本研究以居家復健系統為例，建立一個在虛擬實境中協助使用者完成復健軌跡的系統。在動作捕捉方面，使用 HTC VIVE 追蹤器追蹤使用者的動作姿態，並在追蹤器有限的情況下，使用 FABRIK 演算法來計算動作姿態。復健軌跡設定方面，本系統使用樣條函數擬合復健師指定的動作軌跡，並依使用者人體參數縮放。此外，我們以軌跡為中心建立虛擬通道以及使用者與通道邊界之間的虛擬力。當使用者超出虛擬通道邊界時，系統會依虛擬力大小給予反饋提醒。最後，系統對使用者的動作進行評估並計分，讓復健師能夠了解使用者的復健成效。經由數位受試者在有無反饋提醒的實驗中顯示顯示，加入反饋對於追蹤軌跡之均方誤差有所改善。同時也幫助受試者在每次的試驗中有較穩定一致的表現。

In this study, a home rehabilitation system is established to assist users in completing rehabilitation trajectories within a virtual reality environment. In terms of motion capture, the HTC VIVE tracker is used to track user's movements and postures. When trackers are limited, the FABRIK algorithm is employed to calculate the movement postures. For rehabilitation trajectory settings, the system uses spline functions to fit the motion trajectories specified by the rehabilitation therapist and scales them according to the user's body parameters. Furthermore, a virtual channel centered on the trajectory is created, and virtual forces are applied between the user and the channel boundaries. When the user exceeds the virtual channel boundaries, the system provides feedback based on the magnitude of the virtual force. Finally, the system evaluates and scores the user's movements, enabling the rehabilitation therapist to understand the user's rehabilitation progress. Experiments with digital subjects showed that the addition of feedback improved the mean squared error of trajectory tracking. It also helped subjects achieve more stable and consistent performance in each trial.

[1] W. health organization, “world rehabilitation alliance.” https://www.who.int/initiatives/world-rehabilitation-alliance, 2023.
[2] G. Guerra-Filho, “Optical motion capture: Theory and implementation.,” RITA, vol. 12,no. 2, pp. 61–90, 2005.
[3] S. Qiao et al., “Real-time human gesture grading based on openpose,” in 2017 10th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), pp. 1–6, IEEE, 2017.
[4] E. Ha et al., “Full-body motion capture-based virtual reality multi-remote collaboration system,” Applied Sciences, vol. 12, no. 12, 2022.
[5] N. Kofinas et al., “Complete analytical inverse kinematics for nao,” in 2013 13th International Conference on Autonomous Robot Systems, pp. 1–6, IEEE, 2013.
[6] M. Meredith et al., “Real-time inverse kinematics: The return of the jacobian,” 2004.
[7] A. Aristidou and J. Lasenby, “Fabrik: A fast, iterative solver for the inverse kinematics problem,” Graphical Models, vol. 73, no. 5, pp. 243–260, 2011.
[8] Z. Zhou et al., “Trajectory prediction based on improved sliding window polynomial fitting prediction method,” in 2016 9th International Symposium on Computational Intelligence and Design (ISCID), vol. 2, pp. 202–205, IEEE, 2016.
[9] L. Gan et al., Interpolation: Cubic Spline Interpolation and Hermite Interpolation.Universiti Teknologi Malaysia, 2007.
[10] A. Peretti et al., “Telerehabilitation: review of the state-of-the-art and areas of application,” JMIR rehabilitation and assistive technologies, vol. 4, no. 2, p. e7511, 2017.
[11] P. Maciejasz et al., “A survey on robotic devices for upper limb rehabilitation,” Journal of neuroengineering and rehabilitation, vol. 11, pp. 1–29, 2014.
[12] G. Quattrocchi et al., “Reward and punishment enhance motor adaptation in stroke,”Journal of Neurology, Neurosurgery & Psychiatry, vol. 88, no. 9, pp. 730–736, 2017.
[13] T. Rose, C. S. Nam, and K. B. Chen, “Immersion of virtual reality for rehabilitationreview,” Applied ergonomics, vol. 69, pp. 153–161, 2018.
[14] S. P. Sitole et al., “Application and evaluation of lighthouse technology for precision motion capture,” IEEE Sensors Journal, vol. 20, no. 15, pp. 8576–8585, 2020.
[15] A. Malventano, “STEAMVR HTC VIVE IN-DEPTH –LIGHTHOUSE TRACKING SYSTEM DISSECTED AND EXPLORED.” https://pcper.com/2016/04/steamvr-htcvive-in-depth-lighthouse-tracking-system-dissected-and-explored/2/ftoc-heading-3,2016
[16] M. Borges et al., “Accurate absolute localization methods for the htc vive motion capture system,” 2019.
[17] B. G. Kilberg et al., “Accurate 3d lighthouse localization of a low-power crystal-free single-chip mote,” Journal of Microelectromechanical Systems, vol. 29, no. 5, pp. 818–824, 2020.
[18] H. Corporation, “VIVE Tracker (3.0) Developer Guidelines Ver. 1.1.”https://developer.vive.com/documents/850/HTC_Vive_Tracker_3.0_Developer_Guidelines_v1.1_06022021.pdf, 2021.
[19] L. Zhang et al., “Development and assist-as-needed control of an end-effector upper limb rehabilitation robot,” Applied Sciences, vol. 10, no. 19, 2020.
[20] C. Yuksel et al., “On the parameterization of catmull-rom curves,” in 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, SPM ’09, (New York, NY,USA), p. 47–53, Association for Computing Machinery, 2009.
[21] B. Guenter et al., “Computing the arc length of parametric curves,” IEEE Computer Graphics and Applications, vol. 10, no. 3, pp. 72–78, 1990.
[22] A. Hanson, “Quaternion frenet frames: Making optimal tubes and ribbons from curves,”08 1994.
[23] O. Donnell et al., “Extruded generalized cylinder: a deformable model for object recovery,” pp. 174 – 181, 07 1994.
[24] H. Wang et al., “Robust and efficient computation of the closest point on a spline curve,”in Proceedings of the 5th International Conference on Curves and Surfaces, pp. 397–406, 2002.
[25] S. B. Niku, Introduction to robotics: analysis, control, applications. John Wiley &Sons, 2020.
[26] M. Assad-Uz-Zaman et al., “Kinect controlled nao robot for telerehabilitation,” Journal of Intelligent Systems, vol. 30, pp. 224–239, 07 2020.
[27] D. Chen et al., “Application of wearable device htc vive in upper limb rehabilitation training,” in 2018 2nd IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), pp. 1460–1464, IEEE, 2018.
[28] M. W. Spong et al., Robot modeling and control. John Wiley & Sons, 2020.
[29] P. de Leva, “Adjustments to zatsiorsky-seluyanov’s segment inertia parameters.,” Journal of Biomechanics, vol. 29, pp. 1223–1230, 1996.
[30] C. Ott, Cartesian impedance control of redundant and flexible-joint robots. Springer,2008.
[31] S. Kasera et al., “Trajectory tracking of 3-dof industrial robot manipulator by sliding mode control,” in 2017 4th IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics (UPCON), pp. 364–369, 2017.
[32] R. M. Murray et al., A mathematical introduction to robotic manipulation. CRC press,2017.
[33] R. A. Horn and C. R. Johnson, Matrix analysis. Cambridge university press, 2012.
[34] H. Corporation, “VIVE Product.” https://www.vive.com/tw/product/vive/,2016.
[35] iFixint, “Htc vive images..” https://zh.ifixit.com/Teardown/HTC+Vive+Teardown/62213, 2017.
[36] M. Shahbazi et al., “Robotics-assisted mirror rehabilitation therapy: a therapist-inthe-loop assist-as-needed architecture,” IEEE/ASME Transactions on Mechatronics,vol. 21, no. 4, pp. 1954–1965, 2016.
[37] M. O. Powell et al., “Openbutterfly: Multimodal rehabilitation analysis of immersive virtual reality for physical therapy,” American Journal of Sports Science and Medicine,vol. 8, no. 1, pp. 23–35, 2020.
[38] K. S. Arun et al., “Least-squares fitting of two 3-d point sets,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-9, no. 5, pp. 698–700, 1987.