Clothoid-Based Three-Dimensional Curve for Attitude Planning

No AccessEngineering NotesClothoid-Based Three-Dimensional Curve for Attitude PlanningVicent Girbés, Gloria Vanegas and Leopoldo ArmestoVicent GirbésPolytechnic University of Valencia, 46022 Valencia, Spain, Gloria VanegasPolytechnic University of Valencia, 46022 Valencia, Spain and Leopoldo ArmestoPolytechnic University of Valencia, 46022 Valencia, SpainPublished Online:24 May 2019https://doi.org/10.2514/1.G003551SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail About References [1] Goerzen C., Kong Z., Mettler B., Goerzen C., Kong Z. and Mettler B., "A Survey of Motion Planning Algorithms from the Perspective of Autonomous UAV Guidance," Journal of Intelligent Robots and Systems, Vol. 57, Nos. 1–4, 2010, pp. 65–100. doi:https://doi.org/10.1007/s10846-009-9383-1 CrossrefGoogle Scholar[2] Sujit P., Saripalli S. and Sousa J. B., "Unmanned Aerial Vehicle Path Following: A Survey and Analysis of Algorithms for Fixed-Wing Unmanned Aerial Vehicless," IEEE Control Systems, Vol. 34, No. 1, 2014, pp. 42–59. doi:https://doi.org/10.1109/MCS.2013.2287568 ISMAD7 0272-1708 CrossrefGoogle Scholar[3] Zeng Z., Lian L., Sammut K., He F., Tang Y. and Lammas A., "A Survey on Path Planning for Persistent Autonomy of Autonomous Underwater Vehicles," Ocean Engineering, Vol. 110, Part A, Dec. 2015, pp. 303–313. doi:https://doi.org/10.1016/j.oceaneng.2015.10.007 OCENBQ 0029-8018 CrossrefGoogle Scholar[4] Adiprawita W., Suwandi Ahmad A. and Sembiring J., "Development of AHRS (Attitude and Heading Reference System) for Autonomous UAV (Unmanned Aerial Vehicle)," Proceedings of the International Conference on Electrical Engineering and Informatics, Institut Teknologi Bandung, Indonesia, June 2007. Google Scholar[5] Zhai R., Zhou Z., Zhang W., Sang S. and Li P., "Control and Navigation System for a Fixed-Wing Unmanned Aerial Vehicle," AIP Advances, Vol. 4, No. 3, 2014, Paper 031306. doi:https://doi.org/10.1063/1.4866169 AAIDBI 2158-3226 CrossrefGoogle Scholar[6] Rubio Hervas J., Reyhanoglu M., Tang H. and Kayacan E., "Nonlinear Control of Fixed-Wing UAVs in Presence of Stochastic Winds," Communications in Nonlinear Science and Numerical Simulation, Vol. 33, April 2016, pp. 57–69. doi:https://doi.org/10.1016/j.cnsns.2015.08.026 1007-5704 CrossrefGoogle Scholar[7] Bhandari S., Lu Y., Raheja A. and Tang D., "Nonlinear Control of a Fixed-Wing UAV Using Support Vector Machine," AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2016-0107, 2016. doi:https://doi.org/10.2514/6.2016-0107 LinkGoogle Scholar[8] Nguen V. F., Putov A. V. and Nguen T. T., "Adaptive Control of an Unmanned Aerial Vehicle," AIP Conference Proceedings, Vol. 1798, AIP Publishing LLC Paper 020124, La Rochelle, France, 2017. doi:https://doi.org/10.1063/1.4972716 Google Scholar[9] Prabhakar N., Painter A., Prazenica R. and Balas M., "Trajectory-Driven Adaptive Control of Autonomous Unmanned Aerial Vehicles with Disturbance Accommodation," Journal of Guidance, Control, and Dynamics, Vol. 41, No. 9, 2018, pp. 1976–1989. doi:https://doi.org/10.2514/1.G003341 JGCODS 0731-5090 LinkGoogle Scholar[10] Eren U., Prach A., Koçer B. B., Raković S. V., Kayacan E. and Açıkmeşe B., "Model Predictive Control in Aerospace Systems: Current State and Opportunities," Journal of Guidance, Control, and Dynamics, Vol. 40, No. 7, 2017, pp. 1541–1566. doi:https://doi.org/10.2514/1.G002507 JGCODS 0731-5090 LinkGoogle Scholar[11] Liu M., Liu H. and Wei X., "Autonomous Position Holding and Point to Point Flying Control of Quadrotor UAVs," Proceeding of the 11th World Congress on Intelligent Control and Automation, IEEE Publ., Piscataway, NJ, 2014, pp. 2389–2394. doi:https://doi.org/10.1109/wcica.2014.7053095 Google Scholar[12] Liang H., Zhong W. and Chunhui Z., "Point-to-Point Near-Optimal Obstacle Avoidance Path for the Unmanned Aerial Vehicle," 2015 34th Chinese Control Conference (CCC), IEEE Publ., Piscataway, NJ, 2015, pp. 5413–5418. doi:https://doi.org/10.1109/chicc.2015.7260486 Google Scholar[13] Kan E.-M., Lim M.-H., Yeo S.-P., Ho J.-S. and Shao Z., "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. 03, No. 03, 2011, pp. 122–130. doi:https://doi.org/10.4236/jilsa.2011.33014 CrossrefGoogle Scholar[14] Jung D. and Tsiotras P., "On-Line Path Generation for Unmanned Aerial Vehicles Using B-Spline Path Templates," Journal of Guidance, Control, and Dynamics, Vol. 36, No. 6, 2013, pp. 1642–1653. doi:https://doi.org/10.2514/1.60780 JGCODS 0731-5090 LinkGoogle Scholar[15] Choe R., Puig-Navarro J., Cichella V., Xargay E. and Hovakimyan N., "Cooperative Trajectory Generation Using Pythagorean Hodograph Bézier Curves," Journal of Guidance, Control, and Dynamics, Vol. 39, No. 8, 2016, pp. 1744–1763. doi:https://doi.org/10.2514/1.G001531 JGCODS 0731-5090 LinkGoogle Scholar[16] de Dilectis F., Mortari D. and Zanetti R., "Bézier Description of Space Trajectories," Journal of Guidance, Control, and Dynamics, Vol. 39, No. 11, 2016, pp. 2535–2539. doi:https://doi.org/10.2514/1.G000719 JGCODS 0731-5090 LinkGoogle Scholar[17] Wang X., Jiang P., Li D. and Sun T., "Curvature Continuous and Bounded Path Planning for Fixed-Wing UAVs," Sensors (Switzerland), Vol. 17, No. 9, 2017, pp. 1–21. doi:https://doi.org/10.3390/s17092155 CrossrefGoogle Scholar[18] Pérez L. H., Aguilar M. C. M., Sánchez N. M. and Montesinos A. F., "Path Planning Based on Parametric Curves," Advanced Path Planning for Mobile Entities, InTech, 2018. doi:https://doi.org/10.5772/intechopen.72574 Google Scholar[19] Mittal S. and Deb K., "Three-Dimentional Offline Path Planning for UAVs Using Multiobjective Evolutionary Algorithms," 2007 IEEE Congress on Evolutionary Computation (CEC'2007), No. i, 2007, pp. 3195–3202. doi:https://doi.org/10.1109/CEC.2007.4424880 Google Scholar[20] Hota S. and Ghose D., "Optimal Path Planning for an Aerial Vehicle in 3D Space," 49th IEEE Conference on Decision and Control (CDC), 2010, pp. 4902–4907. doi:https://doi.org/10.1109/CDC.2010.5717246 Google Scholar[21] Rikovitch N. and Sharf I., "Kinodynamic Motion Planning for UAVs: A Minimum Energy Approach," AIAA Guidance, Navigation, and Control (GNC) Conference, AIAA Paper 2013-5231, 2013. doi:https://doi.org/10.2514/6.2013-5231 LinkGoogle Scholar[22] Ataei M. and Yousefi-Koma A., "Three-Dimensional Optimal Path Planning for Waypoint Guidance of an Autonomous Underwater Vehicle," Robotics and Autonomous Systems, Vol. 67, May 2015, pp. 23–32. doi:https://doi.org/10.1016/j.robot.2014.10.007 RASOEJ 0921-8890 CrossrefGoogle Scholar[23] Gonzalez D., Perez J., Milanes V. and Nashashibi F., "A Review of Motion Planning Techniques for Automated Vehicles," IEEE Transactions on Intelligent Transportation Systems, Vol. 17, No. 4, 2016, pp. 1135–1145. doi:https://doi.org/10.1109/TITS.2015.2498841 CrossrefGoogle Scholar[24] Shin D. H. and Singh S., "Path Generation for Robot Vehicles Using Composite Clothoid Segments," Robotics Inst. Tech. Rept. CMU-RI-TR-90-31, Pittsburgh, PA, 1990. CrossrefGoogle Scholar[25] Delingette H., Hebert M. and Lkeuchi K., "Trajectory Generation with Curvature Constraint based on Energy Minimization," IEEE International Conference on Intelligent Robots and Systems, 1991. Google Scholar[26] Tounsi M. and Le Corre J. F., "Trajectory Generation for Mobile Robots," Mathematics and Computers in Simulation, Vol. 41, Nos. 3–4, 1996, pp. 367–376. doi:https://doi.org/10.1016/0378-4754(95)00085-2 CrossrefGoogle Scholar[27] Nagy B. and Kelly A., "Trajectory Generation for Car-Like Robots Using Cubic Curvature Polynomials," Field and Service Robots, Vol. 11, Helsinki, Finland, 2001. Google Scholar[28] Levien R., "The Euler Spiral: A Mathematical History," Tech. Rept. UCB/EECS-2008-111, EECS Department, Univ. of California, Berkeley, CA, 2008. Google Scholar[29] Fraichard T. and Scheuer A., "From Reeds and Shepp's to Continuous-Curvature Paths," IEEE Transactions on Robotics and Automation, Vol. 20, No. 6, 2004, pp. 1025–1035. doi:https://doi.org/10.1109/TRO.2004.833789 IRAUEZ 1042-296X CrossrefGoogle Scholar[30] Girbés V., Armesto L. and Tornero J., "Path Following Hybrid Control for Vehicle Stability Applied to Industrial Forklifts," Robotics and Autonomous Systems, Vol. 62, No. 6, 2014, pp. 910–922. doi:https://doi.org/10.1016/j.robot.2014.01.004 RASOEJ 0921-8890 CrossrefGoogle Scholar[31] Armesto L., Girbés V., Vincze M., Olufs S. and Muñoz-Benavent P., "Mobile Robot Obstacle Avoidance Based on Quasi-Holonomic Smooth Paths," Advances in Autonomous Robotics, Vol. 7429 LNAI, Springer, Berlin, 2012, pp. 244–255. doi:https://doi.org/10.1007/978-3-642-32527-4_22 CrossrefGoogle Scholar[32] Brezak M. and Petrovic I., "Real-Time Approximation of Clothoids With Bounded Error for Path Planning Applications," IEEE Transactions on Robotics, Vol. 30, No. 2, 2014, pp. 507–515. doi:https://doi.org/10.1109/TRO.2013.2283928 ITREAE 1552-3098 CrossrefGoogle Scholar[33] Yang K. and Sukkarieh S., "3D Smooth Path Planning for a UAV in Cluttered Natural Environments," 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, 2008, pp. 794–800. doi:https://doi.org/10.1109/IROS.2008.4650637 Google Scholar[34] Wan T. R., Tang W. and Chen H., "A Real-Time 3D Motion Planning and Simulation Scheme for Nonholonomic Systems," Simulation Modelling Practice and Theory, Vol. 19, No. 1, 2011, pp. 423–439. doi:https://doi.org/10.1016/j.simpat.2010.08.002 1569-190X CrossrefGoogle Scholar[35] Wilburn J. N., Perhinschi M. G. and Wilburn B. K., "Implementation of Composite Clothoid Paths for Continuous Curvature Trajectory Generation for UAVs," AIAA Guidance, Navigation, and Control (GNC) Conference, AIAA Paper 2013-5230, 2013. doi:https://doi.org/10.2514/6.2013-5230 LinkGoogle Scholar[36] Kommer A. and Weidner T., "Some Aspects of Clothoids," Proceedings of 7th International Conference on Applied Informatics, Vol. 1, 2007, pp. 115–120. Google Scholar[37] Harary G. and Tal A., "3D Euler Spirals for 3D Curve Completion," Computational Geometry: Theory and Applications, Vol. 45, No. 3, 2012, pp. 115–126. doi:https://doi.org/10.1016/j.comgeo.2011.10.001 CGOME6 0925-7721 CrossrefGoogle Scholar[38] Bertails-Descoubes F., "Super-Clothoids," Computer Graphics Forum, Vol. 31, No. 2, 2012, pp. 509–518. doi:https://doi.org/10.1111/j.1467-8659.2012.03030.x CGFODY 0167-7055 CrossrefGoogle Scholar[39] Çelik S. S., Yayli Y. and Güler E., "On Generalized Euler Spirals in E3," Differential Geometry, Vol. 5, No. 1, 2016, pp. 5–14. DGAPEO 0926-2245 Google Scholar[40] Banchoff T. and Lovett S. S. T., Differential Geometry of Curves and Surfaces, 2nd ed., Chapman and Hall/CRC Press, Florida, 2015, pp. 71–102, Chap. 3. Google Scholar[41] Meek D. S. and Walton D. J., "A Note on Finding Clothoids," Journal of Computational and Applied Mathematics, Vol. 170, No. 2, 2004, pp. 433–453. doi:https://doi.org/10.1016/j.cam.2003.12.047 JCAMDI 0377-0427 CrossrefGoogle Scholar[42] Marzbani H., Jazar R. N. and Fard M., "Better Road Design Using Clothoids," Sustainable Automotive Technologies 2014, Springer International Publ., 2015, pp. 25–40. doi:https://doi.org/10.1007/978-3-319-17999-5_3. CrossrefGoogle Scholar[43] Marzbani H., Simic M., Fard M. and Jazar R. N., "Better Road Design for Autonomous Vehicles Using Clothoids," Intelligent Interactive Multimedia Systems and Services, Springer International Publ., 2015, pp. 265–278. doi:https://doi.org/10.1007/978-3-319-19830-9_24 CrossrefGoogle Scholar[44] Gim S., Adouane L., Lee S. and Dérutin J. P., "Clothoids Composition Method for Smooth Path Generation of Car-Like Vehicle Navigation," Journal of Intelligent and Robotic Systems: Theory and Applications, Vol. 88, No. 1, 2017, pp. 129–146. doi:https://doi.org/10.1007/s10846-017-0531-8 JIRSES 0921-0296 Google Scholar[45] Mielenz K. D., "Computation of Fresnel Integrals II," Journal of Research of the National Institute of Standards and Technology, Vol. 105, No. 4, 2000, pp. 589–590. doi:https://doi.org/10.6028/jres JRITEF 1044-677X CrossrefGoogle Scholar[46] Montés N., Herraez A., Armesto L. and Tornero J., "Real-Time Clothoid Approximation by Rational Bezier Curves," IEEE International Conference on Robotics and Automation, 2008, pp. 2246–2251. doi:https://doi.org/10.1109/ROBOT.2008.4543548 Google Scholar[47] Narayan S., "Approximating Cornu Spirals by Arc Splines," Journal of Computational and Applied Mathematics, Vol. 255, Jan. 2014, pp. 789–804. doi:https://doi.org/10.1016/j.cam.2013.06.038 JCAMDI 0377-0427 CrossrefGoogle Scholar[48] Chen Y., Cai Y., Zheng J. and Thalmann D., "Accurate and Efficient Approximation of Clothoids Using Bézier Curves for Path Planning," IEEE Transactions on Robotics, Vol. 33, No. 5, 2017, pp. 1242–1247. doi:https://doi.org/10.1109/TRO.2017.2699670 ITREAE 1552-3098 CrossrefGoogle Scholar[49] Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P., Numerical Recipes: The Art of Scientific Computing, 3rd ed., Cambridge Univ. Press, 2007. Google Scholar[50] Knuth D. E., "Mathematical Typography," Bulletin of the American Mathematical Society, Vol. 1, No. 2, 1979, pp. 337–372. doi:https://doi.org/10.1090/S0273-0979-1979-14598-1 BAMOAD 0273-0979 CrossrefGoogle Scholar[51] Kostov V. and Degtiariova-Kostova E., "Some Properties of Clothoids," INRIA Tech. Rept. RR-2752, Cedex, France, 1995. Google Scholar[52] Velasco-Carrau J., Garca-Nieto S., Salcedo J. and Bishop R. H., "Multi-Objective Optimization for Wind Estimation and Aircraft Model Identification," Journal of Guidance, Control, and Dynamics, Vol. 39, No. 2, 2016, pp. 372–389. doi:https://doi.org/10.2514/1.G001294 JGCODS 0731-5090 LinkGoogle Scholar Previous article FiguresReferencesRelatedDetailsCited byElementary Clothoid-Based Three-Dimensional Curve for Unmanned Aerial VehiclesLeopoldo Armesto, Gloria Vanegas and Vicent Girbés-Juan 1 November 2022 | Journal of Guidance, Control, and Dynamics, Vol. 45, No. 12Minimal Deviation from Mission Path After Automated Collision Avoidance for Small Fixed Wing UAVsJeremy P. Browne, Cole Neuhart, Travis W. 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TopicsAircraft Operations and TechnologyAircraft Stability and ControlAircraftsComputer GraphicsComputer Programming and LanguageComputing and InformaticsComputing, Information, and CommunicationFlight Control SurfacesRobot KinematicsRoboticsRobotsUnmanned Aerial Vehicle KeywordsAileronsAeroplaneUAVMotion PlanningAutonomous Underwater VehicleObstacle AvoidanceMobile RobotsComputingAutonomous Navigation SystemNumerical IntegrationAcknowledgmentsThis work was supported by Generalitat Valenciana under the postdoctoral grant APOSTD/2017/055. The authors are also grateful to the financial support of Spanish Ministry of Economy and European Union, grant DPI2016-81002-R (AEI/FEDER, UE). Thanks to Sergio Garcia-Nieto and Franklin Samaniego for their help to setup the simulator.PDF Received6 January 2018Accepted25 March 2019Published online24 May 2019