The Mixed Kalman and H Infinity Filter Based Robust Model Following Control Algorithm for CABG Beating Heart Surgery

Abstract:

In the CABG surgery the robot dynamically cancels the relative motion between the point of interest (POI) on the beating heart and robotic instruments, such that the surgeon can operate as if the heart is stationary. However, the highly nonlinear and non-stationary nature of the beating heart motion poses difficulties for robot to follow the characteristics of the beating heart motion. Furthermore, the surgery has potential safety risk if the robot system could not track the POI properly. Therefore, in order to minimize the effects caused by the uncertainty in the heart motion model during the surgery, a robust prediction based model following control algorithm is proposed here. The adaptive Autoregressive (AR) model integrated the mixed Kalman and H infinity filter to estimate the state of the beating heart motion in the sense of minimizing minimize both RMS motion estimation error and worst case motion estimation error. In addition, the linear quadratic optimal tracking theory was used to implement the model following controller. In such way a complicated heart motion tracking problem transformed to dynamic model following problem and the robust property of the tracking control is more effective. The method is verified by two prerecorded distinguished datasets on 3D test bed robotics.

• Periodical: Applied Mechanics and Materials (Volumes 543-547)
• Pages: 1360-1364
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.543-547.1360
• Online since: March 2014
• Authors: Fan Liang*, Xing Li Wu, Shi Gang Cui, Li Zhao
• Keywords: Adaptive Heart Motion Model, Beating Heart Tracking Control, H Infinity Filter, Heart Motion Robust Prediction, Mixed Kalman, Surgical Assisted Robotics Safety

References

[1] M. F. Newman, J. L. Kirchner, B. Phillips-Bute, V. Gaver, H. Grocott, R. H. Jones, et al(2001)., Longitudinal assessment of neurocognitive function after coronaryartery bypass surgery New England Journal of Medicine, vol. 344, no. 6, p.395–402.

DOI: 10.1056/nejm200102083440601

[2] J.D. Puskas, C. E. Wright, R. S. Ronson, W. M. Brown, J. P. Gott, and R. A. Guyton(1998), Off-pump multi-vessel coronary bypass via sternotomy is safe and effective Annals of Thoracic Surgery, vol. 66, no. 3, p.1068–1072.

DOI: 10.1016/s0003-4975(98)00657-2

[3] Trejos, A., S. Salcudean, F. Sassani, and S. Lichtenstein. (1999). On the feasibility of a moving support for surgery on the beating heart. In Medical Image Computing and Computer-Assisted Intervention–MICCAI'99, 1088–1097.

DOI: 10.1007/10704282_118

[4] A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 1980). L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988).

[5] Pinna GD, Maestri R, Mortara A, and La Rovere MT. Cardiorespiratory interactions during periodic breathing in awake chronic heart failure patients. Am. J. Physiol. Heart Circ. Physiol., 278: H932–H941, (2000).

DOI: 10.1152/ajpheart.2000.278.3.h932

[6] Eckberg DL. Sympathovagal balance: a critical appraisal. Circulation, 96: 3224–3232, (1997).

DOI: 10.1161/01.cir.96.9.3224

[7] Cavusoglu, M.C., J. Rotella, W.S. Newman, S. Choi, J. Ustin, and S.S. Sastry. (2005).

[8] Y. Nakamura, K. Kishi, and H. Kawakami, Heartbeat synchronization for robotic cardiac surgery, in Proc. of IEEE International Conference on Robotics and Automation (ICRA), vol. 2, Seoul, Korea, May 2001, p.2014–(2019).

DOI: 10.1109/robot.2001.932903

[9] Rotella, J. (2005).

[10] Ortmaier, T. (2003). Motion compensation in minimally invasive robotic surgery. Technische Universität München, Universitätsbibliothek.

[11] Fan Liang, Xiaofeng Meng, Dengfeng Dong, Model following control of assisted robotics of CABG surgery, Optics and Precision Engineering, 2012 Vol. 20 (1): 131-139(in Chinese).