematic data, and weight data of the original legged robot to obtain the kinematic and weight parameters of the new legged robot; Step S20: The joint parameters of the new legged robot are obtained using a scaled-down model, combining the kinematic data, weight data, and joint data of the original legged robot with the kinematic and weight parameters of the new legged robot; Step S30: The design input parameters of the power system of the new legged robot are obtained based on the joint parameters of the new legged robot and the body speed and endurance proposed according to task requirements; Step S40: The design of the kinematic parameters, joint parameters, and power system of the new legged robot... Under the constraints of input parameters, preliminary mechanical design is carried out. Based on the preliminary mechanical design scheme, and combined with the joint parameters of the new configuration legged robot, the leg mechanical system is designed. Step S50: Based on the design scheme of the leg mechanical system, and combined with the design input parameters of the power system of the new configuration legged robot, the power system of the new configuration legged robot is designed. Step S60: Based on the design scheme of the leg mechanical system, the design scheme of the power system, and the load-carrying capacity of the new configuration legged robot proposed according to the task requirements, the body mechanical system of the new configuration legged robot is designed. Step S70: Based on the design parameters corresponding to the design schemes of the leg mechanical system, power system, and body mechanical system of the new configuration legged robot, the gait simulation of the new configuration legged robot is carried out, and the leg mechanical system, power system, and body mechanical system of the new configuration legged robot are iteratively optimized.

[0007] In the data-driven legged robot system design method described above, preferably, step S10 includes the following sub-steps: The body speed is combined with the gait data of the original legged robot at the corresponding speed to calculate the body travel distance of the new legged robot during foot support; while ensuring that the body travel distance of the new legged robot during foot support is limited to the leg movement space of the new legged robot, the leg length and body height of the new legged robot are obtained by combining the body travel distance during foot support with the terrain traversal capability of the new legged robot proposed according to the task requirements; wherein, the leg movement space of the new legged robot is constrained by the terrain traversal capability of the new legged robot proposed according to the task requirements, and the leg length and body height of the new legged robot are kinematic parameters of the new legged robot.

[0008] In the data-driven legged robot system design method described above, preferably, the formula for calculating the body travel distance during foot support in the novel legged robot configuration is as follows: ; in, The distance the robot travels during foot support in the new configuration of the legged robot; For the body speed of the new legged robot configuration; This represents the leg support ratio coefficient. Gait frequency, the leg support ratio coefficient and gait frequency These are all gait data.

[0009] In the data-driven legged robot system design method described above, preferably, the body width of the new legged robot is obtained by using the scaling factor between the new and original legged robots and the body width of the original legged robot; the weight parameter of the new legged robot is obtained by using the scaling factor between the new and original legged robots and the weight data of the original legged robot; wherein, the body width of the original legged robot belongs to the kinematic data of the original legged robot, and the body width of the new legged robot belongs to the kinematic parameter of the new legged robot.

[0010] The data-driven legged robot system design method described above preferably involves combining the body height, weight, and joint data of the original legged robot with the body height and weight parameters of the new legged robot, and using a scaled-down model to obtain the joint parameters of the new legged robot when the joint angles of the new legged robot are the same as those of the original legged robot. Among them, the joint parameters are joint torque and joint angular velocity.

[0011] In the data-driven legged robot system design method described above, preferably, the scaled-down model of the joint torque of the novel legged robot configuration is as follows: ; in, For the first legged robot of the original configuration One leg Torque of each joint; For the first legged robot of the new configuration One leg Torque of each joint; The weight data is for the original configuration of the legged robot; The weight parameters for the new legged robot configuration; This represents the body height of the original legged robot configuration; The height of the new legged robot.

[0012] In the data-driven legged robot system design method described above, preferably, the scaled-down model of the joint angular velocity of the novel legged robot configuration is as follows: ; in, For the first legged robot of the original configuration One leg Angular velocity of each joint; For the first legged robot of the new configuration One leg angular velocity of each joint ω is the scaling factor for angular velocity.

[0013] In the data-driven legged robot system design method described above, preferably, the overall power of the new configuration legged robot is obtained based on the joint torque and joint angular velocity; then, the battery capacity of the new configuration legged robot is obtained by combining the body speed and endurance of the new configuration legged robot proposed according to the task requirements; wherein, the overall power and battery capacity of the new configuration legged robot are the design input parameters of the power system of the new configuration legged robot.

[0014] In the data-driven legged robot system design method described above, preferably, the formula for calculating the overall power of the novel legged robot configuration is as follows: ; in, The overall power of the new legged robot configuration For the first legged robot of the new configuration One leg Torque of each joint For the first legged robot of the new configuration One leg angular velocity of each joint The number of joints in the new legged robot configuration. The number of legs for the new configuration legged robot.

[0015] In the data-driven legged robot system design method described above, preferably, the formula for calculating the battery capacity of the novel legged robot configuration is as follows: ; in, Battery capacity for the new legged robot configuration; The theoretical total energy consumption of the new legged robot configuration is given. , The actual continuous working time required for the new legged robot configuration. , For the battery life of the new legged robot configuration; For power system efficiency; This is the redundancy coefficient.

[0016] Compared to the aforementioned background technologies, the data-driven legged robot system design method in this application integrates traditional legged robot design experience with multidisciplinary technologies such as electric drive, mechanics, and control to construct a top-down system design method. It utilizes the performance parameters, kinematic data, and gait parameters of existing isomorphic robots, combined with scaled-down models, to derive the size, joint torque, angular velocity, and overall power requirements of the new configuration robot, and optimizes the design of the leg mechanical system, power system, and body mechanical system accordingly. In addition, through iterative simulation and multi-system collaborative optimization, it achieves improved dynamic motion capabilities, enhanced adaptability to complex environments, and reduced hardware costs. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0018] Figure 1 This is a flowchart of the data-driven legged robot system design method provided in this application; Figure 2 This is a schematic diagram illustrating the limitation of the leg movement space provided in this application on the distance the fuselage can travel. Detailed Implementation

[0019] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0020] like Figure 1 As shown, this application provides a data-driven method for designing a legged robot system, including the following steps: Step S10: Based on the task requirements, the body speed and terrain-crossing ability of the new configuration legged robot are combined with the gait data, kinematic data and weight data of the original configuration legged robot to obtain the kinematic parameters and weight parameters of the new configuration legged robot. Based on the task requirements of the new configuration legged robot, performance requirements such as body speed, terrain traversal ability, endurance and payload capacity are proposed. The body speed is combined with the gait data of the original configuration legged robot at the corresponding speed to calculate the body travel distance of the new configuration legged robot during foot support.

[0021] Furthermore, the formula for calculating the body travel distance during foot support in the novel legged robot configuration is as follows: ; in, The distance the robot travels during foot support in the new configuration of the legged robot; For the body speed of the new legged robot configuration; This represents the leg support ratio coefficient. Gait frequency, the leg support ratio coefficient and gait frequency These are all gait data, specifically the leg support ratio coefficients for the new and original legged robot configurations. With gait frequency The values ​​are the same.

[0022] like Figure 2 As shown, the body travel distance while ensuring foot support for the new legged robot configuration. Limited to the leg movement space of the new configuration legged robot In this case, the leg movement space of the new configuration legged robot The key constraint is the terrain-crossing capability of the new configuration legged robot proposed according to the task requirements. The leg length and body height of the new configuration legged robot are obtained by combining the body travel distance during the foot support period with the terrain-crossing capability proposed according to the task requirements. Then, the body width of the new configuration legged robot is obtained by using the scaling factor between the new configuration legged robot and the original configuration legged robot and the body width of the original configuration legged robot. The leg length, body height and body width of the new configuration legged robot are all kinematic parameters of the new configuration legged robot.

[0023] Furthermore, the formula for calculating the leg length of the new legged robot is as follows: ; in, The leg length of the new legged robot; The minimum ground clearance of the new legged robot configuration can be determined by considering the robot's terrain-crossing capability based on mission requirements, such as its ability to climb a 30° slope. ≥0.15m; This is the height coefficient, typically taken as 0.6 to 0.8.

[0024] Furthermore, the formula for calculating the body height of the new legged robot is as follows: ; in, The height of the new legged robot.

[0025] Furthermore, the formula for calculating the body width of the new legged robot is as follows: ; in, The width of the body of the new legged robot; This represents the width of the original legged robot's body. This is the scaling factor. , The height of the original legged robot; the width of the original legged robot. The body height of the original legged robot This is the kinematic data for the original configuration of the legged robot.

[0026] The body travel distance during foot support and the leg movement space of the novel legged robot are compared. By combining the constraints of the original legged robot with the gait and kinematic data of the original legged robot, quantitative calculations are performed to achieve efficient and quantifiable derivation of the core kinematic parameters of the new legged robot from the historical data of the original legged robot, thereby improving the accuracy and efficiency of the design of the new legged robot.

[0027] The weight parameters of the new legged robot were obtained by using the scaling factor between the new and original legged robots and the weight data of the original legged robot.

[0028] Furthermore, the formula for calculating the weight parameters of the new legged robot is as follows: ; in, The weight data is for the original configuration of the legged robot. These are the weight parameters for the new legged robot configuration.

[0029] Step S20: Using the kinematic data, weight data, and joint data of the original legged robot, combined with the kinematic parameters and weight parameters of the new legged robot, the joint parameters of the new legged robot are obtained using a scaled-down model.

[0030] The body height and weight data of the original legged robot, as well as the joint torque and angular velocity of the relevant gait (the joint torque and angular velocity of the original legged robot are the joint data of the original legged robot), are combined with the previous steps to obtain the body height and weight parameters of the new legged robot. With the joint angles of the new legged robot being the same as those of the original legged robot, the joint torque and angular velocity of the new legged robot are obtained using a scaled-down model (the joint torque and angular velocity of the new legged robot are the joint parameters of the new legged robot).

[0031] Furthermore, the scaled-down model of the joint torque of the new legged robot is as follows: ; in, For the first legged robot of the original configuration One leg Torque of each joint; For the first legged robot of the new configuration One leg Torque of each joint.

[0032] Furthermore, the scaled-down model of the joint angular velocity of the new legged robot is as follows: ;

[0033] in, For the first legged robot of the original configuration One leg angular velocity of each joint This represents the body height of the original legged robot configuration; For the first legged robot of the new configuration One leg angular velocity of each joint The body height of the new legged robot An angular velocity scaling factor is introduced in the range of 0.5 to 1. The first legged robot adapted to the new configuration after size scaling One leg angular velocity of each joint This avoids parameter deviations caused by traditional linear scaling.

[0034] Step S30: Based on the joint parameters of the new configuration legged robot and the body speed and endurance of the new configuration legged robot proposed according to the task requirements, obtain the design input parameters of the power system of the new configuration legged robot.

[0035] Based on the joint torque and joint angular velocity of the new configuration legged robot, the overall power of the new configuration legged robot is obtained. Then, combined with the body speed and endurance of the new configuration legged robot proposed according to the task requirements, the battery capacity of the new configuration legged robot is obtained. The overall power and battery capacity of the new configuration legged robot are the power system design input parameters of the new configuration legged robot.

[0036] Furthermore, the formula for calculating the overall power of the new legged robot is as follows: ; in, The overall power of the new legged robot configuration The number of joints in the new legged robot configuration. The number of legs for the new configuration legged robot.

[0037] Furthermore, the formula for calculating the battery capacity of the new legged robot is as follows: ; in, Battery capacity for the new legged robot configuration; The theoretical total energy consumption of the new legged robot configuration is given. , The actual continuous working time required for the new legged robot configuration. , For the battery life of the new legged robot configuration; The efficiency of the power system (including actuator efficiency, transmission efficiency, and power conversion efficiency, with a value range of 0.65 to 0.85). This is the redundancy factor (considering energy redundancy under conditions such as complex terrain, load fluctuations, and low temperatures; its value is generally between 1.1 and 1.3).

[0038] Step S40: Under the constraints of the kinematic parameters, joint parameters, and power system design input parameters of the new configuration legged robot, conduct preliminary mechanical design. Based on the preliminary mechanical design scheme, and combined with the joint parameters of the new configuration legged robot, design the leg mechanical system. Under the constraints of kinematic parameters (leg length, body height, and body width), joint parameters (joint torque and joint angular velocity), and power system design input parameters (total power and battery capacity) of the novel legged robot, preliminary mechanical design of the novel legged robot is carried out to select a suitable leg mechanical mechanism and joint transmission scheme. Based on the structural parameters corresponding to the selected leg mechanical mechanism and the selected joint transmission scheme, and combined with the joint torque and joint angular velocity of the novel legged robot, the output speed, torque, power, and actuator volume and weight design parameters of the actuator of the novel legged robot are determined. These design parameters are then input into the leg mechanical system design model to design the leg mechanical system of the novel legged robot.

[0039] Step S50: Based on the design scheme of the leg mechanical system, and combined with the design input parameters of the power system of the new configuration legged robot, design the power system of the new configuration legged robot; The design parameters (output speed, torque, power, volume and weight) of the actuator determined in the design scheme of the leg mechanical system in step S40, as well as the overall power and battery capacity obtained in step S30, are input into the power system design model to design the power system of the new configuration legged robot.

[0040] Step S60: Based on the design scheme of the leg mechanical system, the design scheme of the power system, and the load-bearing capacity of the new configuration legged robot proposed according to the task requirements, design the body mechanical system of the new configuration legged robot. Taking into account the payload capacity of the new configuration legged robot proposed according to the task requirements, the design scheme of the leg mechanical system of the new configuration legged robot obtained in step S40, and the design scheme of the power system of the new configuration legged robot obtained in step S50, the body mechanical system of the new configuration legged robot is designed.

[0041] In addition, the design of the leg mechanical system in step S40, the design of the power system in step S50, and the design of the fuselage mechanical system in step S60 can be the same as the design of the leg mechanical system, the power system, and the fuselage mechanical system in the prior art.

[0042] Step S70: Based on the design parameters corresponding to the design schemes of the leg mechanical system, power system and body mechanical system of the new configuration legged robot, perform gait simulation of the new configuration legged robot, thereby iteratively optimizing the leg mechanical system, power system and body mechanical system of the new configuration legged robot.

[0043] The design parameters corresponding to the design scheme of the leg mechanical system of the new configuration legged robot obtained in step S40, the design parameters corresponding to the design scheme of the power system of the new configuration legged robot obtained in step S50, and the design parameters corresponding to the design scheme of the body mechanical system of the new configuration legged robot obtained in step S60 are input into the legged robot gait simulation system to perform gait simulation on the new configuration legged robot, so as to obtain the actual joint parameters that meet the task requirements of the new configuration legged robot. The actual joint parameters are used as input parameters for the design of the leg mechanical system and the power system of the new configuration legged robot, so as to iteratively optimize the leg mechanical system, power system and body mechanical system of the new configuration legged robot and continuously improve the performance of the new configuration legged robot.

[0044] The data-driven legged robot system design method presented in this application overcomes the over-reliance of existing technologies on expert experience and specific open-source platforms. By utilizing historical data and scaled-down models of isomorphic legged robots to derive initial parameters, it provides a scientific quantitative basis for new designs, thereby improving R&D efficiency from the outset. Furthermore, by coordinating and matching the design parameters of the leg mechanical system, power system, and body mechanical system in a unified simulation environment, it breaks through the performance bottlenecks caused by independent optimization of each subsystem in traditional designs. In addition, it can improve dynamic motion capabilities and environmental adaptability while avoiding "over-design," achieving precise matching between component selection and performance requirements, and significantly reducing the overall hardware cost.

[0045] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0046] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A data-driven method for designing a legged robot system, characterized in that, Includes the following steps: Step S10: Based on the task requirements, the body speed and terrain-crossing ability of the new configuration legged robot are combined with the gait data, kinematic data and weight data of the original configuration legged robot to obtain the kinematic parameters and weight parameters of the new configuration legged robot. Step S20: By combining the kinematic data, weight data, and joint data of the original legged robot with the kinematic parameters and weight parameters of the new legged robot, the joint parameters of the new legged robot are obtained using a scaled-down model. Step S30: Based on the joint parameters of the new configuration legged robot and the body speed and endurance of the new configuration legged robot proposed according to the task requirements, obtain the design input parameters of the power system of the new configuration legged robot. Step S40: Under the constraints of the kinematic parameters, joint parameters, and power system design input parameters of the new configuration legged robot, conduct preliminary mechanical design. Based on the preliminary mechanical design scheme, and combined with the joint parameters of the new configuration legged robot, design the leg mechanical system. Step S50: Based on the design scheme of the leg mechanical system, and combined with the design input parameters of the power system of the new configuration legged robot, design the power system of the new configuration legged robot; Step S60: Based on the design scheme of the leg mechanical system, the design scheme of the power system, and the load-bearing capacity of the new configuration legged robot proposed according to the task requirements, design the body mechanical system of the new configuration legged robot. Step S70: Based on the design parameters corresponding to the design schemes of the leg mechanical system, power system and body mechanical system of the new configuration legged robot, perform gait simulation of the new configuration legged robot, and iteratively optimize the leg mechanical system, power system and body mechanical system of the new configuration legged robot.

2. The data-driven legged robot system design method according to claim 1, characterized in that, Step S10 includes the following sub-steps: By combining the body speed with the gait data of the original legged robot at the corresponding speed, the body travel distance of the new legged robot during foot support was calculated. With the body travel distance during the foot support period of the new configuration legged robot limited to the leg movement space of the new configuration legged robot, the leg length and body height of the new configuration legged robot are obtained by combining the body travel distance during the foot support period with the terrain passability of the new configuration legged robot proposed according to the task requirements. Among them, the leg movement space of the new configuration legged robot is constrained by the terrain traversal capability of the new configuration legged robot proposed according to the task requirements, and the leg length and body height of the new configuration legged robot are kinematic parameters of the new configuration legged robot.

3. The data-driven legged robot system design method according to claim 2, characterized in that, The formula for calculating the body travel distance during foot support in the novel legged robot configuration is as follows: ； in, The distance the robot travels during foot support in the new configuration of the legged robot; For the body speed of the new legged robot configuration; This represents the leg support ratio coefficient. Gait frequency, the leg support ratio coefficient and gait frequency These are all gait data.

4. The data-driven legged robot system design method according to claim 2, characterized in that, The body width of the new legged robot is obtained by using the scaling factor between the new and original legged robots and the body width of the original legged robot. The weight parameters of the new legged robot were obtained by using the scaling factor between the new and original legged robots and the weight data of the original legged robot. Among them, the body width of the original legged robot belongs to the kinematic data of the original legged robot, while the body width of the new legged robot belongs to the kinematic parameters of the new legged robot.

5. The data-driven legged robot system design method according to claim 2, characterized in that, By combining the body height, weight, and joint data of the original legged robot with the body height and weight parameters of the new legged robot, and assuming that the joint angles of the new legged robot are the same as those of the original legged robot, the joint parameters of the new legged robot are obtained using a scaled-down model. Among them, the joint parameters are joint torque and joint angular velocity.

6. The data-driven legged robot system design method according to claim 5, characterized in that, The scaled-down model of the joint torque of the new legged robot is as follows: ； in, For the first legged robot of the original configuration One leg Torque of each joint; For the first legged robot of the new configuration One leg Torque of each joint; The weight data is for the original configuration of the legged robot; The weight parameters for the new legged robot configuration; This represents the body height of the original legged robot configuration; The height of the new legged robot.

7. The data-driven legged robot system design method according to claim 6, characterized in that, The scaled-down model of the joint angular velocity of the new legged robot is as follows: ； in, For the first legged robot of the original configuration One leg Angular velocity of each joint; For the first legged robot of the new configuration One leg angular velocity of each joint ω is the scaling factor for angular velocity.

8. The data-driven legged robot system design method according to claim 5, characterized in that, The overall power of the new legged robot is obtained based on the joint torque and joint angular velocity of the new configuration legged robot. By combining the battery life of the new legged robot configuration proposed based on the task requirements, the battery capacity of the new legged robot was determined. Among them, the overall power and battery capacity of the new legged robot are the design input parameters of the power system of the new legged robot.

9. The data-driven legged robot system design method according to claim 8, characterized in that, The formula for calculating the overall power of the new legged robot is as follows: ； in, The overall power of the new legged robot configuration For the first legged robot of the new configuration One leg Torque of each joint For the first legged robot of the new configuration One leg angular velocity of each joint The number of joints in the new legged robot configuration. The number of legs for the new configuration legged robot.

10. The data-driven legged robot system design method according to claim 9, characterized in that, The formula for calculating the battery capacity of the new legged robot is as follows: ； in, Battery capacity for the new legged robot configuration; The theoretical total energy consumption of the new legged robot configuration is given. , The actual continuous working time required for the new legged robot configuration. , For the battery life of the new legged robot configuration; For power system efficiency; This is the redundancy coefficient.

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