# Angle Measurements during 2D and 3D Movements of a Rigid Body Model of Lower Limb - Comparison between Integral-based and Quaternion-based Methods

### Takashi Watanabe, Kento Ohashi

#### Abstract

Angle measurement system using inertial sensors was developed by our research group, in which lower limb angles were calculated based on the integral of angular velocity using Kalman filter. The angle calculation method was shown to be practical in measurement of angles in the sagittal plane during gait of healthy subjects. In this paper, in order to realize practical measurements of 3 dimensional (3D) movements with inertial sensors, the integral-based and the quaternion-based methods were tested in measurement of 2D movements in the sagittal plane and 3D movements of rigid body models of lower limb. The tested three calculation methods, extended integral-based method, quaternion-based method proposed in this study and simplified previous quaternion-based method, were suggested to measure the 2D movements with high measurement accuracy. It was also suggested that there were no large difference in measurement of 2D and 3D movements between 3 methods. Visualization by stick figure animation of circumduction gait simulated by a healthy subject also suggested that the angle calculation methods can be useful. It is expected to improve measurement accuracies of 3D movements to those of 2D movements.

#### References

- Chou, J. C. K., 1992. Quaternion Kinematic and Dynamic Differential Equations. IEEE Trans. Robotics Automat., 8(1), 53-64.
- Cooper, G., Sheret, I., McMillian, L., Siliverdis, K., Sha, N., Hodgins, D., Kenney, L., Howard, D., 2009. Inertial sensor-based knee flexion/extension angle estimation. J. Biomech., 42, 2678-2685.
- Dejnabadi, H., Jolles, B. M., Aminian, K., 2005. A New Approach to Accurate Measurement of Uniaxial Joint Angles based on a Combination of Accelerometers and Gyroscopes. IEEE Trans. Biomed. Eng., 52, 1478- 1484.
- Favre, J., 2006. Quaternion-based Fusion of Gyroscopes and Accelerometers to Improve 3D Angle Measurement. Electronics Letters., 42(11), 612-614.
- Findlow, A., Goulermas, J. Y., Nester, C., Howard, D., Kenney, L. P., 2008. Predicting Lower Limb Joint Kinematics Using Wearable Motion Sensors. Gait Posture, 28, 120-126.
- MazzĂ , C., Donati, M., McCamley, J., Picerno, P., Cappozzo, A., 2012. An Optimized Kalman Filter for the Estimate of Trunk Orientation from Inertial Sensors Data during Treadmill Walking. Gait & Posture, 35(1), 138-142.
- Sabatini, A. M., 2006. Quaternion-Based Extended Kalman Filter for Determining Orientation by Inertial and Magnetic Sensing. IEEE Trans. Biomed. Eng., 53(7), 1346-1356.
- Saito, H. and Watanabe, T., 2011. Kalman-filtering-based Joint Angle Measurement with Wireless Wearable Sensor System for Simplified Gait Analysis. IEICE Trans. Inf. & Syst., E94-D, 1716-1720.
- Teruyama, Y. and Watanabe, T., 2013. Effectiveness of Variable-Gain Kalman Filter based on Angle Error Calculated from Acceleration Signals in Lower Limb Angle Measurement with Inertial Sensors. Comput. Math. Methods Med. (in press).
- Tong, K., Granat, M. H., 1999. A Practical Gait Analysis System Using Gyroscopes. Med. Eng. Phys., 21, 87- 94.
- Watanabe, T., Saito, H., Koike, E., Nitta, K., 2011. A Preliminary Test of Measurement of Joint Angles and Stride Length with Wireless Inertial Sensors for Wearable Gait Evaluation System. Comput. Intel. Neurosci., 2011, Article ID: 975193.
- Watanabe, T. and Saito, H., 2011. Tests of Wireless Wearable Sensor System in Joint Angle Measurement of Lower Limbs. In Proc. 33rd. IEEE Eng. Med. Biol., 5469-5472.

#### Paper Citation

#### in Harvard Style

Watanabe T. and Ohashi K. (2014). **Angle Measurements during 2D and 3D Movements of a Rigid Body Model of Lower Limb - Comparison between Integral-based and Quaternion-based Methods** . In *Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2014)* ISBN 978-989-758-011-6, pages 35-44. DOI: 10.5220/0004793600350044

#### in Bibtex Style

@conference{biosignals14,

author={Takashi Watanabe and Kento Ohashi},

title={Angle Measurements during 2D and 3D Movements of a Rigid Body Model of Lower Limb - Comparison between Integral-based and Quaternion-based Methods},

booktitle={Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2014)},

year={2014},

pages={35-44},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004793600350044},

isbn={978-989-758-011-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2014)

TI - Angle Measurements during 2D and 3D Movements of a Rigid Body Model of Lower Limb - Comparison between Integral-based and Quaternion-based Methods

SN - 978-989-758-011-6

AU - Watanabe T.

AU - Ohashi K.

PY - 2014

SP - 35

EP - 44

DO - 10.5220/0004793600350044