Skip to content Skip to sidebar Skip to footer
Home / Continuous Path Smoothing for Car like Robots Using B spline Curves

Continuous Path Smoothing for Car like Robots Using B spline Curves

Post a Comment

Abstract

A practical approach for generating motion paths with continuous steering for car-like mobile robots is presented here. This paper addresses two key issues in robot motion planning; path continuity and maximum curvature constraint for nonholonomic robots. The advantage of this new method is that it allows robots to account for their constraints in an efficient manner that facilitates real-time planning. B-spline curves are leveraged for their robustness and practical synthesis to model the vehicle's path. Comparative navigational-based analyses are presented to selected appropriate curve and nominate its parameters. Path continuity is achieved by utilizing a single path, to represent the trajectory, with no limitations on path, or orientation. The path parameters are formulated with respect to the robot's constraints. Maximum curvature is satisfied locally, in every segment using a smoothing algorithm, if needed. It is demonstrated that any local modifications of single sections have minimal effect on the entire path. Rigorous simulations are presented, to highlight the benefits of the proposed method, in comparison to existing approaches with regards to continuity, curvature control, path length and resulting acceleration. Experimental results validate that our approach mimics human steering with high accuracy. Accordingly, efficiently formulated continuous paths ultimately contribute towards passenger comfort improvement. Using presented approach, autonomous vehicles generate and follow paths that humans are accustomed to, with minimum disturbances.

References

  1. Reif, J.H.: Complexity of the mover's problem and generalizations. In: Foundations of Computer Science, 1979., 20th Annual Symposium on, pp. 421–427 (1979)

  2. Latombe, J.-C.: Motion Planning: A journey of robots, molecules, digital actors, and other artifacts. Int. J. Robot. Res. 18(11), 1119–1128 (1999). doi:10.1177/02783649922067753

    Article  Google Scholar

  3. Choset, H.M.: Principles of Robot Motion, Theory, Algorithms, and Implementation. Prentice Hall of India (2005)

  4. Brooks, R.A., Lozano-Perez, T.: A subdivision algorithm in configuration space for findpath with rotation. IEEE Trans. Syst. Man Cybern. 15(2), 224–233 (1985). doi:10.1109/TSMC.1985.6313352

    Article  Google Scholar

  5. Canny, J.: A Voronoi method for the piano-movers problem. In: Robotics and Automation. Proceedings. 1985 IEEE International Conference on, pp. 530–535 (1985)

  6. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986). doi:10.1177/027836498600500106

    Article  MathSciNet  Google Scholar

  7. Arkin, R.C.: Motor Schema Based Mobile Robot Navigation. Int. J. Robot. Res. 8(4), 92–112 (1989). doi:10.1177/027836498900800406

    Article  Google Scholar

  8. Koren, Y., Borenstein, J.: Potential field methods and their inherent limitations for mobile robot navigation. In: Robotics and Automation, 1991. Proceedings., 1991 IEEE International Conference on, vol. 1392, pp. 1398–1404 (1991)

  9. Elbanhawi, M., Simic, M.: Sampling-based robot motion planning: a review. IEEE Access 2, 56–77 (2014). doi:10.1109/ACCESS.2014.2302442

    Article  Google Scholar

  10. Geraerts, R., Overmars, M.H.: Creating high-quality paths for motion planning. Int. J. Robot. Res. 26(8), 845–863 (2007). doi:10.1177/0278364907079280

    Article  Google Scholar

  11. Laumond, J.P., Sekhavat, S., Lamiraux, F.: Guidelines in nonholonomic motion planning for mobile robots. In: J.P. Laumond (ed.) Robot Motion Planning and Control, vol. 229. Lecture Notes in Control and Information Sciences, pp. 1–53. Springer Berlin Heidelberg (1998)

  12. Cheng, P.: Sampling-based motion planning with differential constraints. Ph.D. University of Illinois at Urbana-Champaign (2005)

  13. Wallace, R., Stentz, A., Thorpe, C., Moravec, H., Whittaker, W., Kanade, T.: First Results in Robot Road Following. In: 1985, pp. 381–387

  14. Antonelli, G., Chiaverini, S., Fusco, G.: A fuzzy-logic-based approach for mobile robot path tracking. IEEE Trans. Fuzzy Syst. 15(2), 211–221 (2007)

    Article  Google Scholar

  15. Perez, J., Milanes, V., Onieva, E.: Cascade architecture for lateral control in autonomous vehicles. IEEE Intell. Transp. Syst. 12(1), 73–82 (2011). doi:10.1109/TITS.2010.2060722

    Article  Google Scholar

  16. Jazar, R.N.: Mathematical theory of autodriver for autonomous vehicles. J. Vib. Control. 16(2), 253–279 (2010)

    Article  MathSciNet  MATH  Google Scholar

  17. Marzbani, H., Ahmad Salahuddin, M.H., Simic, M., Fard, M., Jazar, R.N.: Steady-state dynamic steering. In: Frontiers in Artificial Intelligence and Applications, vol. 262 (2014)

  18. Cheein, F.A., Scaglia, G.: Trajectory Tracking Controller Design for Unmanned Vehicles: A New Methodology. Journal of Field Robotics, n/a-n/a. doi:10.1002/rob.21492 (2013)

  19. Magid, E., Keren, D., Rivlin, E., Yavneh, I.: Spline-Based Robot Navigation. In: Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on, pp. 2296–2301 (2006)

  20. Roth, S., Batavia, P.: Evaluating Path Tracker Performance for Outdoor Mobile Robots. Paper presented at the Automation Technology for Off-Road Equipment, Chicago, Illinois, USA, 26–27/07

  21. Lau, B., Sprunk, C., Burgard, W.: Kinodynamic motion planning for mobile robots using splines. In: Intelligent Robots and Systems, 2009. IROS 2009. IEEE/RSJ International Conference on, pp. 2427–2433 (2009)

  22. Gulati, S., Kuipers, B.: High performance control for graceful motion of an intelligent wheelchair. In: Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, pp. 3932–3938 (2008)

  23. Berglund, T., Brodnik, A., Jonsson, H., Staffanson, M., Soderkvist, I.: Planning smooth and obstacle-avoiding b-spline paths for autonomous mining vehicles. IEEE Trans. Autom. Sci. Eng. 71), 167–172 (2010). doi:10.1109/TASE.2009.2015886

    Article  Google Scholar

  24. Maekawa, T., Noda, T., Tamura, S., Ozaki, T., Machida, K.-i.: Curvature continuous path generation for autonomous vehicle using B-spline curves. Comput. Aided Des. 42(4), 350–359 (2010) doi:10.1016/j.cad.2009.12.007

    Article  Google Scholar

  25. Sabelhaus, D., Röben, F., Meyer zu Helligen, L.P., Schulze Lammers, P.: Using continuous-curvature paths to generate feasible headland turn manoeuvres. Biosyst. Eng. 116(4), 399–409 (2013). doi:10.1016/j.biosystemseng.2013.08.012

    Article  Google Scholar

  26. Girbés, V., Armesto, L., Tornero, J.: Path following hybrid control for vehicle stability applied to industrial forklifts. Robot. Auton. Syst. 0 (2014). doi:10.1016/j.robot.2014.01.004

  27. Xuan-Nam, B., Boissonnat, J.-d., Soueres, P., Laumond, J.P.: Shortest path synthesis for Dubins non-holonomic robot. In: Robotics and Automation, 1994. Proceedings., 1994 IEEE International Conference on, 8–13 1994, Vol. 1, pp. 2–7

  28. Anderson, E.P., Beard, R.W., McLain, T.W.: Real-time dynamic trajectory smoothing for unmanned air vehicles. IEEE Trans. Control Syst. Technol. 13(3), 471–477 (2005). doi:10.1109/TCST.2004.839555

    Article  Google Scholar

  29. Myung, H., Kuffner, J., Kanade, T.: Efficient Two-phase 3D Motion Planning for Small Fixed-wing UAVs. In: Robotics and Automation, 2007 IEEE International Conference on, pp. 1035–1041 (2007)

  30. LaValle, S.: Planning Algorithms. Cambridge University Press (2006)

  31. Suzuki, Y., Kagami, S., Kuffner, J.J.: Path Planning with Steering Sets for Car-Like Robots and Finding an Effective Set. In: Robotics and Biomimetics, 2006. ROBIO '06. IEEE International Conference on, pp. 1221–1226 (2006)

  32. Pivtoraiko, M., Knepper, R.A., Kelly, A.: Differentially constrained mobile robot motion planning in state lattices. J. Field Robot. 26(3), 308–333 (2009)

    Article  Google Scholar

  33. Fraichard, T., Scheuer, A.: From Reeds and Shepp's to continuous-curvature paths. Robot. IEEE Trans. 20(6), 1025–1035 (2004). doi:10.1109/TRO.2004.833789

    Article  Google Scholar

  34. Wang, L.Z., Miura, K.T., Nakamae, E., Yamamoto, T., Wang, T.J.: An approximation approach of the clothoid curve defined in the interval [0, π/2] and its offset by free-form curves. Comput. Aided Des. 33(14), 1049–1058 (2001). doi:10.1016/S0010-4485(00)00142-1

    Article  Google Scholar

  35. Meek, D.S., Walton, D.J.: An arc spline approximation to a clothoid. J. Comput. Appl. Math. 170(1), 59–77 (2004) doi:10.1016/j.cam.2003.12.038

    Article  MathSciNet  MATH  Google Scholar

  36. Montes, N., Herraez, A., Armesto, L., Tornero, J.: Real-time clothoid approximation by Rational Bezier curves. In: In: Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, pp. 2246–2251 (2008)

  37. McCrae, J., Singh, K.: Sketching piecewise clothoid curves. Comput. Graph. 33(4), 452–461 (2009) doi:10.1016/j.cag.2009.05.006

    Article  Google Scholar

  38. Brezak, M., Petrovic, I.: Real-time approximation of clothoids with bounded error for path planning applications. IEEE Trans. Robot. PP(99), 1–9 (2013). doi:10.1109/TRO.2013.2283928

    Article  Google Scholar

  39. Farin, G.: From conics to NURBS: A tutorial and survey. IEEE Comput. Graph. Appl. 12(5), 78–86 (1992). doi:10.1109/38.156017

    Article  MathSciNet  Google Scholar

  40. Piegl, L.: On NURBS: a survey. IEEE Comput. Graph. Appl. 11(1), 55–71 (1991). doi:10.1109/38.67702

    Article  Google Scholar

  41. Farin, G.: Curves and Surfaces for CAGD. Computing. Morgan Kaufmann (2002)

  42. Lepetič, M., Klančar, G., Škrjanc, I., Matko, D., Potočnik, B.: Time optimal path planning considering acceleration limits. Robot. Auton. Syst. 45(3–4), 199–210 (2003). doi:10.1016/j.robot.2003.09.007

    Article  Google Scholar

  43. Jolly, K.G., Sreerama Kumar, R., Vijayakumar, R.: A Bezier curve based path planning in a multi-agent robot soccer system without violating the acceleration limits. Robot. Auton. Syst. 57(1), 23–33 (2009). doi:10.1016/j.robot.2008.03.009

    Article  Google Scholar

  44. Schoenberg, I.J.: Contributions to the problem of approximation of equidistant data by analytic functions - b. on the problem of osculatory interpolation - a 2nd class of approximation formulae. Q. Appl. Math. 4(2), 112–141 (1946)

    MathSciNet  Google Scholar

  45. Thompson, S.E., Patel, R.V.: Formulation of joint trajectories for industrial robots using b-splines. IEEE Trans. Ind. Electron. 34(2), 192–199 (1987). doi:10.1109/TIE.1987.350954

    Article  Google Scholar

  46. Dyllong, E., Visioli, A.: Planning and real-time modifications of a trajectory using spline techniques. Robotica 21(05), 475–482 (2003). doi:10.1017/S0263574703005009

    Article  Google Scholar

  47. Hodgins, J.K., O'Brien, J.F., Tumblin, J.: Perception of human motion with different geometric models. IEEE Trans. Vis. Comput. Graph. 4(4), 307–316 (1998). doi:10.1109/2945.765325

    Article  Google Scholar

  48. Schmid, A.J., Woern, H.: Path planning for a humanoid using NURBS curves. In: Automation Science and Engineering, 2005. IEEE international conference on, pp. 351–356 (2005)

  49. Sungchul, J., Taehoon, K.: Tool-path generation for NURBS surface machining. In: American control conference, 2003. Proceedings of the 200, Vol. 2613, pp. 2614–2619 (2003)

  50. Cheng, M.Y., Kuo, J.C.: Real-time NURBS command generators for CNC servo controllers. Int. J. Mach. Tools Manuf. 42(7), 801–813 (2002) doi:10.1016/S0890-6955(02)00015-9

    Article  Google Scholar

  51. Zhang, Y., Bazilevs, Y., Goswami, S., Bajaj, C.L., Hughes, T.J.R.: Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Comput. Methods Appl. Mech. Eng. 196(29–30), 2943–2959 (2007). doi:10.1016/j.cma.2007.02.009

    Article  MathSciNet  MATH  Google Scholar

  52. Ma, W., Kruth, J.P.: NURBS curve and surface fitting for reverse engineering. Int. J. Adv. Manuf. Technol. 14(12), 918–927 (1998). doi:10.1007/BF01179082

    Article  Google Scholar

  53. Piegl, L.A., Tiller, W.: Parametrization for surface fitting in reverse engineering. Comput. Aided Des. 33(8), 593–603 (2001). doi:10.1016/S0010-4485(00)00103-2

    Article  Google Scholar

  54. Hughes, T.J.R., Reali, A., Sangalli, G.: Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: Comparison of p-method finite elements with k-method NURBS. Comput. Methods Appl. Mech. Eng. 197(49–50), 4104–4124 (2008). doi:10.1016/j.cma.2008.04.006

    Article  MathSciNet  MATH  Google Scholar

  55. Koyuncu, E., Inalhan, G.: A probabilistic B-spline motion planning algorithm for unmanned helicopters flying in dense 3D environments. In: Intelligent Robots and Systems, 2008. IROS 2008. IEEE/RSJ International Conference on, pp. 815–821 (2008)

  56. Zhou, F., Song, B., Tian, G.: Bézier curve based smooth path planning for mobile robot. J. Inf. Comput. Sci. 8(12), 2441–2450 (2011)

    Google Scholar

  57. Kwangjin, Y., Sukkarieh, S.: An analytical continuous-curvature path-smoothing algorithm. Robot. IEEE Trans. 26(3), 561–568 (2010). doi:10.1109/TRO.2010.2042990

    Article  Google Scholar

  58. Kwangjin, Y., Jung, D., Sukkarieh, S.: Continuous curvature path-smoothing algorithm using cubic Bezier spiral curves for non-holonomic robots. Adv. Robot. 27(4), 247–258 (2013). doi:10.1080/01691864.2013.755246

    Article  Google Scholar

  59. Walton, D.J., Meek, D.S., Ali, J.M.: Planar G2 transition curves composed of cubic Bézier spiral segments. J. Comput. Appl. Math. 157(2), 453–476 (2003). doi:10.1016/s0377-0427(03)00435-7

    Article  MathSciNet  MATH  Google Scholar

  60. Huh, U.-Y., Chang, S.-R.: A G 2 continuous path-smoothing algorithm using modified quadratic polynomial interpolation. Int. J. Adv. Robot. Syst. 25(11) (2014). doi:10.5772/57340

  61. Piazzi, A., Bianco, C.G.L., Romano, M.: η3-Splines for the smooth path generation of wheeled mobile robots. robotics-splines for the smooth path generation of wheeled mobile robots. Robot. IEEE Trans. 23(5), 1089–1095 (2007). doi:10.1109/TRO.2007.903816

    Article  Google Scholar

  62. Pan, J., Zhang, L., Manocha, D.: Collision-free and smooth trajectory computation in cluttered environments. Int. J. Robot. Res. 31(10), 1155–1175 (2012). doi:10.1177/0278364912453186

    Article  Google Scholar

  63. Nikolos, I.K., Valavanis, K.P., Tsourveloudis, N.C., Kostaras, A.N.: Evolutionary algorithm based offline/online path planner for UAV navigation. Systems, Man, and Cybernetics, Part B. Cybern. IEEE Trans. 33(6), 898–912 (2003). doi:10.1109/TSMCB.2002.804370

    Article  Google Scholar

  64. Guarino Lo Bianco, C.: Minimum-jerk velocity planning for mobile robot applications. Robot. IEEE Trans. 29(5), 1317–1326 (2013). doi:10.1109/TRO.2013.2262744

    Article  Google Scholar

  65. Kunz, T., Stilman, M.: Time-optimal trajectory generation for path following with bounded acceleration and velocity. Robotics: Science and Systems, p 209 (2013)

  66. Velenis, E., Tsiotras, P.: Minimum-time travel for a vehicle with acceleration limits: theoretical analysis and receding-horizon implementation. J. Optim. Theory Appl. 138(2), 275–296 (2008). doi:10.1007/s10957-008-9381-7

    Article  MathSciNet  MATH  Google Scholar

  67. Johnson, J., Hauser, K.: Optimal acceleration-bounded trajectory planning in dynamic environments along a specified path. In: Robotics and Automation (ICRA), 2012 IEEE International Conference on, pp. 2035–2041 (2012)

  68. Elbanhawi, M., Simic, M., Jazar, R.: Continuous-curvature bounded trajectory planning using parametric splines. In: Frontiers in Artificial Intelligence and Applications, vol. 262, pp. 513–522 (2014)

  69. Kelly, A., Stentz, A.: Rough terrain autonomous mobility—part 1: A theoretical analysis of requirements. Auton. Robot. 2(5), 129–161 (1998). doi:10.1023/A:1008801421636

    Article  Google Scholar

  70. Ahmed, F., Deb, K.: Multi-objective path planning using spline representation. In: Robotics and Biomimetics (ROBIO), 2011 IEEE International Conference on, pp. 1047–1052 (2011)

  71. De Boor, C.: On calculating with B-splines. J. Appro. Theory 6(1), 50–62 (1972)

    Article  MathSciNet  MATH  Google Scholar

  72. Barsky, B.A., Derose, T.D.: Geometric continuity of parametric curves: constructions of geometrically continuous splines. IEEE Comput. Graph. Appl. 10(1), 60–68 (1990). doi:10.1109/38.45811

    Article  Google Scholar

  73. Jan, G.E., Sun, C.C., Tsai, W.C., Lin, T.H.: An O(n log n) Shortest Path Algorithm Based on Delaunay Triangulation, Mechatronics. IEEE/ASME Trans. PP(99), 1–7 (2013). doi:10.1109/TMECH.2013.2252076

    Article  Google Scholar

  74. Likhachev, M., Ferguson, D., Gordon, G., Stentz, A., Thrun, S.: Anytime search in dynamic graphs. Artif. Intell. 172(14), 1613–1643 (2008). doi:10.1016/j.artint.2007.11.009

    Article  MathSciNet  MATH  Google Scholar

  75. Bruce, J.R., Veloso, M.M.: Safe multirobot navigation within dynamics constraints. IEEE Proc. 94(7), 1398–1411 (2006). doi:10.1109/JPROC.2006.876915

    Article  Google Scholar

  76. LaValle, S.M.: Planning Algorithms. Cambridge University Press (2006)

  77. LaValle, S.M.: Rapidly-exploring random trees: A new tool for path planning. In. Iowa state university (1998)

  78. Wein, R., van den Berg, J., Halperin, D.: Planning high-quality paths and corridors amidst obstacles. Int. J. Robot. Res. 27(11-12), 1213–1231 (2008). doi:10.1177/0278364908097213

    Article  Google Scholar

Download references

Author information

Authors and Affiliations

  1. School of Aerospace, Mechanical, and Manufacturing Engineering (SAMME), RMIT University.Bundoora East Campus, Corner of Plenty Road, McKimmies Road, Bundoora VIC, 3083, Melbourne, Australia

    Mohamed Elbanhawi, Milan Simic & Reza N. Jazar

Corresponding author

Correspondence to Mohamed Elbanhawi.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Elbanhawi, M., Simic, M. & Jazar, R.N. Continuous Path Smoothing for Car-Like Robots Using B-Spline Curves. J Intell Robot Syst 80 (Suppl 1), 23–56 (2015). https://doi.org/10.1007/s10846-014-0172-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI : https://doi.org/10.1007/s10846-014-0172-0

Keywords

  • Path planning
  • Path smoothing
  • Nonholonomic robots
  • C2 continuity
  • Maximum curvature
  • Real time planning

corneliushicithore.blogspot.com

Source: https://link.springer.com/content/pdf/10.1007/s10846-014-0172-0.pdf

Post a Comment for "Continuous Path Smoothing for Car like Robots Using B spline Curves"