Algorithmic Foundations of Robotics IX pp 373-389

Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 68) | Cite as

LQG-Based Planning, Sensing, and Control of Steerable Needles

  • Jur van den Berg
  • Sachin Patil
  • Ron Alterovitz
  • Pieter Abbeel
  • Ken Goldberg

Abstract

This paper presents a technique for planning and controlling bevel-tip steerable needles towards a target location in 3-D anatomy under the guidance of partial, noisy sensor feedback. Our approach minimizes the probability that the needle intersects obstacles such as bones and sensitive organs by (1) explicitly taking into account motion uncertainty and sensor types, and (2) allowing for efficient optimization of sensor placement.We allow for needle trajectories of arbitrary curvature through duty-cycled spinning of the needle, which is conjectured to make a needle path small-time locally “trackable” [13]. This enables us to use LQG control to guide the needle along the path. For a given path and sensor placement, we show that a priori probability distributions of the needle state can be estimated in advance. Our approach then plans a set of candidate paths and sensor placements and selects the pair for which the estimated uncertainty is least likely to cause intersections with obstacles. We demonstrate the performance of our approach in a modeled prostate cancer treatment environment.

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References

  1. 1.
    Alterovitz, R., Goldberg, K., Okamura, A.: Planning for steerable bevel-tip needle insertion through 2D soft tissue with obstacles. In: IEEE Int. Conf. on Robotics and Automation (2005)Google Scholar
  2. 2.
    Alterovitz, R., Branicky, M., Goldberg, K.: Motion planning under uncertainty for image-guided medical needle steering. Int. J. Robotics Research 27(11-12), 1361–1374 (2008)CrossRefGoogle Scholar
  3. 3.
    Alterovitz, R., Siméon, T., Goldberg, K.: The stochastic motion roadmap: a sampling framework for planning with Markov motion uncertainty. In: Robotics: Science and Systems (2007)Google Scholar
  4. 4.
    Baldwin, G., Mahony, R., Trumph, J., Hamel, T., Cheviron, T.: Complementary filter design on the Special Euclidean group SE(3). In: European Control Conference (2007)Google Scholar
  5. 5.
    Bertsekas, D.: Dynamic programming and optimal control. Athena Scientific (2001)Google Scholar
  6. 6.
    Chentanez, N., Alterovitz, R., Ritchie, D., Cho, L., Hauser, K., Goldberg, K., Shewchuk, J., O’Brien, J.F.: Interactive Simulation of Surgical Needle Insertion and Steering. ACM Trans. on Graphics 28(3), 88.1–88.10 (2009)Google Scholar
  7. 7.
    Cowan, N.J., Goldberg, K., Chirikjian, G.S., Fichtinger, G., Alterovitz, R., Reed, K.B., Kallem, V., Park, W., Misra, S., Okamura, A.M.: Robotic Needle Steering: Design, Modeling, Planning, and Image Guidance. In: Surgical Robotics - Systems, Applications, and Visions. Springer, Heidelberg (2010)Google Scholar
  8. 8.
    Duindam, V., Alterovitz, R., Sastry, S., Goldberg, K.: Screw-based motion planning for bevel-tip flexible needles in 3D environments with obstacles. In: IEEE Int. Conf. on Robotics and Automation (2008)Google Scholar
  9. 9.
    Duindam, V., Xu, J., Alterovitz, R., Sastry, S., Goldberg, K.: Three-dimensional motion planning algorithms for steerable needles using inverse kinematics. Int. J. Robotics Research 29(7), 789–800 (2010)CrossRefGoogle Scholar
  10. 10.
    Hall, J., Knoebel, N., McLain, T.: Quaternion attitude estimation for miniature air vehicles using a multiplicative extended Kalman filter. In: IEEE/ION Position, Location and Navigation Symp. (2008)Google Scholar
  11. 11.
    Hauser, K., Alterovitz, R., Chentanez, N., Okamura, A., Goldberg, K.: Feedback control for steering needles through 3D deformable tissue using helical paths. In: Robotics: Science and Systems (2009)Google Scholar
  12. 12.
    Kallem, V., Cowan, N.: Image-guided control of flexible bevel-tip needles. In: IEEE Int. Conf. on Robotics and Automation (2007)Google Scholar
  13. 13.
    Kallem, V.: Vision-based control on lie groups with application to needle steering. PhD Thesis, Johns Hopkins University (2008)Google Scholar
  14. 14.
    LaValle, S., Kuffner, J.: Randomized kinodynamic planning. Int. J. Robotics Research 20(5), 378–400 (2001)CrossRefGoogle Scholar
  15. 15.
    Lefferts, E., Markley, F., Shuster, M.: Kalman filtering for spacecraft attitude estimation. Journal of Guidance, Control and Dynamics 5(5), 417–429 (1982)CrossRefGoogle Scholar
  16. 16.
    Minhas, D., Engh, J., Fenske, M., Riviere, C.: Modeling of needle steering via duty-cycled spinning. In: Int. Conf. IEEE Engineering in Medicine and Biology Society (2007)Google Scholar
  17. 17.
    Olver, F.W., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge (2010)MATHGoogle Scholar
  18. 18.
    Park, W., Kim, J., Zhou, Y., Cowan, N., Okamura, A., Chirikjian, G.: Diffusion-based motion planning for a nonholonomic flexible needle model. In: IEEE Int. Conf. on Robotics and Automation (2005)Google Scholar
  19. 19.
    Park, W., Wang, Y., Chirikjian, G.: Path planning for flexible needles using second order error propagation. In: Workshop on Algorithmic Foundations of Robotics (2008)Google Scholar
  20. 20.
    Patil, S., Alterovitz, R.: Interactive motion planning for steerable needles in 3D environments with obstacles. In: IEEE Int. Conf. on Biomedical Robotics and Biomechatronics (2010)Google Scholar
  21. 21.
    Petersen, K., Pedersen, M.: The Matrix Cookbook. Tech. Univ. of Denmark (2008)Google Scholar
  22. 22.
    Reed, K., Kallem, V., Alterovitz, R., Goldberg, K., Okamura, A., Cowan, N.: Integrated planning and image-guided control for planar needle steering. In: IEEE/RAS-EMBS Int. Conf. Biomedical Robotics and Biomechatronics (2008)Google Scholar
  23. 23.
    Reed, K., Okamura, A., Cowan, N.: Controlling robotically steered needle in the presence of torsional friction. In: IEEE Int. Conf. on Robotics and Automation (2009)Google Scholar
  24. 24.
    Trawny, N., Roumeliotis, S.: Indirect Kalman filter for 3D attitude estimation; a tutorial for quaternion algebra. Tech. report TR-2005-002, University of Minnesota (2005)Google Scholar
  25. 25.
    van den Berg, J., Abbeel, P., Goldberg, K.: LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information. In: Robotics: Science and Systems (2010)Google Scholar
  26. 26.
    van den Bergen, G.: Collision detection in interactive 3D environments. Morgan Kaufmann Publishers, San Francisco (2004)Google Scholar
  27. 27.
    Webster, R., Kim, J., Cowan, N., Chirikjian, G., Okamura, A.: Nonholonomic modeling of needle steering. Int. J. Robotics Research 25(5-6), 509–525 (2006)CrossRefGoogle Scholar
  28. 28.
    Welch, G., Bishop, G.: An introduction to the Kalman filter. Tech. Report TR 95-041, University of North Carolina at Chapel Hill (2006)Google Scholar
  29. 29.
    Xu, J., Duindam, V., Alterovitz, R., Goldberg, K.: Motion planning for steerable needles in 3D environments with obstacles using rapidly-exploring random trees and backchaining. In: IEEE Int. Conf. on Automation Science and Engineering (2008)Google Scholar
  30. 30.
    Xu, J., Duindam, V., Alterovitz, R., Pouliot, J., Cunha, A., Hsu, I., Goldberg, K.: Planning fireworks trajectories for steerable medical needles to reduce patient trauma. In: IEEE Int. Conf. on Intelligent Robots and Systems (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jur van den Berg
    • 1
  • Sachin Patil
    • 1
  • Ron Alterovitz
    • 1
  • Pieter Abbeel
    • 2
  • Ken Goldberg
    • 2
  1. 1.University of North CarolinaChapel Hill
  2. 2.University of CaliforniaBerkeley

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