Deformation-as-control for a biologically inspired steerable needle

STING, a biologically inspired steerable needle robot, has the potential to improve diagnostic and drug delivery therapies in neurosurgery. Real-time path planning for steerable needles remains challenging due to complex kinematic constraints and tissue deformation. Inspired by deformation theory, this paper introduces a “deformation-as-control” method for transforming non-linear path planning problems into linear formulations. Both theoretical analysis and simulations in two-and three-dimensional space confirm that the method is fast, robust, smooth and accurate. As a result, it can be used for real-time control of steerable needles to overcome tissue deformation, as well as being easily adaptable to other continuum style or nonholonomic robots.

[1]  Ferdinando Rodriguez y Baena,et al.  Risk-based path planning for a steerable flexible probe for neurosurgical intervention , 2012, 2012 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob).

[2]  Edgar J. Lobaton,et al.  Planning curvature-constrained paths to multiple goals using circle sampling , 2011, 2011 IEEE International Conference on Robotics and Automation.

[3]  Seong-Young Ko,et al.  Smooth path planning for a biologically-inspired neurosurgical probe , 2012, 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[4]  Ron Alterovitz,et al.  Motion planning under uncertainty using iterative local optimization in belief space , 2012, Int. J. Robotics Res..

[5]  K. Lynch.  Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[6]  Jin Seob Kim,et al.  Nonholonomic Modeling of Needle Steering , 2006, Int. J. Robotics Res..

[7]  Jin Seob Kim,et al.  Diffusion-Based Motion Planning for a Nonholonomic Flexible Needle Model , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[8]  Riccardo Secoli,et al.  Closed-loop 3D motion modeling and control of a steerable needle for soft tissue surgery , 2013, 2013 IEEE International Conference on Robotics and Automation.

[9]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[10]  Barry Mazur,et al.  An Introduction to the Deformation Theory of Galois Representations , 1997 .

[11]  P. Tsiotras,et al.  Control design for chained-form systems with bounded inputs , 2000 .

[12]  Hugh F. Durrant-Whyte,et al.  Using Lie Group Symmetries for Fast Corrective Motion Planning , 2010, WAFR.

[13]  R. Bishop.  There is More than One Way to Frame a Curve , 1975 .

[14]  Kun Zhou,et al.  Mesh editing with poisson-based gradient field manipulation , 2004, ACM Trans. Graph..

[15]  Seong-Young Ko,et al.  Closed-Loop Planar Motion Control of a Steerable Probe With a “Programmable Bevel” Inspired by Nature , 2011, IEEE Transactions on Robotics.

[16]  L Frasson,et al.  STING: a soft-tissue intervention and neurosurgical guide to access deep brain lesions through curved trajectories , 2010, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[17]  S. Shankar Sastry,et al.  Three-dimensional Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics , 2010, Int. J. Robotics Res..

[18]  Mubarak Shah,et al.  A differential geometric approach to representing the human actions , 2008, Comput. Vis. Image Underst..

[19]  D. Levin,et al.  Linear rotation-invariant coordinates for meshes , 2005, SIGGRAPH 2005.

[20]  Nancy M. Amato,et al.  Probabilistic roadmap motion planning for deformable objects , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[21]  David Mumford,et al.  2D-Shape Analysis Using Conformal Mapping , 2004, CVPR.

[22]  Jian J. Zhang,et al.  Motion Adaptation With Motor Invariant Theory , 2013, IEEE Transactions on Cybernetics.

[23]  Steven M. LaValle,et al.  Randomized Kinodynamic Planning , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[24]  Allison M. Okamura,et al.  Feedback control for steering needles through 3D deformable tissue using helical paths , 2009, Robotics: Science and Systems.

[25]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[26]  Matthew R. Walter,et al.  Reachability-guided sampling for planning under differential constraints , 2009, 2009 IEEE International Conference on Robotics and Automation.