Contour Based Path Planning with B-Spline Trajectory Generation for Unmanned Aerial Vehicles (UAVs) over Hostile Terrain

ABSTRACT

This research focuses on trajectory generation algorithms that take into account the stealthiness of autonomous UAVs; generating stealthy paths through a region laden with enemy radars. The algorithm is employed to estimate the risk cost of the navigational space and generate an optimized path based on the user-specified threshold altitude value. Thus the generated path is represented with a set of low-radar risk waypoints being the coordinates of its control points. The radar-aware path planner is then approximated using cubic B-splines by considering the least radar risk to the destination. Simulated results are presented, illustrating the potential benefits of such algorithms.

This research focuses on trajectory generation algorithms that take into account the stealthiness of autonomous UAVs; generating stealthy paths through a region laden with enemy radars. The algorithm is employed to estimate the risk cost of the navigational space and generate an optimized path based on the user-specified threshold altitude value. Thus the generated path is represented with a set of low-radar risk waypoints being the coordinates of its control points. The radar-aware path planner is then approximated using cubic B-splines by considering the least radar risk to the destination. Simulated results are presented, illustrating the potential benefits of such algorithms.

Cite this paper

nullE. Kan, M. Lim, S. Yeo, J. Ho and Z. Shao, "Contour Based Path Planning with B-Spline Trajectory Generation for Unmanned Aerial Vehicles (UAVs) over Hostile Terrain,"*Journal of Intelligent Learning Systems and Applications*, Vol. 3 No. 3, 2011, pp. 122-130. doi: 10.4236/jilsa.2011.33014.

nullE. Kan, M. Lim, S. Yeo, J. Ho and Z. Shao, "Contour Based Path Planning with B-Spline Trajectory Generation for Unmanned Aerial Vehicles (UAVs) over Hostile Terrain,"

References

[1] A. Agarwal, M. H. Lim, M. J. Er and T. N. Nguyen, “Rectilinear Workspace Partitioning for Parallel Coverage Using Multiple UAVs,” Advanced Robotics, Vol. 21, No. 1, 2007, pp. 105-120.

[2] K. K. Lim, Y. S. Ong, M. H. Lim and A. Agarwal, “Hybrid Ant Colony Algorithm for Path Planning in Sparse Graphs,” Soft Computing Journal, Vol. 12, No. 10, 2008, pp. 981-994.

[3] C. W. Yeu, M. H. Lim, G. Huang, A. Agarwal and Y. S. Ong, “A New Machine Learning Paradigm for Terrain Reconstruction,” IEEE Geoscience and Remote Sensing Letters, Vol. 3, No. 3, 2006, pp. 981-994. doi:10.1109/LGRS.2006.873687

[4] L. Davis, “Warp Speed: Path Planning for Star Trek: Armada,” AAAI Spring Symposium, AAAI Press, Menlo Park, 2000.

[5] E. Frazzoli, M. Dahleh and E. Feron, “Real-Time Motion Planning for Agile Autonomous Vehicles,” Journal of Guidance, Control and Dynamics, Vol. 25, No. 1, 2002, pp. 116-129. doi:10.2514/2.4856

[6] N. H. Sleumer and N. Tschichold-Gürman, “Exact Cell Decomposition of Arrangements Used for Path Planning in Robotics,” Technical Reports 329, ETH Zürich, Institute of Theoretical Computer Science, 1999.

[7] J. C. Latombe, “Robot Motion Planning,” Kulwer Academic Publishers, Boston, 1991.

[8] T. Lozano-Pyrez and M. A. Wesley, “An Algorithm for Planning Collision-Free Paths among Polyhedral Obstacles,” Communications of the ACM, Vo1. 22, No. 10, 1979, pp. 565-570.

[9] M. Jun, “Path Planning for Unmanned Aerial Vehicles in Uncertain and Adversarial Environments,” In: S. Butenko, R. Murphey and P. Pardalos, Eds., Cooperative Control: Models, Applicarions and Algorithms, Kluwer, 2003, pp. 95-111.

[10] J. Hilgert, K. Hirsch, T. Bertram and M. Hiller, “Emergency Path Planning for AutonomousVehicles Using Elastic Band Theory,” Advanced Intelligent Mechatronics, Vol. 2, 2003, pp. 1390-1395.

[11] T. Sattel and T. Brandt, “Ground Vehicle Guidance Along Collision-Free Trajectories Using Elastic Bands,” Proceedings of 2005 American Control Conference, Portla, 2005, pp. 4991-4999.

[12] J. Hwang, R. C. Arkin and D. Kwon, “Mobile Robots at Your Fingertip: Bezier Curve On-Line Trajectory Generation for Supervisory Control,” Proceedings of Intelligent Robots and Systems (IROS 2003), Las Vegas, Vol. 2, 2003, pp. 1444-1449.

[13] J. Aleotti, S. Caselli and G. Maccherozzi, “Trajectory Reconstruction with NURBS Curves for Robot Programming by Demonstration,” Proceedings of Computational Intelligence in Robotics and Automation, Barcelona, 2005, pp. 73-78.

[14] K. B. Judd and T. W. McLain, “Spline Based Path Planning for Unmanned Air Vehicles,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Montreal, 2001.

[15] E. P. Anderson, R. W. Beard, and T. W. McLain, “Real-Time Dynamic Trajectory Smoothing for Unmanned Air Vehicles,” IEEE Transactions on Control Systems Technology, Vol. 13, No. 3, 2005, pp. 471-477. doi:10.1109/TCST.2004.839555

[16] E. M. Kan, M. H. Lim, S. P. Yeo, S. H. Shao and J. S. Ho, “Radar Aware Path Planning for UAVs,” IEEE Symposium on Intelligent Systems and Applications, Trabzon, June 2009.

[17] E. M. Kan, S. P. Yeo, C. S.Tan, S. H. Shao and J. S. Ho, “Stealth Path Planning for UAVs in Hostile Radar Zones,” Proceedings of the 11th IASTED International Conference on Control and Applications, Cambridge, July 2009, pp. 54-60.

[18] F. W. Moore, “Radar Cross-Section Reduction via Route Planning and Intelligent Control,” IEEE Transactions on Control Systems Technology, Vol. 10, No. 5, 2002, pp. 696-700. doi:10.1109/TCST.2002.801879

[19] U. F. Knott, “Radar Cross Section Measurements,” Van Nostrand Reinhold, New York, 1993.

[20] L. Sevgi, “Complex Electromagnetic Problems and Numerical Simulation Approaches,” IEEE Press/John Wiley & Sons, New York, 2003.

[21] E. F. Knott, J. F. Shaeffer, and M. T. Tuley, “Radar Cross Section,” 2nd Edition, Artech House, Norwood, 1993, p. 231.

[22] M. Pachter, D. R. Jacques and J. M. Hebert, “Minimizing Radar Exposure in Air Vehicle Path Planning,” Proceedings of the 41st Israel Annual Conference on Aerospace Sciences, Tel-Aviv, February 2001.

[23] M. G. Cox, “The Numerical Evaluation of B-Splines,” IMA Journal of Applied Mathematics, Vol. 10, No. 2, 1972, pp. 134-149. doi:10.1093/imamat/10.2.134

[24] R. H. Bartels, J. C. Beatty and B. A. Barsky, “An Introduction to Splines for Use in Computer Graphics and Geometric Modeling,” Morgan Kaufmann Publishers, Massachusetts, 1987.

[25] Q. Cao, M. H. Lim, J. H. Li, Y. S. Ong and W. L. Ng, “A Context Switchable Fuzzy Inference Chip,” IEEE Transactions on Fuzzy Systems, Vol. 14, No. 4, 2006, pp. 552-567. doi:10.1109/TFUZZ.2006.876735

[26] M. H. Lim and Y Takefuji, “Implementing Fuzzy Rule-based systems on Silicon Chips,” IEEE Expert, Vol. 5, No. 1, 1990, pp. 31-45. doi:10.1109/64.50855

[27] R. Meuth, M. H. Lim, Y. S. Ong and D. C. Wunsh, “A Proposition on Memes and Meta-Memes in Computing for Higher-Order Learning,” Memetic Computing, Vol. 1, No. 2, 2009, pp. 85-100. doi:10.1007/s12293-009-0011-1

[28] M. H. Lim, Q. Cao, J. H. Li and W. L. Ng, “Evolvable Hardware Using Context Switchable Fuzzy Inference Processor,” IEEE Proceedings: Computers and Digital Techniques, Vol. 151, No. 4, 2004, pp. 301-311. doi:10.1049/ip-cdt:20040666

[1] A. Agarwal, M. H. Lim, M. J. Er and T. N. Nguyen, “Rectilinear Workspace Partitioning for Parallel Coverage Using Multiple UAVs,” Advanced Robotics, Vol. 21, No. 1, 2007, pp. 105-120.

[2] K. K. Lim, Y. S. Ong, M. H. Lim and A. Agarwal, “Hybrid Ant Colony Algorithm for Path Planning in Sparse Graphs,” Soft Computing Journal, Vol. 12, No. 10, 2008, pp. 981-994.

[3] C. W. Yeu, M. H. Lim, G. Huang, A. Agarwal and Y. S. Ong, “A New Machine Learning Paradigm for Terrain Reconstruction,” IEEE Geoscience and Remote Sensing Letters, Vol. 3, No. 3, 2006, pp. 981-994. doi:10.1109/LGRS.2006.873687

[4] L. Davis, “Warp Speed: Path Planning for Star Trek: Armada,” AAAI Spring Symposium, AAAI Press, Menlo Park, 2000.

[5] E. Frazzoli, M. Dahleh and E. Feron, “Real-Time Motion Planning for Agile Autonomous Vehicles,” Journal of Guidance, Control and Dynamics, Vol. 25, No. 1, 2002, pp. 116-129. doi:10.2514/2.4856

[6] N. H. Sleumer and N. Tschichold-Gürman, “Exact Cell Decomposition of Arrangements Used for Path Planning in Robotics,” Technical Reports 329, ETH Zürich, Institute of Theoretical Computer Science, 1999.

[7] J. C. Latombe, “Robot Motion Planning,” Kulwer Academic Publishers, Boston, 1991.

[8] T. Lozano-Pyrez and M. A. Wesley, “An Algorithm for Planning Collision-Free Paths among Polyhedral Obstacles,” Communications of the ACM, Vo1. 22, No. 10, 1979, pp. 565-570.

[9] M. Jun, “Path Planning for Unmanned Aerial Vehicles in Uncertain and Adversarial Environments,” In: S. Butenko, R. Murphey and P. Pardalos, Eds., Cooperative Control: Models, Applicarions and Algorithms, Kluwer, 2003, pp. 95-111.

[10] J. Hilgert, K. Hirsch, T. Bertram and M. Hiller, “Emergency Path Planning for AutonomousVehicles Using Elastic Band Theory,” Advanced Intelligent Mechatronics, Vol. 2, 2003, pp. 1390-1395.

[11] T. Sattel and T. Brandt, “Ground Vehicle Guidance Along Collision-Free Trajectories Using Elastic Bands,” Proceedings of 2005 American Control Conference, Portla, 2005, pp. 4991-4999.

[12] J. Hwang, R. C. Arkin and D. Kwon, “Mobile Robots at Your Fingertip: Bezier Curve On-Line Trajectory Generation for Supervisory Control,” Proceedings of Intelligent Robots and Systems (IROS 2003), Las Vegas, Vol. 2, 2003, pp. 1444-1449.

[13] J. Aleotti, S. Caselli and G. Maccherozzi, “Trajectory Reconstruction with NURBS Curves for Robot Programming by Demonstration,” Proceedings of Computational Intelligence in Robotics and Automation, Barcelona, 2005, pp. 73-78.

[14] K. B. Judd and T. W. McLain, “Spline Based Path Planning for Unmanned Air Vehicles,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Montreal, 2001.

[15] E. P. Anderson, R. W. Beard, and T. W. McLain, “Real-Time Dynamic Trajectory Smoothing for Unmanned Air Vehicles,” IEEE Transactions on Control Systems Technology, Vol. 13, No. 3, 2005, pp. 471-477. doi:10.1109/TCST.2004.839555

[16] E. M. Kan, M. H. Lim, S. P. Yeo, S. H. Shao and J. S. Ho, “Radar Aware Path Planning for UAVs,” IEEE Symposium on Intelligent Systems and Applications, Trabzon, June 2009.

[17] E. M. Kan, S. P. Yeo, C. S.Tan, S. H. Shao and J. S. Ho, “Stealth Path Planning for UAVs in Hostile Radar Zones,” Proceedings of the 11th IASTED International Conference on Control and Applications, Cambridge, July 2009, pp. 54-60.

[18] F. W. Moore, “Radar Cross-Section Reduction via Route Planning and Intelligent Control,” IEEE Transactions on Control Systems Technology, Vol. 10, No. 5, 2002, pp. 696-700. doi:10.1109/TCST.2002.801879

[19] U. F. Knott, “Radar Cross Section Measurements,” Van Nostrand Reinhold, New York, 1993.

[20] L. Sevgi, “Complex Electromagnetic Problems and Numerical Simulation Approaches,” IEEE Press/John Wiley & Sons, New York, 2003.

[21] E. F. Knott, J. F. Shaeffer, and M. T. Tuley, “Radar Cross Section,” 2nd Edition, Artech House, Norwood, 1993, p. 231.

[22] M. Pachter, D. R. Jacques and J. M. Hebert, “Minimizing Radar Exposure in Air Vehicle Path Planning,” Proceedings of the 41st Israel Annual Conference on Aerospace Sciences, Tel-Aviv, February 2001.

[23] M. G. Cox, “The Numerical Evaluation of B-Splines,” IMA Journal of Applied Mathematics, Vol. 10, No. 2, 1972, pp. 134-149. doi:10.1093/imamat/10.2.134

[24] R. H. Bartels, J. C. Beatty and B. A. Barsky, “An Introduction to Splines for Use in Computer Graphics and Geometric Modeling,” Morgan Kaufmann Publishers, Massachusetts, 1987.

[25] Q. Cao, M. H. Lim, J. H. Li, Y. S. Ong and W. L. Ng, “A Context Switchable Fuzzy Inference Chip,” IEEE Transactions on Fuzzy Systems, Vol. 14, No. 4, 2006, pp. 552-567. doi:10.1109/TFUZZ.2006.876735

[26] M. H. Lim and Y Takefuji, “Implementing Fuzzy Rule-based systems on Silicon Chips,” IEEE Expert, Vol. 5, No. 1, 1990, pp. 31-45. doi:10.1109/64.50855

[27] R. Meuth, M. H. Lim, Y. S. Ong and D. C. Wunsh, “A Proposition on Memes and Meta-Memes in Computing for Higher-Order Learning,” Memetic Computing, Vol. 1, No. 2, 2009, pp. 85-100. doi:10.1007/s12293-009-0011-1

[28] M. H. Lim, Q. Cao, J. H. Li and W. L. Ng, “Evolvable Hardware Using Context Switchable Fuzzy Inference Processor,” IEEE Proceedings: Computers and Digital Techniques, Vol. 151, No. 4, 2004, pp. 301-311. doi:10.1049/ip-cdt:20040666