Accurate Determination of Joint Angles from Inertial Measurement Unit Data

ECE 687 Graduate Course Project Presentation

Transcript

1. ACCURATE DETERMINATION OF JOINT ANGLES FROM INERTIAL MEASUREMENT UNIT DATA Safwan Choudhury ECE 687: Project Presentation
2. PROBLEM STATEMENT • Need to be able to accurately capture and model 3-axis 6-DOF human arm motion for a variety of different applications. • Inertial Measurement Units (IMUs) gaining traction due to rapid advances in technology and lower costs. • Large source of inaccuracy arising from the integration of angular velocities (gyroscope) and acceleration (accelerometer).
3. MOTIVATION • Automated Rehabilitation Applications • Can save costs, time, etc. • Can be expanded in the future
4. RELATED WORK • Human Motion Capture by Integrating Gyroscopes and Accelerometers Published in 1996 by Sakaguchi, et al. • Two axis joint motion monitoring through the use of IMU data. • Joint Motion Monitoring by Accelerometers Set at Both Near Sides Around the Joint Published in 1998 by Kurata, et al. • Derived a model to extract joint angles from IMU data.
5. RELATED WORK • Estimation of Upper-Limb Orientation Based on Accelerometer and Gyroscope Measurements Published in 2008 by Hyde, et al. • Derived a model which was used as a basis in this project • Reducing Drifts in the Inertial Measurement of Wrist and Elbow Positions Published in 2010 by Zhou, et al. • Used a Kalman filter to reduce error and improve accuracy of IMU data.
6. OVERVIEW OF APPROACH 1. Retrieved real life motion capture and inertial measurement data 2. Generated baseline dataset from VICON motion capture marker positions 3. Extracted model of right arm from overall body motion to model IMUs 4. Derived mathematical model connecting IMU local frame to world frame 5. Ran data through an Extended Kalman Filter (EKF) and compared to baseline.
7. DESCRIPTION OF APPROACH • Motion Capture Data from Carnegie Mellon • VICON Motion Capture 12 Infrared MX-40 Cameras • High Resolution Video Capture from multiple angles • Wired & Wireless IMU Data Capture with 6DOF
8. DESCRIPTION OF APPROACH • Motion Capture Data from Carnegie Mellon • VICON Motion Capture 12 Infrared MX-40 Cameras • High Resolution Video Capture from multiple angles • Wired & Wireless IMU Data Capture with 6DOF
9. DESCRIPTION OF APPROACH • VICON Motion Capture Data Imported to Autodesk MotionBuilder
10. DESCRIPTION OF APPROACH • VICON Motion Capture Data Imported to Autodesk MotionBuilder
11. DESCRIPTION OF APPROACH • Mathematical model relating angular velocities (gyroscopes) and accelerations (accelerometers) in the IMU’s local frame to the world frame: 0 1 2 3 4 5
12. DESCRIPTION OF APPROACH • Transformation matrices are Euler angles performed in ZYX sequence: • Frame 0 is considered to be the world frame after detaching the arm from the full body motion. T 01 = T z (ψ 1 )T y (θ 1 )T x (ϑ 1 ) T 12 = T z (ψ 2 )T y (θ 2 )T x (ϑ 2 )
13. DESCRIPTION OF APPROACH • The total acceleration at a frame is given by the following equation: • The acceleration experienced by the IMU in its local frame is given by: a 2m 12 = T 12 −1(a 2 + g) a 2 01 = a 1 01 +  ω 12 01 × d 12 01 +ω 12 01 × (ω 12 01 × d 12 01)
14. DESCRIPTION OF APPROACH • The displacement vector in the previous equation is simply: d 12 01 = T 01 −1 d 12x d 12y d 12z ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ = T 01 −1 0 l IMU 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥
15. DESCRIPTION OF APPROACH • The angular velocity relationships are given by: ω 01 01 = T 01 −1 0 0  ψ 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ + T z (ψ 1 ) 0  θ 1 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ + T y (θ 1 )  ϑ 1 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ω 12 01 = ω 01 01 + 0 0  ψ 2 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ + T z (ψ 2 ) 0  θ 2 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ + T y (θ 2 )  ϑ 2 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟
16. DESCRIPTION OF APPROACH a 2m 12 = T 12 −1(a 2 01 + g) T 12 a 2m 12 = T 12 T 12 −1(a 2 01 + g) a 2 01 = a 2m 12 − g a 2 01 = a 1 01 +  ω 12 01 × d 12 01 +ω 12 01 × (ω 12 01 × d 12 01) • Rearranging one of the equations for acceleration: • We now have everything we need to solve the equation:
17. DESCRIPTION OF APPROACH • Solving the equation gives us a solution of the form: For each of the joint angles for roll, pitch and yaw.  ψ = f (a 2m 01,ω 12 01,..)  ψ =  ψ (t) ∫ dt ψ =  ψ (t) ∫ dt
18. KALMAN FILTERING • A mathematical model which is used to analyze measurements which are observed over time. • Effective when analyzing measurements which are subject to random variations. • The Extended Kalman Filter is used for non-linear systems as it attempts to linearize the system and make accurate estimates based on a prediction model. • The prediction model becomes more accurate with more ‘training’, as shown in the results.
19. RESULTS
20. RESULTS
21. RESULTS
22. ROOT MEAN SQUARE ERROR Trial 1 2 3 4 5 6 7 8 RMSE 0.124 0.099 0.087 0.076 0.061 0.053 0.049 0.050
23. CONCLUSIONS • The EKC provides a high level of accuracy of joint angles as shown with the comparison to motion capture data from the VICON camera’s. • For applications where computational power requirements is not an issue, EKC or an equivalent algorithm should be implemented.
24. QUESTIONS?