Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

doi:10.23919/JSEE.2024.000050

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (3): 769-779.doi: 10.23919/JSEE.2024.000050

• CONTROL THEORY AND APPLICATION • Previous Articles

Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

Weiwei QIN(), Wenxin GUO(), Chen HU(), Gang LIU(), Tainian SONG()

School of Nuclear Engineering, Rocket Force University of Engineering, Xi’an 710025, China

Received:2021-12-14 Online:2024-06-18 Published:2024-06-19
Contact: Wenxin GUO E-mail:qww_1982@163.com;gwx_97@163.com;chenh628@hotmail.com;1813923249@qq.com;873512274@qq.com
About author:
QIN Weiwei was born in 1982. He received his M.S. degree in guidance, navigation, and control and Ph.D. degree in control science and engineering from the Rocket Force University of Engineering, in 2008 and 2012, respectively, where he is currently an associate professor with the First College. His research interests include model predictive control, robust active control, and human motion capture. E-mail: qww_1982@163.com

GUO Wenxin was born in 1997. He received his M.S. degree in guidance, navigation, and control in control science and engineering from the Rocket Force University of Engineering in 2021, where he is currently a research assistant with the First College. His research interests include human motion capture, kinematic calibration, model predictive control, and robust active control. E-mail: gwx_97@163.com

HU Chen was born in 1989. He received his B.S. degree in automation from the Department of Automation, Xiamen University, Xiamen, China, in 2011, and M.S. and Ph.D. degrees in control science and engineering from the Rocket Force University of Engineering, Xi’an, China, in 2014 and 2018, respectively. He is currently a lecturer with the Rocket Force University of Engineering. His research interests include multiagent systems, distributed state estimation, and machine learning. E-mail: chenh628@hotmail.com

LIU Gang was born in 1964. He received his M.S. degree in guidance, navigation, and control and Ph.D. degree in control science and engineering from Northwestern Polytechnical University, China, in 1995 and 1999, respectively. He is currently a professor with the Rocket Force University of Engineering. His research interests include guidance, navigation and control, and hypersonic flight vehicle. E-mail: 1813923249@qq.com

SONG Tainian was born in 1997. He received his M.S. degree in guidance, navigation, and control from the Rocket Force University of Engineering in 2021, where he is currently a research assistant with the First College. His research interests include human motion capture and target detection. E-mail: 873512274@qq.com
Supported by:
This work was supported by the National Natural Science Foundation of China (61503392).

Abstract

Abstract:

This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift. In this method, the geometric parameters are calibrated by the traditional calibration method at first. Then, in order to calibrate the parameters affected by the random colored noise, the expectation maximization (EM) algorithm is introduced. Through the use of geometric parameters calibrated by the traditional calibration method, the iterations under the EM framework are decreased and the efficiency of the proposed method on embedded system is improved. The performance of the proposed kinematic calibration method is compared to the traditional calibration method. Furthermore, the feasibility of the proposed method is verified on the EI-MoCap system. The simulation and experiment demonstrate that the motion capture precision is significantly improved by 16.79% and 7.16% respectively in comparison to the traditional calibration method.

Key words: human motion capture, kinematic calibration, exoskeleton, gyroscopic drift, expectation maximization (EM)

Weiwei QIN, Wenxin GUO, Chen HU, Gang LIU, Tainian SONG. Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system[J]. Journal of Systems Engineering and Electronics, 2024, 35(3): 769-779.

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References 28

1	NASER A, LOTFI A, MWANJE M D, et al Privacy-preserving, thermal vision with human in the loop fall detection alert system. IEEE Trans. on Human-Machine Systems, 2023, 53 (1): 164- 175. doi: 10.1109/THMS.2022.3203021
2	GAO L, ZHANG G F, YU B, et al Wearable human motion posture capture and medical health monitoring based on wireless sensor networks. Measurement, 2020, 166, 108252. doi: 10.1016/j.measurement.2020.108252
3	AMAT A Z, ADIANI D, TAUSEEF M, et al Design of a desktop virtual reality-based collaborative activities simulator to support teamwork in workplace settings for autistic adults. IEEE Trans. on Neural Systems and Rehabilitation Engineering, 2023, 31, 2184- 2194. doi: 10.1109/TNSRE.2023.3271139
4	DING Z Y, LOO J Y, NURZAMAN S G, et al A zero-shot soft sensor modeling approach using adversarial learning for robustness against sensor fault. IEEE Trans. on Industrial Informatics, 2023, 19 (4): 5891- 5901. doi: 10.1109/TII.2022.3187708
5	DONG Z H, LUCES J V S, RAVANKAR A A, et al A performance evaluation of overground gait training with a mobile body weight support system using wearable sensors. IEEE Sensors Journal, 2023, 23 (11): 12209- 12223. doi: 10.1109/JSEN.2023.3269031
6	SCOTT B, CHADWICK E, MCINNES M, et al Assessing single camera markerless motion capture during upper limb activities of daily living. Gait & Posture, 2023, 106 (1): S184.
7	FAREWIK L G, OLSSON F, DESTRO A, et al Markerless motion capture using iPad pro with LiDAR camera adjusted with artificial neural networks. Gait & Posture, 2022, 97 (1): S72- S73.
8	USLU T, GEZGIN E, OZBEK S, et al Utilization of low cost motion capture cameras for virtual navigation procedures: performance evaluation for surgical navigation. Measurement, 2021, 181, 109624. doi: 10.1016/j.measurement.2021.109624
9	PARK K W, CHOI J, KONG K Data-driven modeling for gait phase recognition in a wearable exoskeleton using estimated forces. IEEE Trans. on Robotics, 2023, 39 (4): 3072- 3086. doi: 10.1109/TRO.2023.3262108
10	WANG W T, LI R, DIEKEL Z M, et al Controlling object hand-over in human-robot collaboration via natural wearable sensing. IEEE Trans. on Human-Machine Systems, 2019, 49 (1): 59- 71. doi: 10.1109/THMS.2018.2883176
11	El-GOHARY M, MCNAMES J Shoulder and elbow joint angle tracking with inertial sensors. IEEE Trans. on Biomedical Engineering, 2012, 59 (9): 2635- 2641. doi: 10.1109/TBME.2012.2208750
12	LU C H, DAI Z Y, JING L Measurement of hand joint angle using inertial-based motion capture system. IEEE Trans. on Instrumentation and Measurement, 2023, 72, 9503211.
13	WANG Z T, GAO F, WU Z H, et al A method for calculating lower extremity anatomical landmark trajectories based on inertial motion capture data. IEEE Trans. on Neural Systems and Rehabilitation Engineering, 2023, 31, 2734- 2746. doi: 10.1109/TNSRE.2023.3285924
14	LAMBRECHT J M, KIRSCH R F Miniature low-power inertial sensors: promising technology for implantable motion capture systems. IEEE Trans. on Neural Systems and Rehabilitation Engineering, 2014, 22 (6): 1138- 1147. doi: 10.1109/TNSRE.2014.2324825
15	QIU S, WANG Z L, ZHAO H Y, et al Using distributed wearable sensors to measure and evaluate human lower limb motions. IEEE Trans. on Instrumentation and Measurement, 2016, 65 (4): 939- 950. doi: 10.1109/TIM.2015.2504078
16	ROBERT-LACHAINE X, PARENT G, FUENTES A, et al Inertial motion capture validation of 3D knee kinematics at various gait speed on the treadmill with a double-pose calibration. Gait & Posture, 2020, 77, 132- 137.
17	MIEZAL M, TAETZ B, BLESER G On inertial body tracking in the presence of model calibration errors. Sensors, 2016, 16 (7): 1132. doi: 10.3390/s16071132
18	KIM M, LEE D Wearable inertial sensor based parametric calibration of lower-limb kinematics. Sensors and Actuators A: Physical, 2017, 265 (1): 280- 296.
19	JIN X, HUANG B, SHOOK D S Multiple model LPV approach to nonlinear process identification with EM algorithm. Journal of Process Control, 2011, 21 (1): 182- 193. doi: 10.1016/j.jprocont.2010.11.008
20	ZHAO Y J, FATEHI A, HUANG B Robust estimation of ARX models with time varying time delays using variational bayesian approach. IEEE Trans. on Cybernetics, 2018, 48 (2): 532- 542. doi: 10.1109/TCYB.2016.2646059
21	SUN Y F, XU X Calibration of MEMS triaxial accelerometers based on the maximum likelihood estimation method. Mathematical Problems in Engineering, 2020, 2020, 4617365.
22	ZHANG X G, LI P, TU R, et al Automatic calibration of process noise matrix and measurement noise covariance for multi-GNSS precise point positioning. Mathematics, 2020, 8 (4): 502. doi: 10.3390/math8040502
23	DENG Y H, CHANG J Y Human-like posture correction for seven degree of freedom robotic arm. Journal of Mechanisms and Robotics, 2022, 14 (2): 024501.
24	SHINTEMIROV A, TAUNYAZOV T, OMARALI B, et al An open-source 7-DoF wireless human arm motion-tracking system for use in robotics research. Sensors, 2020, 20 (11): 3082. doi: 10.3390/s20113082
25	TAUNYAZOV T, OMARALI B, SHINTEMIROV A. A novel low-cost 4-DoF wireless human arm motion tracker. Proc. of the IEEE International Conference on Biomedical Robotics and Biomechatronics, 2016: 157−162.
26	ZAHEDI A, WANG Y S, LAU N, et al A bamboo-inspired exoskeleton based on carbon fiber for shoulder and elbow joints. IEEE Trans. on Medical Robotics and Bionics, 2023, 5 (2): 375- 386. doi: 10.1109/TMRB.2023.3269863
27	WANG Z Y, LIU Y, WANG X Y, et al Field calibration method for industrial robots based on single position sensitive device. IEEE Trans. on Instrumentation and Measurement, 2023, 72, 7506112.
28	WU C A kinematic cad tool for the design and control of a robot manipulator. International Journal of Robotics Research, 1984, 3 (1): 58- 67. doi: 10.1177/027836498400300105

$ {\mathrm{Rod}} $	$ a_i/{\mathrm{m}} $	$ \alpha_i/ \left( ^\circ \right) $	$ d_i/{\mathrm{m}} $	$ \theta_i /\left( ^\circ \right) $	$ {\mathrm{Offset}}/\left( ^\circ \right) $
1	0.04	270	0	$ {\theta _1}\left( k \right) $	0
2	0.04	90	0	$ {\theta _2}\left( k \right) $	90
3	0.431	90	0	$ {\theta _3}\left( k \right) $	0
4	0.244	−90	0	$ {\theta _4}\left( k \right) $	0
5	0	90	0	$ {\theta _5}\left( k \right) $	0
6	0	90	0	$ {\theta _6}\left( k \right) $	90
7	0	90	0	$ {\theta _7}\left( k \right) $	0

Parameter	Min	Max
${a_1} $	0.02	0.06
${a_2} $	0.02	0.06
${a_3} $	0.377	0.485
$ {a_4} $	0.211	0.267

Parameter	Initial	Final
$ {\theta _1} $	−90	90
${\theta _2} $	−120	30
$ {\theta _3} $	−10	100
${\theta _4} $	0	150
${\theta _5} $	30	−20
${\theta _6} $	40	−30
${\theta _7} $	−90	90

$ {\mathrm{Rod}} $	$ a_i/ {\mathrm{m}} $	$ \alpha_i /(^ \circ) $	$ d_i/ {\mathrm{m}} $	$ \theta_i + \Delta \theta_i /\left( ^\circ \right) $	$ {\mathrm{Offset}}/\left( ^\circ \right) $
1	0.03	270	0.03	$ {\theta _1}\left( k \right) + \Delta {\theta _1}\left( k \right) $	0
2	0.05	93	0.02	$ {\theta _2}\left( k \right) + \Delta {\theta _2}\left( k \right) $	90
3	0.401	90	0	$ {\theta _3}\left( k \right) + \Delta {\theta _3}\left( k \right) $	0
4	0.264	−95	0	$ {\theta _4}\left( k \right) + \Delta {\theta _4}\left( k \right) $	0
5	0.02	90	0.01	$ {\theta _5}\left( k \right) + \Delta {\theta _5}\left( k \right) $	0
6	0.01	92	0	$ {\theta _6}\left( k \right) + \Delta {\theta _6}\left( k \right) $	90
7	0	90	0	$ {\theta _7}\left( k \right) + \Delta {\theta _7}\left( k \right) $	0

$ {\mathrm{Rod}} $	$ \Delta a_i/ {\mathrm{m}} $	$ \Delta \alpha_i/ {{\mathrm{rad}}} $	$ \Delta d_i/ {\mathrm{m}} $	$ \Delta \theta_i/ {{\mathrm{rad}}} $
1	−0.0102	0.0005	0.0302	0.0004
2	0.0080	0.0514	0.0183	0.0010
3	−0.0280	0.0002	−0.0003	−0.0010
4	0.0180	−0.0856	−0.0021	−0.0013
5	0.0203	0.0010	0.0104	−0.0005
6	0.0100	0.0336	−0.0010	0.0004
7	0.0008	−0.0001	−0.0014	−0.0016

Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

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Figures/Tables 16

References 28

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Parameter	$ \Delta {\theta _1} $	$ \Delta {\theta _2} $	$ \Delta {\theta _3} $	$ \Delta {\theta _4} $	$ \Delta {\theta _5} $	$ \Delta {\theta _6} $	$ \Delta {\theta _7} $
Mean value	−0.0877	−0.0219	−0.8644	0.5719	−0.1644	−0.1369	−0.2155
Variance	0.0004	0.0005	0.0261	0.0114	0.0001	0.0015	0.0006
Responsibility	0.0321	0.0134	0.0000	0.0000	0.5366	0.0001	0.4179

$ {\mathrm{Rod}} $	$ \Delta a_i/ {\mathrm{m}} $	$ \Delta \alpha_i/{{\mathrm{rad}}} $	$ \Delta d_i/ {\mathrm{m}} $	$ \Delta \theta_i/ {{\mathrm{rad}}} $
1	−0.0099	−0.0004	0.0300	−0.0002
2	0.0106	0.0518	0.0199	0.0004
3	−0.0304	0.0006	0.0001	−0.0006
4	0.0183	−0.0862	−0.0008	0.0001
5	0.0203	0.0003	0.0093	0.0005
6	0.0091	0.0351	−0.0002	−0.0005
7	−0.0004	0.0001	0.0101	0.0005

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