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繩牽引上肢并聯康復機器人柔索誤差逆向建模與分析

Inverse modeling and analysis of flexible cable error of cable-pulled upper limb parallel rehabilitation robot

  • 摘要: 針對柔索牽引上肢康復機器人在康復訓練過程中柔索的形變誤差導致機器人運動精度降低的問題,提出了一種基于形變本構方程的柔索誤差逆向建模方法. 首先,結合人體上肢生理結構和運動特性對康復機器人機構進行設計,并利用改進Denavit–Hartenberg(D–H)法建立機器人的空間等效模型,驗證了機器人運動的合理性和等效模型的正確性. 其次,在綜合考慮柔索形變、柔索與滑輪的摩擦以及柔索出繩點位置的基礎上,結合力旋量法和逆向求解思想建立了沿著實際柔索矢量方向的機器人柔索牽引系統動力學模型,并對康復訓練過程中柔索的運動狀態、配置情況和張力進行分析. 最后,給定一組人體上肢康復實例,通過仿真得到了康復訓練軌跡下柔索形變誤差,與柔索的受力和長度變化趨勢進行對比分析,并結合柔索形變方程驗證了柔索誤差逆向模型的正確性,該模型為柔索牽引康復機器人的控制和安全性分析提供基礎,同時也為柔索牽引并聯系統的誤差分析提供思路.

     

    Abstract: To address the problem of reduced accuracy of robot motion due to the deformation error of a flexible cable during the training of an upper limb rehabilitation robot, an inverse modeling method is proposed based on the intrinsic equation of deformation of the flexible cable error. First, by combining the physiological structure and movement characteristics of the shoulder, elbow, and wrist of the human upper limb, the arm exoskeleton, which is the wearing mechanism of the rehabilitation robot, is designed to increase the compatibility of the mechanism and the human body. The robot drive system has a parallel structure of flexible cable traction, which improves the flexibility of the robot, effectively reducing the impact of robot rehabilitation training on the human upper limb, thereby making the robot perform better than that with a parallel structure. Second, based on the structural parameters and motion range of the human upper limb, the improved Denavit–Hartenberg (D–H) method was used to establish a model spatially equivalent to the wearable arm exoskeleton of a human upper limb motion in MATLAB. The rationality and correctness of the wearable arm exoskeleton mechanism design were further verified. Subsequently, the traditional method for calculating the deformation error of a flexible cable was compared with the inverse method, and the superiority of the inverse method was discussed. According to the elastic deformation mechanism in material mechanics, the deformation of the flexible cable, friction between the flexible cable and pulley, and position of the flexible cable outlet point were considered for combining the reverse solution idea with the force rotation method to calculate the deformation error of the flexible cable in the actual pulling direction. A dynamic model of the cable traction system under the expected trajectory was obtained. Based on a discussion of the motion state and quantity configuration of the flexible cable in the rehabilitation training process, a real-time dynamic model of the traction system was obtained. According to the generalized inverse matrix theory, the optimal feasible solution for the tension of each cable was determined, and the tension of the cable was obtained in real time. Finally, the relevant parameters of the system were defined, and human upper limb rehabilitation examples were provided. The deformation error of the flexible cable along the actual stress direction under the given rehabilitation training track was obtained through simulations. A comparison and analysis of the variation trend of stress and length of the flexible cable indicated that the law of deformation error of the flexible cable was consistent with the variation trend of the tension and length of the flexible cable. The length before and after the deformation of the flexible cable was compared, and the correctness of the reverse model of the flexible cable error was verified based on the flexible cable deformation equation. This provided a basis for the control and safety analysis of the flexible cable traction rehabilitation robot and a future direction for the error-solving and analysis of the flexible cable traction parallel system.

     

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