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Sensor-Based Reactive Navigation in Unknown Convex Sphere Worlds

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Algorithmic Foundations of Robotics XII

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 13))

Abstract

We construct a sensor-based feedback law that provably solves the real-time collision-free robot navigation problem in a compact convex Euclidean subset cluttered with unknown but sufficiently separated and strongly convex obstacles. Our algorithm introduces a novel use of separating hyperplanes for identifying the robot’s local obstacle-free convex neighborhood, affording a reactive (online-computed) piecewise smooth and continuous closed-loop vector field whose smooth flow brings almost all configurations in the robot’s free space to a designated goal location, with the guarantee of no collisions along the way. We further extend these provable properties to practically motivated limited range sensing models.

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References

  1. Trautman, P., Ma, J., Murray, R.M., Krause, A.: Robot navigation in dense human crowds:Statistical models and experimental studies of humanrobot cooperation. The InternationalJournal of Robotics Research 34(3) (2015) 335-356

    Google Scholar 

  2. Henry, P., Vollmer, C., Ferris, B., Fox, D.: Learning to navigate through crowded environments. In: Robotics and Automation, IEEE International Conference on. (2010) 981-986

    Google Scholar 

  3. Karaman, S., Frazzoli, E.: High-speed flight in an ergodic forest. In: Robotics and Automation (ICRA), IEEE International Conference on. (2012) 2899-2906

    Google Scholar 

  4. Paranjape, A.A.,Meier, K.C., Shi, X., Chung, S.J.,Hutchinson, S.: Motion primitives and 3Dpath planning for fast flight through a forest. The Int. J. Robot. Res. 34(3) (2015) 357-377

    Google Scholar 

  5. Wooden, D., Malchano, M., Blankespoor, K., Howardy, A., Rizzi, A.A., Raibert, M.: Autonomous navigation for BigDog. In: IEEE Int. Conf. Robot. Autom. (2010) 4736-4741

    Google Scholar 

  6. Johnson, A.M., Hale, M.T., Haynes, G.C., Koditschek, D.E.: Autonomous legged hill and stairwell ascent. In: IEEE Int. Symp. on Safety, Security, Rescue Robotics. (2011) 134-142

    Google Scholar 

  7. Choset, H., Lynch, K.M., Hutchinson, S., Kantor, G.A., Burgard, W., Kavraki, L.E., Thrun, S.: Principles of RobotMotion: Theory, Algorithms, and Implementations. MIT Press (2005)

    Google Scholar 

  8. LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge, U.K. (2006)

    Google Scholar 

  9. Koditschek, D.E., Rimon, E.: Robot navigation functions on manifolds with boundary. Advancesin Applied Mathematics 11(4) (1990) 412-442

    Google Scholar 

  10. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. The International Journal of Robotics Research 5(1) (1986) 90-98

    Google Scholar 

  11. Koditschek, D.E.: Exact robot navigation by means of potential functions: Some topological considerations. In: Robotics and Automation, IEEE International Conference on. (1987) 1-6

    Google Scholar 

  12. Borenstein, J., Koren, Y.: The vector field histogram-fast obstacle avoidance for mobile robots. IEEE Transactions on Robotics and Automation 7(3) (1991) 278-288

    Google Scholar 

  13. Simmons, R.: The curvature-velocity method for local obstacle avoidance. In: Robotics and Automation (ICRA), IEEE International Conference on. (1996) 3375-3382

    Google Scholar 

  14. Fox, D., Burgard, W., Thrun, S.: The dynamic window approach to collision avoidance. IEEE Robotics Automation Magazine 4(1) (1997) 23-33

    Google Scholar 

  15. Fiorini, P., Shiller, Z.: Motion planning in dynamic environments using velocity obstacles. The International Journal of Robotics Research 17(7) (1998) 760-772

    Google Scholar 

  16. Rimon, E., Koditschek, D.E.: Exact robot navigation using artificial potential functions. Robotics and Automation, IEEE Transactions on 8(5) (1992) 501-518

    Google Scholar 

  17. Lionis, G., Papageorgiou, X., Kyriakopoulos, K.J.: Locally computable navigation functions for sphere worlds. In: Robotics and Automation, IEEE Int. Conf. on. (2007) 1998-2003

    Google Scholar 

  18. Filippidis, I., Kyriakopoulos, K.J.: Adjustable navigation functions for unknown sphere worlds. In: IEEE Decision and Control and European Control Conf. (2011) 4276-4281

    Google Scholar 

  19. Burridge, R.R., Rizzi, A.A., Koditschek, D.E.: Sequential composition of dynamically dexterous robot behaviors. The International Journal of Robotics Research 18(6) (1999) 535-555

    Google Scholar 

  20. Conner, D.C., Choset, H., Rizzi, A.A.: Flow-through policies for hybrid controller synthesis applied to fully actuated systems. Robotics, IEEE Transactions on 25(1) (2009) 136-146

    Google Scholar 

  21. Choset, H., Burdick, J.: Sensor-based exploration: The hierarchical generalized Voronoi graph. The International Journal of Robotics Research 19(2) (2000) 96-125

    Google Scholar 

  22. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)

    Google Scholar 

  23. Arslan, O., Koditschek, D.E.: Exact robot navigation using power diagrams. In: Robotics and Automation (ICRA), IEEE International Conference on. (2016) 1-8

    Google Scholar 

  24. Aurenhammer, F.: Power diagrams: Properties, algorithms and applications. SIAM Journal on Computing 16(1) (1987) 78-96

    Google Scholar 

  25. Webster, R.: Convexity. Oxford University Press (1995)

    Google Scholar 

  26. Arslan, O., Koditschek, D.E.: Sensor-based reactive navigation in unknown convex sphere worlds. Technical report, University of Pennsylvania (2016) Online available at: http://kodlab.seas.upenn.edu/Omur/WAFR2016.

  27. Ó’Dúnlaing, C., Yap, C.K.: A retraction method for planning the motion of a disc. Journal of Algorithms 6(1) (1985) 104 - 111

    Google Scholar 

  28. Cortés, J.,Martınez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. Robotics and Automation, IEEE Transactions on 20(2) (2004) 243-255

    Google Scholar 

  29. Kwok, A., Martnez, S.: Deployment algorithms for a power-constrained mobile sensor network. International Journal of Robust and Nonlinear Control 20(7) (2010) 745-763

    Google Scholar 

  30. Pimenta, L.C., Kumar, V.,Mesquita, R.C., Pereira, G.A.: Sensing and coverage for a network of heterogeneous robots. In: Decision and Control, IEEE Conference on. (2008) 3947-3952

    Google Scholar 

  31. Arslan, O., Koditschek, D.E.: Voronoi-based coverage control of heterogeneous disk-shaped robots. In: Robotics and Automation, IEEE International Conference on. (2016) 4259-4266

    Google Scholar 

  32. Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. 2nd edn. Volume 501. John Wiley & Sons (2000)

    Google Scholar 

  33. Haralick, R.M., Sternberg, S.R., Zhuang, X.: Image analysis using mathematical morphology. Pattern Analysis and Machine Intelligence, IEEE Transactions on 9(4) (1987) 532-550

    Google Scholar 

  34. Munkres, J.: Topology. 2nd edn. Pearson (2000)

    Google Scholar 

  35. Kozlov, M., Tarasov, S., Khachiyan, L.: The polynomial solvability of convex quadratic programming. USSR Comp. Mathematics and Mathematical Physics 20(5) (1980) 223-228

    Google Scholar 

  36. Bullo, F., Cortés, J.,Martinez, S.: Distributed Control of Robotic Networks: AMathematical Approach to Motion Coordination Algorithms. Princeton University Press (2009)

    Google Scholar 

  37. Rockafellar, R.: Lipschitzian properties of multifunctions. Nonlinear Analysis: Theory, Methods & Applications 9(8) (1985) 867-885

    Google Scholar 

  38. Kuntz, L., Scholtes, S.: Structural analysis of nonsmooth mappings, inverse functions, and metric projections. Journal of Math. Analysis and Applications 188(2) (1994) 346-386

    Google Scholar 

  39. Shapiro, A.: Sensitivity analysis of nonlinear programs and differentiability properties of metric projections. SIAM Journal on Control and Optimization 26(3) (1988) 628-645

    Google Scholar 

  40. Liu, J.: Sensitivity analysis in nonlinear programs and variational inequalities via continuous selections. SIAM Journal on Control and Optimization 33(4) (1995) 1040-1060

    Google Scholar 

  41. Chaney, R.W.: Piecewise \(\text{C}^{\text{ k }}\) functions in nonsmooth analysis. Nonlinear Analysis: Theory, Methods & Applications 15(7) (1990) 649 - 660

    Google Scholar 

  42. Khalil, H.K.: Nonlinear Systems. 3rd edn. Prentice Hall (2001)

    Google Scholar 

  43. Paternain, S., Koditschek, D.E., Ribeiro, A.: Navigation functions for convex potentials in a space with convex obstacles. IEEE Transactions on Automatic Control (submitted)

    Google Scholar 

  44. Holmes, R.B.: Smoothness of certain metric projections on Hilbert space. Transactions of the American Mathematical Society 184 (1973) 87-100

    Google Scholar 

  45. Fitzpatrick, S., Phelps, R.R.: Differentiability of the metric projection in Hilbert space. Transactions of the American Mathematical Society 270(2) (1982) 483-501

    Google Scholar 

  46. Hirsch, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems, and an Introduction to Chaos. 2nd edn. Academic Press (2003)

    Google Scholar 

  47. Stewart, J.: Calculus: Early Transcendentals. 7th edn. Cengage Learning (2012)

    Google Scholar 

  48. Kolmanovsky, I., Garone, E., Cairano, S.D.: Reference and command governors: A tutorial on their theory and automotive applications. In: American Control Conf. (2014) 226-241

    Google Scholar 

  49. Arslan, O., Koditschek, D.E.: Smooth extensions of feedback motion planners via reference governors. In: (accepted) Robotics and Automation (ICRA), IEEE Int. Conf. on. (2017)

    Google Scholar 

  50. Vasilopoulos, V., Arslan, O., De, A., Koditschek, D.E.: Minitaur bounds home through a locally sensed artificial forest. In: (submitted) IEEE/RSJ Int. Conf. Intel. Robot. Sys. (2017)

    Google Scholar 

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Authors and Affiliations

  1. University of Pennsylvania, Philadelphia, PA, 19103, USA

    Omur Arslan & Daniel E. Koditschek

Authors
  1. Omur Arslan
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  2. Daniel E. Koditschek
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Corresponding author

Correspondence to Omur Arslan .

Editor information

Editors and Affiliations

  1. Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA

    Ken Goldberg

  2. Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA

    Pieter Abbeel

  3. Rutgers University, Piscataway, NJ, USA

    Kostas Bekris

  4. University of California, Berkeley, CA, USA

    Lauren Miller

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Arslan, O., Koditschek, D.E. (2020). Sensor-Based Reactive Navigation in Unknown Convex Sphere Worlds. In: Goldberg, K., Abbeel, P., Bekris, K., Miller, L. (eds) Algorithmic Foundations of Robotics XII. Springer Proceedings in Advanced Robotics, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-43089-4_11

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