Clothoid-Based Three-Dimensional Curve for Attitude Planning

Abstract

This 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.Girbés, V.; Vanegas, G.; Armesto Ángel, L. (2019). Clothoid-Based Three-Dimensional Curve for Attitude Planning. Journal of Guidance Control and Dynamics. 42(8):1886-1898. https://doi.org/10.2514/1.G00355118861898428Goerzen, C., Kong, Z., & Mettler, B. (2009). A Survey of Motion Planning Algorithms from the Perspective of Autonomous UAV Guidance. Journal of Intelligent and Robotic Systems, 57(1-4), 65-100. doi:10.1007/s10846-009-9383-1Zeng, Z., Lian, L., Sammut, K., He, F., Tang, Y., & Lammas, A. (2015). A survey on path planning for persistent autonomy of autonomous underwater vehicles. Ocean Engineering, 110, 303-313. doi:10.1016/j.oceaneng.2015.10.007Zhai, R., Zhou, Z., Zhang, W., Sang, S., & Li, P. (2014). Control and navigation system for a fixed-wing unmanned aerial vehicle. AIP Advances, 4(3), 031306. doi:10.1063/1.4866169Rubio Hervas, J., Reyhanoglu, M., Tang, H., & Kayacan, E. (2016). Nonlinear control of fixed-wing UAVs in presence of stochastic winds. Communications in Nonlinear Science and Numerical Simulation, 33, 57-69. doi:10.1016/j.cnsns.2015.08.026Bhandari, S., Lu, Y., Raheja, A., & Tang, D. (2016). Nonlinear Control of a Fixed-Wing UAV using Support Vector Machine. AIAA Guidance, Navigation, and Control Conference. doi:10.2514/6.2016-0107Eren, U., Prach, A., Koçer, B. B., Raković, S. V., Kayacan, E., & Açıkmeşe, B. (2017). Model Predictive Control in Aerospace Systems: Current State and Opportunities. Journal of Guidance, Control, and Dynamics, 40(7), 1541-1566. doi:10.2514/1.g002507Kan, E.-M., Lim, M.-H., Yeo, S.-P., Ho, J.-S., & Shao, Z. (2011). Contour Based Path Planning with B-Spline Trajectory Generation for Unmanned Aerial Vehicles (UAVs) over Hostile Terrain. Journal of Intelligent Learning Systems and Applications, 03(03), 122-130. doi:10.4236/jilsa.2011.33014Jung, D., & Tsiotras, P. (2013). On-Line Path Generation for Unmanned Aerial Vehicles Using B-Spline Path Templates. Journal of Guidance, Control, and Dynamics, 36(6), 1642-1653. doi:10.2514/1.60780De Dilectis, F., Mortari, D., & Zanetti, R. (2016). Bézier Description of Space Trajectories. Journal of Guidance, Control, and Dynamics, 39(11), 2535-2539. doi:10.2514/1.g000719Wang, X., Jiang, P., Li, D., & Sun, T. (2017). Curvature Continuous and Bounded Path Planning for Fixed-Wing UAVs. Sensors, 17(9), 2155. doi:10.3390/s17092155Rikovitch, N., & Sharf, I. (2013). Kinodynamic Motion Planning for UAVs: A Minimum Energy Approach. AIAA Guidance, Navigation, and Control (GNC) Conference. doi:10.2514/6.2013-5231Ataei, M., & Yousefi-Koma, A. (2015). Three-dimensional optimal path planning for waypoint guidance of an autonomous underwater vehicle. Robotics and Autonomous Systems, 67, 23-32. doi:10.1016/j.robot.2014.10.007Gonzalez, D., Perez, J., Milanes, V., & Nashashibi, F. (2016). A Review of Motion Planning Techniques for Automated Vehicles. IEEE Transactions on Intelligent Transportation Systems, 17(4), 1135-1145. doi:10.1109/tits.2015.2498841ShinD. H.SinghS. “Path Generation for Robot Vehicles Using Composite Clothoid Segments,” Robotics Inst. Tech. Rept. CMU-RI-TR-90-31, Pittsburgh, PA, 1990.Tounsi, M., & Le Corre, J. F. (1996). Trajectory generation for mobile robots. Mathematics and Computers in Simulation, 41(3-4), 367-376. doi:10.1016/0378-4754(95)00085-2LevienR. “The Euler Spiral: A Mathematical History,” Tech. Rept. UCB/EECS-2008-111, EECS Department, Univ. of California, Berkeley, CA, 2008.Fraichard, T., & Scheuer, A. (2004). From Reeds and Shepp’s to Continuous-Curvature Paths. IEEE Transactions on Robotics, 20(6), 1025-1035. doi:10.1109/tro.2004.833789Girbés, V., Armesto, L., & Tornero, J. (2014). Path following hybrid control for vehicle stability applied to industrial forklifts. Robotics and Autonomous Systems, 62(6), 910-922. doi:10.1016/j.robot.2014.01.004Armesto, L., Girbés, V., Vincze, M., Olufs, S., & Muñoz-Benavent, P. (2012). Mobile Robot Obstacle Avoidance Based on Quasi-Holonomic Smooth Paths. Lecture Notes in Computer Science, 244-255. doi:10.1007/978-3-642-32527-4_22Wan, T. R., Tang, W., & Chen, H. (2011). A real-time 3D motion planning and simulation scheme for nonholonomic systems. Simulation Modelling Practice and Theory, 19(1), 423-439. doi:10.1016/j.simpat.2010.08.002Wilburn, J. N., Perhinschi, M. G., & Wilburn, B. K. (2013). Implementation of Composite Clothoid Paths for Continuous Curvature Trajectory Generation for UAVs. AIAA Guidance, Navigation, and Control (GNC) Conference. doi:10.2514/6.2013-5230Harary, G., & Tal, A. (2012). 3D Euler spirals for 3D curve completion. Computational Geometry, 45(3), 115-126. doi:10.1016/j.comgeo.2011.10.001BanchoffT.LovettS. S. T., Differential Geometry of Curves and Surfaces, 2nd ed., Chapman and Hall/CRC Press, Florida, 2015, pp. 71–102, Chap. 3.Meek, D. S., & Walton, D. J. (2004). A note on finding clothoids. Journal of Computational and Applied Mathematics, 170(2), 433-453. doi:10.1016/j.cam.2003.12.047Marzbani, H., Jazar, R. N., & Fard, M. (2015). Better Road Design Using Clothoids. Lecture Notes in Mobility, 25-40. doi:10.1007/978-3-319-17999-5_3Marzbani, H., Simic, M., Fard, M., & Jazar, R. N. (2015). Better Road Design for Autonomous Vehicles Using Clothoids. Smart Innovation, Systems and Technologies, 265-278. doi:10.1007/978-3-319-19830-9_24Gim, S., Adouane, L., Lee, S., & Dérutin, J.-P. (2017). Clothoids Composition Method for Smooth Path Generation of Car-Like Vehicle Navigation. Journal of Intelligent & Robotic Systems, 88(1), 129-146. doi:10.1007/s10846-017-0531-8Mielenz, K. D. (2000). Computation of Fresnel integrals. II. Journal of Research of the National Institute of Standards and Technology, 105(4), 589. doi:10.6028/jres.105.049Narayan, S. (2014). Approximating Cornu spirals by arc splines. Journal of Computational and Applied Mathematics, 255, 789-804. doi:10.1016/j.cam.2013.06.038Chen, Y., Cai, Y., Zheng, J., & Thalmann, D. (2017). Accurate and Efficient Approximation of Clothoids Using Bézier Curves for Path Planning. IEEE Transactions on Robotics, 33(5), 1242-1247. doi:10.1109/tro.2017.2699670Knuth, D. E. (1979). Mathematical typography. Bulletin of the American Mathematical Society, 1(2), 337-372. doi:10.1090/s0273-0979-1979-14598-1KostovV.Degtiariova-KostovaE. “Some Properties of Clothoids,” INRIA Tech. Rept. RR-2752, Cedex, France, 1995.Velasco-Carrau, J., García-Nieto, S., Salcedo, J. V., & Bishop, R. H. (2016). Multi-Objective Optimization for Wind Estimation and Aircraft Model Identification. Journal of Guidance, Control, and Dynamics, 39(2), 372-389. doi:10.2514/1.g00129