足底壓力中心軌跡（Center of Pressure，COP）為人體腳底於特定時間內之所有壓力的平均位置，其被使用於了解人體步態平衡之良好指標，亦可直接反映出腳踝肌肉之神經控制的好壞程度。而直接使用測力板或壓力墊量測COP為大家普遍常用的方法。然而，地板、地面感測器雖可取得較高品質之資料，但這些感測器皆屬於力接觸式感測器，長期使用將可能暴露其因硬體耗損而降低精準程度之問題，與設備費用高昂的缺點。
本研究將透過7個慣性感測元件（Inertial measurement unit，IMU）與F-scan蒐集加速度、角速度與壓力資料。其中，7個黏貼於L形金屬片與金屬夾片之IMU嵌於涼鞋之底部（分別置於左右腳的腳跟、腳側邊和腳尖）以及受測者腰部後方之褲頭上。最後，本研究使用此些IMU所收集之加速度與角速度資料透過LSTM演算法進行COP預測。其中，本研究欲探討究竟使用不同組合之IMU會有甚麼差異，並從中尋得最佳IMU預測組合（即預測誤差最小之組合）。
本研究透過交叉比較安裝於不同位置之IMU所預測之COP，以找出較佳IMU組合（即預測誤差最小）。結果表示左、右腳皆為使用腳側邊與腳跟之組合（IMULL+IMULH與IMURL+IMURH）進行預測得到的最佳預測表現分別為RMSE 0.62公分與RMSE 0.77公分，亦說明腳側邊與腳後跟為預測COP之較佳的IMU安裝位置。
然而，使用一個安裝於腳跟之IMU（IMULH與IMURH）進行預測也能取得與最佳IMU組合相當之結果（IMULH：RMSE 0.7公分；IMURH：RMSE 0.84公分），故若實際應用層面有成本或其他限制考量，則可考慮使用一個安裝於腳跟之IMU進行COP之預測。

The Center of pressure (COP) is the average position of all pressure on the soles of the human body within a certain time. It is used as a good indicator to understand the balance of the gait of the human body. It can also directly reflect the nerve control of the ankle muscle problem. The measurement tool of COP using force plates or pressure mat is a commonly used method. However, although force plate and pressure sensors can obtain higher quality data, these sensors are all force-contact sensors. Long-term use may expose the problem of reduced accuracy due to hardware abrasion.
This study collected acceleration, angular velocity and pressure data through 7 Inertial Measurement Units (IMU) and F-scan. Among them, 7 IMUs attached to the L-shaped metal sheet and metal clip was embedded in the bottom of the sandals (placed on the heels, lateral and toes, respectively) and on the waist of the participant. This study useds the acceleration and angular velocity data collected by these IMUs to conduct COP predictions by LSTM algorithms. The current study also intendeds to explore what is the difference between using different combinations of IMU, and to find the best combination of IMU prediction (the smallest prediction error).
The results indicated that the combination of the side and the heel (IMULL + IMULH and IMURL + IMURH) could obtain the best prediction for both the left and right foot (RMSE 0.62 cm and RMSE 0.77 cm, respectively). However, using a heel-mounted IMU (IMULH and IMURH) for prediction could also achieve a comparable result to the best IMU combination (RMSE 0.7 cm and RMSE 0.84 cm, respectively). Therefore, if there are costs or other restrictions in an application, one IMU for the COP prediction could consider placing at the heel.

第一章 緒論...................................................8
1.1.研究背景與動機..............................................8
1.2.研究目的...................................................10
1.3.研究架構...................................................10
第二章 文獻探討...............................................11
2.1.步態動作...................................................11
2.2.步態壓力中心之定義與應用.....................................13
2.3.步態壓力中心擷取方式........................................17
2.4.慣性感測元件（Inertial measurement unit，IMU）..............21
2.5.步態壓力中心軌跡之預測......................................24
2.6.小結......................................................26
第三章 研究方法...............................................28
3.1.實驗流程...................................................28
3.2.實驗受試者.................................................28
3.3.實驗設備...................................................29
3.4.實驗設置...................................................30
3.5.資料分析...................................................33
3.6. LSTM.....................................................37
3.7.預測結果評估指標............................................44
第四章 實驗結果...............................................47
4.1. 以單腳IMU組合預測COP之結果..............................47
4.2.以雙腳IMU組合預測COP之結果..................................54
第五章 討論..................................................56
5.1.COP預測結果................................................56
5.2.不同IMU組合之表現..........................................58
5.3.預測誤差...................................................60
5.4.實驗限制...................................................62
第六章 結論與未來方向..........................................63
參考文獻.......................................................72

1. Aminian, K., et al. (2002). "Spatio-temporal parameters of gait measured by an ambulatory system using miniature gyroscopes." Journal of biomechanics 35(5): 689-699.
2. Anwary, A. R., et al. (2018). "Optimal foot location for placing wearable IMU sensors and automatic feature extraction for gait analysis." IEEE Sensors Journal 18(6): 2555-2567.
3. Bishop, E. and Q. Li (2010). Walking speed estimation using shank-mounted accelerometers. 2010 IEEE International Conference on Robotics and Automation, IEEE.
4. Blum, A. L. and P. Langley (1997). "Selection of relevant features and examples in machine learning." Artificial intelligence 97(1-2): 245-271.
5. Braddom, R. L. (2010). Physical Medicine and Rehabilitation E-Book, Elsevier Health Sciences.
6. Brenton-Rule, A., et al. (2012). "Reliability of the TekScan MatScan® system for the measurement of postural stability in older people with rheumatoid arthritis." Journal of foot and ankle research 5(1): 21.
7. Catalfamo, P., et al. (2010). "Gait event detection on level ground and incline walking using a rate gyroscope." Sensors 10(6): 5683-5702.
8. Chen, B. and B. T. Bates (2000). "Comparison of F-Scan in-sole and AMTI forceplate system in measuring vertical ground reaction force during gait." Physiotherapy Theory and Practice 16(1): 43-53.
9. Choi, A., et al. (2019). "Single Inertial Sensor-Based Neural Networks to Estimate COM-COP Inclination Angle During Walking." Sensors 19(13): 2974.
10. Dadashi, F., et al. (2014). "Gait and foot clearance parameters obtained using shoe-worn inertial sensors in a large-population sample of older adults." Sensors 14(1): 443-457.
11. Fernandes, Â., et al. (2015). "Standing balance in individuals with Parkinson's disease during single and dual-task conditions." Gait & posture 42(3): 323-328.
12. Gafurov, D., et al. (2006). Gait recognition using acceleration from MEMS. First International Conference on Availability, Reliability and Security (ARES'06), IEEE.
13. Graves, A. (2012). "Supervised sequence labelling with recurrent neural networks. 2012." URL http://books. google. com/books.
14. Graves, A., et al. (2008). "A novel connectionist system for unconstrained handwriting recognition." IEEE transactions on pattern analysis and machine intelligence 31(5): 855-868.
15. Greene, B. R., et al. (2010). "An adaptive gyroscope-based algorithm for temporal gait analysis." Medical & biological engineering & computing 48(12): 1251-1260.
16. Höflinger, F., et al. (2013). "A wireless micro inertial measurement unit (IMU)." IEEE Transactions on instrumentation and measurement 62(9): 2583-2595.
17. Han, T. R., et al. (1999). "Quantification of the path of center of pressure (COP) using an F-scan in-shoe transducer." Gait & posture 10(3): 248-254.
18. Hass, C. J., et al. (2004). "The influence of Tai Chi training on the center of pressure trajectory during gait initiation in older adults." Archives of physical medicine and rehabilitation 85(10): 1593-1598.
19. Hundza, S. R., et al. (2013). "Accurate and reliable gait cycle detection in Parkinson's disease." IEEE Transactions on Neural Systems and Rehabilitation Engineering 22(1): 127-137.
20. Hunter, J. P., et al. (2005). "Relationships between ground reaction force impulse and kinematics of sprint-running acceleration." Journal of applied biomechanics 21(1): 31-43.
21. Inaba, K., et al. (2018). Center of pressure estimation and gait pattern recognition using shoes with photo-reflective sensors. Proceedings of the 30th Australian Conference on Computer-Human Interaction, ACM.
22. Lau, H. and K. Tong (2008). "The reliability of using accelerometer and gyroscope for gait event identification on persons with dropped foot." Gait & posture 27(2): 248-257.
23. Mannini, A. and A. M. Sabatini (2012). "Gait phase detection and discrimination between walking–jogging activities using hidden Markov models applied to foot motion data from a gyroscope." Gait & posture 36(4): 657-661.
24. Mariani, B., et al. (2013). "Quantitative estimation of foot-flat and stance phase of gait using foot-worn inertial sensors." Gait & posture 37(2): 229-234.
25. Marsland, S. (2014). Machine learning: an algorithmic perspective, Chapman and Hall/CRC.
26. Mikolov, T., et al. (2010). Recurrent neural network based language model. Eleventh annual conference of the international speech communication association.
27. Muro-De-La-Herran, A., et al. (2014). "Gait analysis methods: An overview of wearable and non-wearable systems, highlighting clinical applications." Sensors 14(2): 3362-3394.
28. Ngo, T. T., et al. (2014). "The largest inertial sensor-based gait database and performance evaluation of gait-based personal authentication." Pattern Recognition 47(1): 228-237.
29. Perry, J. and J. Burnfield (2010). "Gait analysis: normal and pathological function. 2nd." Thorofare, NJ: Slack Incorporated.
30. Segel, J. D. (2014). "Anatomy of the COP Gait Line and Computer-Aided Gait Analysis." Podiatry management 33(7): 151-158.
31. Shahabpoor, E. and A. Pavic (2017). "Measurement of walking ground reactions in real-life environments: A systematic review of techniques and technologies." Sensors 17(9): 2085.
32. Shahabpoor, E. and A. Pavic (2018). "Estimation of vertical walking ground reaction force in real-life environments using single IMU sensor." Journal of biomechanics 79: 181-190.
33. Shimada, Y., et al. (2005). "Clinical application of acceleration sensor to detect the swing phase of stroke gait in functional electrical stimulation." The Tohoku journal of experimental medicine 207(3): 197-202.
34. Srivastava, N., et al. (2014). "Dropout: a simple way to prevent neural networks from overfitting." The journal of machine learning research 15(1): 1929-1958.
35. Storm, F. A., et al. (2016). "Gait event detection in laboratory and real life settings: Accuracy of ankle and waist sensor based methods." Gait & posture 50: 42-46.
36. Trojaniello, D., et al. (2014). "Estimation of step-by-step spatio-temporal parameters of normal and impaired gait using shank-mounted magneto-inertial sensors: application to elderly, hemiparetic, parkinsonian and choreic gait." Journal of neuroengineering and rehabilitation 11(1): 152.
37. Whittle, M. W. (2014). Gait analysis: an introduction, Butterworth-Heinemann.
38. Winter, D. A. (1995). "Human balance and posture control during standing and walking." Gait & posture 3(4): 193-214.
39. Yao, Z.-M., et al. (2010). A novel biometrie recognition system based on ground reaction force measurements of continuous gait. 3rd International Conference on Human System Interaction, IEEE.