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Tremor Estimation and Removal in Robot-Assisted Surgery Using Lie Groups and EKF

Published online by Cambridge University Press:  15 April 2019

Rohit Rana Open the ORCID record for Rohit Rana [Opens in a new window] ,
Prerna Gaur ,
Vijyant Agarwal  and
Harish Parthasarathy
Rohit Rana*
Affiliation:
Instrumentation and Control Division, Netaji Subhas Institute of Technology, University of Delhi, New Delhi, India. E-mails: [email protected], [email protected]
Prerna Gaur
Affiliation:
Instrumentation and Control Division, Netaji Subhas Institute of Technology, University of Delhi, New Delhi, India. E-mails: [email protected], [email protected]
Vijyant Agarwal
Affiliation:
MPAE Division, Netaji Subhas Institute of Technology, University of Delhi, New Delhi, India. E-mail: [email protected]
Harish Parthasarathy
Affiliation:
Electronics and Communication Division, Netaji Subhas Institute of Technology, University of Delhi, New Delhi, India. E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper aims at estimating the tremor torque using extended Kalman filter (EKF) applied to a two-link 3-DOF robot with nonlinear dynamics modelled using Lie-group and Lie-algebra theory. Later, it is generalised to d number of links with (d + 1) -DOF. The configuration of each link at any time is described by its rotation relative to the preceding link. Using this formulation, an elegant formula for the kinetic energy of the (d + 1) -DOF system is obtained as a quadratic form in the angular velocities with coefficients being highly nonlinear trigonometric functions of the angles. Properties of the Lie algebra generators and the Lie adjoint map are used to arrive at this expression. Further, the gravitational potential energy and the torque potential energy are expressed as nonlinear trigonometrical functions of the angles using properties of the SO(3) group. The input torque comprises a nonrandom intentional torque component and a highly nonlinear tremor torque component. The tremor torque is modelled as a stochastic differential equation (sde) satisfying Ornstein–Uhlenbeck (OU) process with diffusion and damping coefficients. Further, the tremor is treated as the disturbance. The Euler–Lagrange equations for the angles are derived. These form a system of sdes, and the EKF is used to get a more accurate disturbance estimate than that provided by the usual disturbance observer. The EKF is based on noisy angle measurements and yields as a bonus the angle and angular velocity estimates on a real-time basis. The parameters in the OU process model of the tremor torque, and parameters of the Fourier components of the intentional torque have also been estimated.

Keywords

TremorEKF (extended Kalman filter)Lie groupOmni BundleNonlinear phenomenaSurgical robotsOU process
Type
Articles
Information
Robotica , Volume 37 , Issue 11 , November 2019 , pp. 1904 - 1921
Copyright
© Cambridge University Press 2019 

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References

Taheri, B., Case, D. and Richer, E., “Adaptive suppression of severe pathological tremor by torque estimation method,” IEEE/ASME Trans. Mechatron. 20(2), 717–727 (2015). doi: 10.1109/TMECH.2014.2317948CrossRefGoogle Scholar
Case, D., Taheri, B. and Richer, E., “Design and characterization of a small-scale magnetorheological damper for tremor suppression,” IEEE/ASME Trans. Mechatron 18(1), 96–103 (2013). doi: 10.1109/TMECH.2011.2151204CrossRefGoogle Scholar
Vinjamuri, R., Crammond, D. J., Kondziolka, D., Lee, H-N. and Mao, Z.-H., “Extraction of sources of tremor in hand movements of patients with movement disorders,” IEEE Trans. Inform. Technol. Biomed. 13(1), 49–56 (2009). doi: 10.1109/TITB.2008.2006403CrossRefGoogle ScholarPubMed
He, X., Handa, J., Gehlbach, P., Taylor, R. and Iordachita, I., “A submillimetric 3-DOF force sensing instrument with integrated fiber Bragg grating for retinal microsurgery,” IEEE Trans. Biomed. Eng. 61(2), 522–534 (2014). doi: 10.1109/TBME.2013.2283501Google ScholarPubMed
Sanes, J. N., LeWitt, P. A. and Mauritz, K.-H., “Visual and mechanical control of postural and kinetic tremor in cerebellar system disorders,” J. Neurol. Neurosurg. Psychiatry 51, 934–943 (1988).CrossRefGoogle ScholarPubMed
Aisen, M. L., Arnold, A., Baiges, I., Maxwell, S. and Rosen, M., “The effect of mechanical damping loads on disabling action tremor,” Neurology 43, 1346–1350 (1993).CrossRefGoogle ScholarPubMed
Taheri, B., Case, D. and Richer, E., “Robust controller for tremor suppression at musculoskeletal level in human wrist,” IEEE Trans. Neural Syst. Rehabilit. Eng. 22(2), 379–388 (2014). doi: 10.1109/TNSRE.2013.2295034CrossRefGoogle ScholarPubMed
Riviere, C. N., Reich, S. G., and Thakor, N. V., “Adaptive Fourier modeling for quantification of tremor,” J. Neurosci. Methods 74(1), 77–87 (1997).CrossRefGoogle ScholarPubMed
Veluvolu, K. C. and Ang, W. T., “Estimation of physiological tremor from accelerometers for real-time applications,” Sensors 11, 3020–3036 (2011).CrossRefGoogle ScholarPubMed
Riviere, C. N., Ang, W. T and K. P. K, “Toward active tremor canceling in handheld microsurgical instruments,” IEEE Trans. Robot. Autom. 19(5), 793–800 (2003).CrossRefGoogle Scholar
Gallego, J. A., Rocon, E., Roa, J. O., Moreno, J. C. and Pons, J. L., “Real time estimation of pathological tremor parameters from gyroscope data,” Sensors 10, 2129–2149 (2010).CrossRefGoogle ScholarPubMed
Bo, A. P. L., Poignet, P., Widjaja, F., and Ang, W. T., “Online Pathological Tremor Characterization using Extended Kalman Filtering,” Proceeding on IEEE 30th Annual Internaltion Conference Eng. Med. Bio. Soc., Vancouver, Canada (2008) pp. 1753–1756.Google Scholar
Yuen, S. G., Kettler, D. T., Novotny, P. M., Plowes, R. D. and Howe, R. D., “Robotic motion compensation for beating heart intracardiac surgery,” Int. J. Robot. Res. 28, 1355–1372 (2009).CrossRefGoogle ScholarPubMed
Tatinati, S., Veluvolu, K. C. and Ang, W. T., “Multistep prediction of physiological tremor based on machine learning for robotics assisted microsurgery,” IEEE Trans. Cybernetics 45(2), 328–339 (2015). doi: 10.1109/TCYB.2014.2381495CrossRefGoogle ScholarPubMed
Veluvolu, K., Tatinati, S., Hong, S.-M., Tech, W., “Multistep prediction of physiological tremor for surgical robotics applications,” IEEE Trans. Biomed. Eng. 60(11), 3074–3082 (2013). doi: 10.1109/TBME.2013.2264546CrossRefGoogle ScholarPubMed
Barrau, A. and Bobnnabel, S., “Intrinsic filtering on Lie Groups with applications to attitude estimation,” IEEE Trans. Autom. Control 60(2), 436–449 (2015). doi: 10.1109/TAC.2014.2342911CrossRefGoogle Scholar
Chen, G., Wang, H. and Lin, Z., “Determination of the identifiable parameters in robot calibration based on the POE formula,” IEEE Trans. Robotics 30(5), 1066–1077 (Oct. 2014). doi: 10.1109/TRO.2014.2319560CrossRefGoogle Scholar
Di Salvo, R., Gorgone, M. and Oliveri, F., “A consistent approach to approximate Lie symmetries of differential equations”, Nonlinear Dyn. 91(1), 371–386 (2018). https://doi.org/10.1007/s11071-017-3875-5CrossRefGoogle Scholar
Nass, A. M. and Fredericks, E., “W-symmetries of jump-diffusion Itô stochastic differential equations,” Nonlinear Dyn. 90(4), 2869–2877 (2017). https://doi.org/10.1007/s11071-017-3848-8CrossRefGoogle Scholar
Agarwal, V. and Parthasarathy, H., “Disturbance estimator as a state observer with extended Kalman filter for robotic manipulator”, Nonlinear Dyn. 85(4), 2809–2825 (2016).CrossRefGoogle Scholar
Yang, S., MacLachlan, R. A. and Riviere, C. N., “Manipulator design and operation of a six degree-of-freedom handheld tremor-canceling microsurgical instrument,” IEEE/ASME Trans. Mechatron. 20(2), 761–772 (2015). doi: 10.1109/TMECH.2014.2320858CrossRefGoogle ScholarPubMed
MacLachlan, R. A., Becker, B. C., Tabares, J. C., Podnar, G. W., Lobes, L. A. and Riviere, C. N., “Micron: An actively stabilized handheld tool for microsurgery,” IEEE Trans. Robotics 25(1), 195–212 (2012). doi: 10.1109/TRO.2011.2169634CrossRefGoogle Scholar
Timmer, J., Hussler, S., Lauk, M. and Lcking, C.-H., “Pathological tremors: deterministic chaos or nonlinear stochastic oscillators?” Chaos 10(1), 278–288 (2000). doi: 10.1063/1.166494CrossRefGoogle ScholarPubMed
Zeng, C., Yang, Q. and Chen, Y. Q., “Solving nonlinear stochastic differential equations with fractional Brownian motion using reducibility approach,” Nonlinear Dyn. 67(4), 2719–2726 (2012). https://doi.org/10.1007/s11071-011-0183-3CrossRefGoogle Scholar
Yu Meigal, A., Rissanen, S. M., Tarvainen, M. P., Georgiadis, S. D., Karjalainen, P. A., Airaksinen, O. and Kankaanp, M., “Linear and nonlinear tremor acceleration characteristics in patients with Parkinson’s disease,” Physiol. Measurement 33(3), 395–412 (2012). doi:10.1088/0967-3334/33/3/395CrossRefGoogle Scholar
Qin, Y. H. and Li, J. C., “Random parameters induce chaos in power systems,” Nonlinear Dyn. 77(4), 1609–1615 (2014). https://doi.org/10.1007/s11071-014-1403-4CrossRefGoogle Scholar
Dick, O. E. and Nozdrachev, A. D., “Nonlinear dynamics of involuntary shaking of the human hand under motor dysfunction,” Hum. Physiol. 41(2), 156–161 (2015). https://doi.org/10.1134/S0362119715010041CrossRefGoogle ScholarPubMed
Yang, K., Yang, W., and Wang, C., “Inverse dynamic analysis and position error evaluation of the heavy-duty industrial robot with elastic joints: an efficient approach based on Lie group,” Nonlinear Dyn. 93(2), 487–504 (2018). https://doi.org/10.1007/s11071-018-4205-2CrossRefGoogle Scholar
High-Level Control System for. Remote Controlled Surgical Robots. Haptic Guidance of Surgical Robot. Trondheim, June 2008. Master’s thesis. NTNU.Google Scholar
Singla, R., Parthasarathy, H. and Agarwal, V., “Classical robots perturbed by Lévy processes: analysis and Lévy disturbance rejection methods,” Nonlinear Dyn. 89(1), 553–575 (2017). https://doi.org/10.1007/s11071-017-3471-8CrossRefGoogle Scholar