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Anna Yershova Dept. of Computer Science, Duke University October 20, 2009

Sampling and Searching Methods in Robotics and Computational Biology. Anna Yershova Dept. of Computer Science, Duke University October 20, 2009. Anna Yershova. NIFP Workshop, Rice University. Introduction. Research Theme.

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Anna Yershova Dept. of Computer Science, Duke University October 20, 2009

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  1. Sampling and Searching Methods inRobotics and Computational Biology Anna Yershova Dept. of Computer Science, Duke University October 20, 2009 Anna Yershova NIFP Workshop, Rice University

  2. Introduction Research Theme • Underlying spaces in many real-world problems have similar geometric and topological structures. Ideas and methods used to solve these problems are shared across disciplines. • Examples: • Configuration and state spaces in motion planning • Information spaces in robotics • Conformation spaces in structural computational biology • High-dimensional manifolds, or collections of manifolds Anna Yershova NIFP Workshop, Rice University

  3. Technical Contributions Motion Planning Contributions by Topic Motion Planning • uniform deterministic sampling over configuration spaces • efficient nearest-neighbor computations • guided sampling for efficient exploration Planning Under Sensing Uncertainty • mapping and pursuit-evasion with a wall-following robot Structural Computational Biology • exact protein structure determination from sparse NMR data NIFP Workshop, Rice University Anna Yershova

  4. Technical Contributions Motion Planning Sampling Spheres • Performance of many motion planning algorithms can be significantly improved using careful sampling over configuration spaces + uniform + deterministic + incremental + grid structure Ordering on faces + Ordering inside faces NIFP Workshop, Rice University Anna Yershova

  5. Technical Contributions Motion Planning Sampling SO(3) • Hopf coordinates preserve the fiber bundle structure of RP3 • Locally, RP3 is a product of S1 and S2 Joint work with J.C.Mitchell NIFP Workshop, Rice University Anna Yershova

  6. Technical Contributions Motion Planning Outcomes • Publications: • Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibrations(with S. Jain, S. M. LaValle and J.C. Mitchell)International Journal on Robotics Research (IJRR 2009), in press • Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibrations(with S. M. LaValle and J. C. Mitchell)International Workshop on the Algorithmic Foundations of Robotics (WAFR 2008) • Deterministic sampling methods for spheres and SO(3) (with S. M. LaValle)IEEE International Conference on Robotics and Automation (ICRA 2004) • Incremental Grid Sampling Strategies in Robotics (with S. R. Lindemann, and S. M. LaValle)International Workshop on the Algorithmic Foundations of Robotics (WAFR 2004) • Open-source library: • http://msl.cs.uiuc.edu/~yershova/sampling/sampling.tar.gz NIFP Workshop, Rice University Anna Yershova

  7. Technical Contributions Motion Planning Contributions by Topic Motion Planning • uniform deterministic sampling over configuration spaces • efficient nearest-neighbor computations • guided sampling for efficient exploration Planning Under Sensing Uncertainty • mapping and pursuit-evasion with a wall-following robot Structural Computational Biology • exact protein structure determination from sparse NMR data NIFP Workshop, Rice University Anna Yershova

  8. Technical Contributions Motion Planning l1 4 6 l9 7 l5 l6 8 l3 l2 5 9 10 3 l10 l8 l7 2 1 l4 11 2 5 4 11 8 1 3 9 10 6 7 Kd-trees with modified metric Main idea: construction: unchanged procedure query: modify metric between the query point and enclosing rectangles in the kd-tree l1 l3 l2 [0,1]xS1 l4 l5 l7 l6 l8 l10 l9 NIFP Workshop, Rice University Anna Yershova

  9. Technical Contributions Motion Planning Outcomes • Publications: • Improving Motion Planning Algorithms by Efficient Nearest Neighbor Searching(with S. M. LaValle)IEEE Transactions on Robotics23(1):151-157, February 2007 • Efficient Nearest Neighbor Searching for Motion Planning(with S. M. LaValle)In Proc. IEEE International Conference on Robotics and Automation (ICRA 2002) • Open-source library: • http://msl.cs.uiuc.edu/~yershova/mpnn/mpnn.tar.gz Also implemented in Move3D at LAAS, and KineoWorksTM NIFP Workshop, Rice University Anna Yershova

  10. Technical Contributions Sensing Uncertainty in Robotics Contributions by Topic Motion Planning • uniform deterministic sampling over configuration spaces • efficient nearest-neighbor computations • guided sampling for efficient exploration Planning Under Sensing Uncertainty • mapping and pursuit-evasion with a wall-following robot Structural Computational Biology • exact protein structure determination from sparse NMR data NIFP Workshop, Rice University Anna Yershova

  11. Technical Contributions Sensing Uncertainty in Robotics Planning in Information Spaces I-space:space of all cut diagrams of planar environments NIFP Workshop, Rice University Anna Yershova

  12. Technical Contributions Sensing Uncertainty in Robotics Outcomes • Publications: • Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot(with B. Tovar, R. Ghrist, and S. M. LaValle)submitted to IEEE Transactions on Robotics, 2009 • Extracting Visibility Information by Following Walls(with B. Tovar, and S. M. LaValle)In Dagstuhl Seminar Proceedings, 06421,Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI),Schloss Dagstuhl, Germany, 2007. • Information Spaces for Mobile Robots(with B. Tovar, J. M. O'Kane, and S. M. LaValle)invited paper at Fifth International Workshop on Robot Motion and Control (RoMoCo 2005)  • Bitbots: Simple Robots Solving Complex Tasks(with B. Tovar, R. Ghrist, and S. M. LaValle)In Proc. The Twentieth National Conference on Artificial Intelligence (AAAI 2005)  NIFP Workshop, Rice University Anna Yershova

  13. Technical Contributions Structural Computational Geometry Contributions by Topic Motion Planning • uniform deterministic sampling over configuration spaces • efficient nearest-neighbor computations • guided sampling for efficient exploration Planning Under Sensing Uncertainty • mapping and pursuit-evasion with a wall-following robot Structural Computational Biology • exact protein structure determination from sparse NMR data NIFP Workshop, Rice University Anna Yershova

  14. Technical Contributions Structural Computational Geometry RDC Equations for a Protein Portion 14 NIFP Workshop, Rice University Anna Yershova

  15. Technical Contributions Structural Computational Geometry Preliminary Results: 13dz helix Conformation of the portion [25-31] of the helix for human ubiquitin computed using NH and CH RDCs in two media (red) has been superimposed on the same portion from high-resolution X-ray structure (PDB Id: 1UBQ) (green). The backbone RMSD is 0.58 Å. 15

  16. Technical Contributions Structural Computational Geometry Outcomes • Protein Structure Determination using Sparse Orientational Restraints from NMR Data (with C. Tripathy, P. Zhou, B. R. Donald)Biochemistry Department Retreat, NC Biotechnology Center, RTP, NC, 2009.Winner of Best Poster Award.  NIFP Workshop, Rice University Anna Yershova

  17. Conclusions Conclusions and Future Goals • Apply and extend the mathematical tools needed for solving problems in • Robotics • Algebraic varieties • Trajectories • Computational Biology • Other NMR data • Other imaging techniques • potentially other disciplines • Technology transfer between disciplines NIFP Workshop, Rice University Anna Yershova

  18. Conclusions Conclusions and Future Directions Thank you! NIFP Workshop, Rice University Anna Yershova

  19. Technical Contributions Motion Planning Contributions by Topic Motion Planning • uniform deterministic sampling over configuration spaces • efficient nearest-neighbor computations • guided sampling for efficient exploration Planning Under Sensing Uncertainty • mapping and pursuit-evasion with a wall-following robot Structural Computational Biology • exact protein structure determination from sparse NMR data NIFP Workshop, Rice University Anna Yershova

  20. Technical Contributions Motion Planning KD-Tree-Based Dynamic Domain 330 degrees of freedom Courtesy of Kineo CAM NIFP Workshop, Rice University Anna Yershova

  21. Technical Contributions Motion Planning Outcomes • Publications: • Adaptive Tuning of the Sampling Domain for Dynamic-Domain RRTs(with L. Jaillet, S. M. LaValle and T. Simeon)In Proc. IEEE International Conference on Intelligent Robots and Systems (IROS 2005)  • Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain(with L. Jaillet, T. Simeon, and S. M. LaValle)In Proc. IEEE International Conference on Robotics and Automation (ICRA 2005) Also implemented in • Move3D at LAAS • KineoWorksTM • Toyota Corporation NIFP Workshop, Rice University Anna Yershova

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