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A Generalized Real-Time Obstacle Avoidance Method Without the Cspace Calculation

Abstract

An important concept proposed in the early stage of robot path planning field is the shrinking of a robot to a point and meanwhile the expanding of obstacles in the workspace as a set of new obstacles. The resulting grown obstacles are called the Configuration Space (Cspace) obstacles. The find-path problem is then transformed into that of finding a collision-free path for a point robot among the Cspace obstacles. However, the research experiences have shown that the Cspace transformation is very hard when the following situations occur: 1) both the robot and obstacles are not polygons, and 2) the robot is allowed to rotate. This situation gets even worse when the robot and obstacles are three dimensional (3D) objects with various shapes. For this reason, direct path planning approaches without the Cspace transformation is quite useful and expected. Motivated by the practical requirements of robot path planning, a generalized constrained optimization problem (GCOP) with not only logic AND but also logic OR relationships was proposed and a mathematical solution developed previously. This paper inherits the fundamental ideas of inequality and optimization techniques from the previous work, converts the obstacle avoidance problem into a semi-infinite constrained optimization problem with the help of the mathematical transformation, and proposes a direct path planning approach without Cspace calculation, which is quite different from traditional methods. To show its merits, simulation results in 3D space have been presented.

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References

  1. Krishna C M, Shin K G. Real-Time Systems. New York: McGraw-Hill, 1997.

    Google Scholar 

  2. Wang Y J, Lane D M. Subsea vehicle path planning using nonlinear programming and constructive solid geometry. In IEE Proc., Part D, Control Theory and Applications, 1997, 144: 143–152.

  3. Wang Y J, Lane D M, Falconer G J. Two novel approaches for unmanned underwater vehicle path planning: Constrained optimization and semi-infinite constrained optimization. Robotica, 2000, 18: 123–142.

    Article  Google Scholar 

  4. Petillot Y R, Ruiz T I, Lane D M et al. Underwater vehicle path planning using a multi-beam forward looking sonar. In IEEE Oceanic Engineering Society, OCEANS'98, Nice, France, 1998, pp.1194–1199.

  5. Petillot Y, Ruiz I T, Lane D M. Underwater vehicle obstacle avoidance and path planning using a multi-beam forward looking sonar. IEEE Journal of Oceanic Engineering, 2001, 26: 240–251.

    Article  Google Scholar 

  6. Wang Y J. Kinematics, motion analysis and path planning for four kinds of wheeled mobile robots [Dissertation]. Dept. Mechanical Engineering, Edinburgh University, 1995.

  7. Park T J, Ahn J W, Han C S. A path generation algorithm of an automatic guided vehicle using sensor scanning method. KSME International Journal, 2002, 16: 137–146.

    Google Scholar 

  8. Ruiz T, Lane D M, Chantler M J. A comparison of inter-frame feature measures for robust object classification in sector scan sonar image sequences. IEEE Journal of Oceanic Engineering, 1999, 24: 458–469.

    Google Scholar 

  9. Trucco E, Petillot Y R, Ruiz I T et al. Feature tracking in video and sonar subsea sequences with applications. Computer Vision and Image Understanding, 2000, 79: 92–122.

    Article  Google Scholar 

  10. Brooks R A, Lozano-Perez T. A subdivision algorithm in configuration space for findpath with rotation. IEEE Trans. Systems, Man and Cybernetics, 1985, 15: 224–233.

    Google Scholar 

  11. Conn R A, Kam M. On the moving-obstacle path planning algorithm of Shih, Lee, and Gruver. IEEE Trans. Systems, Man and Cybernetics, Part B: Cybernetics, 1997, 27: 136–138.

    Google Scholar 

  12. Connolly I. Harmonic function and collision probabilities. Int. J. Robotics Research, 1997, 16: 497–507.

    Google Scholar 

  13. Hu T C, Kahng A B, Robins G. Optimal robust path planning in general environment. IEEE Trans. Robotics and Automation, 1993, 9: 755–774.

    Article  Google Scholar 

  14. Huang H P, Lee P C. A real-time algorithm for obstacle avoidance of autonomous mobile robots. Robotica, 1992, 10: 217–227.

    Google Scholar 

  15. Hwang Y K, Ahuja N. A potential field approach to path planning. IEEE Trans. Robotics and Automation, 1992, 8: 23–32.

    Article  Google Scholar 

  16. Khatib O. Real-time obstacle avoidance for manipulator and mobile robots. Int. J. Robotics Research, 1986, 5: 90–98.

    Google Scholar 

  17. Latombe J C. Robot Motion Planning. Boston: Kluwer Academic Publishers, 1991.

    Google Scholar 

  18. Lozano-Perez T. Spatial planning: A configuration space approach. IEEE Trans. Computer, 1983, 32: 108–120.

    MATH  MathSciNet  Google Scholar 

  19. Lu H C, Yeh M E. Robot path planning based on modified grey relational analysis. Cybernetics and Systems, 2002, 33: 129–159.

    Google Scholar 

  20. Lumelsky V J. A comparative study on path length performance of maze-searching and robot motion planning. IEEE Trans. Robotics and Automation, 1991, 7: 57–66.

    Article  Google Scholar 

  21. Oriolo G, Ulivi G, Vendittelli M. Real-time map building and navigation for autonomous robots in unknown environments. IEEE Trans. Systems, Man and Cybernetics, Part B: Cybernetics, 1998, 28: 316–333.

    Google Scholar 

  22. Wang Y J. A note on solving the find-path problem by good representation of free space. IEEE Trans. Systems, Man and Cybernetics, Part B: Cybernetics, 1997, 27: 723–724.

    Google Scholar 

  23. Wang Y J, Lane D M. Solving a generalized constrained optimization problem with both logic AND and OR relationships by a mathematical transformation and its application to robot path planning. IEEE Trans. Systems, Man and Cybernetics, Part C: Application and Reviews, 2000, 30: 525–536.

    Google Scholar 

  24. Wang Y J, Cartmell M P. A new overtaking model for passing sight distance, PDS on two-lane highways. ASCE J. Transportation Engineering, 1998, 124: 536–545.

    Google Scholar 

  25. Wang Y J, Cartmell M P. Autonomous vehicle parallel parking design using function fitting approaches. Robotica, 1998, 16: 159–170.

    Google Scholar 

  26. Wang Y J, Cartmell M P. Trajectory generation for four-wheel steering tractor-trailer system: A two-step method. Robotica, 1998, 16: 381–386.

    Google Scholar 

  27. Wang Y J, Linnett J A. Vehicle kinematics and its application to highway design. ASCE J. Transportation Engineering, 1995, 121: 63–74.

    Google Scholar 

  28. Wang Y J, Linnett J A, Roberts J W. Motion feasibility of a wheeled vehicle with a steering angle limit. Robotica, 1994, 12: 217–226.

    Google Scholar 

  29. Wang Y J, Linnett J A, Roberts J W. Kinematics, kinematic constraints and path planning for wheeled mobile robots. Robotica, 1994, 12: 391–400.

    Google Scholar 

  30. Xu W L, Ma B L. Polynomial motion of non-holonomic mechanical systems of chained form. Mathematical Methods in the Applied Sciences, 1999, 22: 1153–1173.

    Article  MathSciNet  Google Scholar 

  31. Zhang Y, Valavanis K P. A 3-D potential panel method for robot motion planning. Robotica, 1997, 15: 421–434.

    Google Scholar 

  32. Ricci A. A constructive geometry for computer graphics. The Computer Journal, 1973, 16: 157–160.

    Article  MATH  Google Scholar 

  33. Blechschmidt J L, Nagasuru D. The use of algebraic functions as a solid modelling alternative: An investigation. In Proc. the 16th ASME Design Automation Conf., Chicago, USA, 1990, pp.33–41.

  34. Barr A H. Superquadrics and angle-preserving transformations. IEEE Computer Graphics and Applications, 1981, 1: 11–23.

    Google Scholar 

  35. Chiyokura H. Solid Modelling with Designbase. New York: Addison-Wesley Publishing Limited, 1988.

    Google Scholar 

  36. Shih C L, Jeng J T. Stabilization of non-holonomic chained systems by gain scheduling. International Journal of Systems Science, 1999, 30: 441–449.

    Article  Google Scholar 

  37. Wang W P, Wang K K. Geometric modeling for swept volume of moving solids. IEEE CG&A, 1986, 12: 8–17.

    Google Scholar 

  38. Blackmore D, Leu M, Wang L P. The sweep-envelope differential equation algorithm and its application to NC machining verification. Computer Aided Design, 1997, 29: 629–637.

    Article  Google Scholar 

  39. Hall M, Warren J. Adaptive polygonalization of implicitly defined surfaces. IEEE Computer Graphics & Applications, 1990, 10: 33–42.

    Google Scholar 

  40. Haug E J, Adkins F A, Cororian D. Domains of mobility for planar body moving among obstacles. Trans. the ASME, Journal of Mechanical Design, 1988, 120: 462–467.

    Google Scholar 

  41. Wang Y J, Liu H, Li M S, Wang Q, Zhou J H, Cartmell M P. A real-time path planning approach without the computation of Cspace obstacles. Robotica, 2004, 22: 173–187.

    Article  Google Scholar 

  42. Fletcher R. Practical Methods of Optimization. New York: John Wiley & Sons, 1987.

    Google Scholar 

  43. Gill P E, Murray W, Wright M H. Practical Optimization. London: Academic Press, 1981.

    Google Scholar 

  44. Luenberger D G. Linear and Nonlinear Programming. London: Addison-Wesley Publishing Company, 2nd Ed., 1984.

    Google Scholar 

  45. Polak E, Mayne D Q. Control system design via semi-infinite optimization: A review. In Proc. IEEE, 1984, 72: 1777–1793.

  46. Rao S S. Optimization theory and applications. New Delhi: Wiley Eastern Ltd, Second Edition, 1984.

    Google Scholar 

  47. Tanak Y, Fukushima M, Ibaraki T. A comparative study of several semi-infinite nonlinear programming algorithms. European Journal of Operational Research, 1988, 36: 92–100.

    MathSciNet  Google Scholar 

  48. Berger M. Computer Graphics. California: The Benjamin/Cummings Publishing Company, Inc., 1986.

    Google Scholar 

  49. Chang J C, Lu H C. Backing up a simulated truck via grey relational analysis. Journal of the Chinese Institute of Engineers, 2001, 24: 745–752.

    Google Scholar 

  50. Comba P G. A procedure for detecting intersections of three-dimensional objects. JACM, 1968, 15: 354–366.

    Article  MATH  Google Scholar 

  51. Sundar S, Shiller S. Optimal obstacle avoidance based on the HJB equation. IEEE Trans. Robotics and Automation, 1997, 13: 305–310.

    Article  Google Scholar 

  52. Franklin W R, Barr A H. Faster calculation of superquadric shapes. IEEE Computer Graphics and Application, 1981, 1: 41–57.

    Google Scholar 

  53. Rose E M. Elementary Theory of Angular Momentum. New York: John Wiley & Sons, 1957.

    Google Scholar 

  54. The Math Works Inc., MATLAB, 1993, Optimization Toolbox User's Guide.

  55. Kreyszig E. Advanced Engineering Mathematics. Seventh Edition, New York: John Wiley & Sons, 1993.

    Google Scholar 

  56. Rosen K H. Discrete Mathematics and Its Applications. Second Edition, New York: McGraw-Hill, Inc., 1991.

    Google Scholar 

Download references

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Correspondence to Yong-Ji Wang.

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Supported by the joint research project of Chinese Academy of Sciences, P.R. China and Royal Society of United Kingdom under Grant No.20030389, 2003–2006, the National High-Tech Development 863 Program of China under Grant No.2003AA1Z2220, the National Natural Science Foundation of China under Grant No.60373053, and Chinese Academy of Sciences and Chinese State Development Planning Commission for The Hundred Talents Plan of the Chinese Academy of Sciences, 2002–2005.

Yong-Ji Wang is a research professor with the Institute of Software, Chinese Academy of Sciences. Prof. Wang received the B.S. and M.S. degrees from Beijing University of Aeronautics and Astronautics, China, in 1984 and 1987, respectively, and the Ph.D. degree from Edinburgh University, U.K., in 1995. From 1987 to 1991, he was a lecturer with Tianjing University, China. From 1995 to 1998, he was a postdoctoral researcher with Heriot-Watt University, U.K. From 1998 to 2002, he was a researcher fellow with the Department of Mechanical Engineering, Centre of Systems and Control, Glasgow University, U.K. He is currently a supervisor of Ph.D. candidates with Laboratory for Internet Software Technologies, Institute of Software, Chinese Academy of Sciences. Prof. Wang has long been engaged in the research on computer-controlled real-time system, advanced numerical methods, autonomous real-time robot systems, non-linear optimization theory, and real-time hybrid control theory. He has published more than fifty papers in important journals and conferences, including IEEE Transactions, IEE Proceedings, ROBOTICA, ASCE, SIAM, and International Journal of Control, and served as a referee for more than ten important international journals and conferences. He has participated in three significant projects sponsored by the European Community. He was awarded Hong Kong Wang Kuancheng Fund Award, the British Overseas Scholars Fund Award, and Ford Fund Award. He is now mainly involved in the research on real-time system and Internet technology.

Matthew Cartmell has worked since the mid nineteen eighties as a lecturer in dynamics at the Universities of Aberdeen, and Wales (Swansea), then as a senior lecturer in computational mechanics at the University of Edinburgh, and finally since 1998 as professor of applied dynamics at the University of Glasgow. He has held a number of EPSRC, Royal Society, EC, and British Council grants in areas and topics relating to design, vibrations, control, computational modelling, and the mechanics of smart materials. Matthew Cartmell's principal current research interests comprise symbolic computational technologies for analytical solutions to problems in nonlinear vibrations, the dynamics and design of space tether propulsion systems, the dynamics and control of gantry cranes, and the application of shape memory alloys within composite structures for vibration control in machinery.

Qiu-Ming Tao received the B.S. degree from Department of Computer Science and Technology, Nanjing University, China, in 2002. He is currently a Ph.D. candidate of Institute of Software, Chinese Academy of Sciences. His main research interests are software testing, software engineering, and real-time system.

Han Liu received the B.S. degree from Department of Computer, Harbin Institute of Technology, China, in 2002. His main research interests are real-time system and software engineering.

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Wang, YJ., Cartmell, M., Tao, QM. et al. A Generalized Real-Time Obstacle Avoidance Method Without the Cspace Calculation. J Comput Sci Technol 20, 774–787 (2005). https://doi.org/10.1007/s11390-005-0774-x

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  • DOI: https://doi.org/10.1007/s11390-005-0774-x

Keywords

  • path planning
  • obstacle avoidance
  • autonomous underwater vehicle
  • non-linear programming
  • robotics
  • semi-infinite constrained optimization