Application of Unscented Kalman Filter to a cable driven surgical robot: A simulation study

Cable driven power transmissions are used in applications such as haptic devices, surgical robots etc. The use of flexible cable based power transmission often causes relative motion between the motor actuator and mechanism joint during operation due to the elasticity of the cable. State-space control methods can be used to improve performance, but may require state estimates. For nonlinear systems, the Unscented Kalman Filter (UKF) provides a computationally efficient way to obtain state estimates. The UKF is applied here to a simulation of a minimially invasive surgical robot, to study the state estimation for a cable driven system with nonlinear dynamics. State estimates from the UKF are compared with the known states available from the simulation. These state estimates are also utilized by two different controllers interacting with the simulation to test the UKF performance under closed loop control. We tested the UKF performance with error perturbations in the system model's cable stiffness parameter.

[1]  J. Y. S. Luh,et al.  On-Line Computational Scheme for Mechanical Manipulators , 1980 .

[2]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[3]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[4]  Thomas H. Massie,et al.  The PHANToM Haptic Interface: A Device for Probing Virtual Objects , 1994 .

[5]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[6]  S. Haykin Kalman Filtering and Neural Networks , 2001 .

[7]  Rudolph van der Merwe,et al.  The square-root unscented Kalman filter for state and parameter-estimation , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[8]  Wisama Khalil,et al.  Modeling, Identification & Control of Robots , 2002 .

[9]  Blake Hannaford,et al.  Smart surgical tools and augmenting devices , 2003, IEEE Trans. Robotics Autom..

[10]  James C. Spall,et al.  Introduction to stochastic search and optimization - estimation, simulation, and control , 2003, Wiley-Interscience series in discrete mathematics and optimization.

[11]  James C. Spall,et al.  Introduction to Stochastic Search and Optimization. Estimation, Simulation, and Control (Spall, J.C. , 2007 .

[12]  Randall J. LeVeque,et al.  Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems , 2007 .

[13]  Bjarne A. Foss,et al.  Applying the unscented Kalman filter for nonlinear state estimation , 2008 .

[14]  Blake Hannaford,et al.  Robustness of the Unscented Kalman filter for state and parameter estimation in an elastic transmission , 2009, Robotics: Science and Systems.

[15]  Blake Hannaford,et al.  The RAVEN: Design and Validation of a Telesurgery System , 2009, Int. J. Robotics Res..

[16]  Blake Hannaford,et al.  Raven: Developing a Surgical Robot from a Concept to a Transatlantic Teleoperation Experiment , 2011 .