Document Type : Original Article

Authors

Faculty of New Sciences and Technologies, University of Tehran

Abstract

This paper is dedicated to the optimal path-planning of a quadrotor to deliver the goods in the form of a round-trip mission. At first, quadrotor modeling is performed by the Newton-Euler method and then the problem is formulated as an optimal control effort problem. Then, by discretization of the equations using the direct colocation method, the problem becomes a nonlinear programming system that can be solved by available optimization methods. This discretization helps to make the derivative values in the equations of motion as simple algebraic expressions and the path optimization problem becomes a standard form of nonlinear programming problem (NLP). In this method, instead of obtaining state and control functions, state and control values are obtained at the beginning and endpoints of smaller time intervals. This method is one of the most explicit methods for the numerical solution of differential equations. It should be noted that in this research, safe areas around urban obstacles are considered fixed cylinders. Extensive simulations are evidence of the usefulness of this method, while the vehicle realizes all geometric, dynamic, and kinematic constraints.

Keywords

Main Subjects

[1] A. Mohammadi, E. Abbasi, M. Ghayour, and M. Danesh, “Formation Control and Path Tracking for a Group of Quadrotors to Carry Out a Suspended Load,” Modarres Mechanical Engineering, vol. 19, no. 4, 2019.
[2]  Li Qing, “Aircraft route optimization using genetic algorithms,” pp. 394–397, 2005, doi: 10.1049/cp:19971212.
[3]  L. Yang, J. Qi, D. Song, J. Xiao, J. Han, and Y. Xia, “Survey of robot 3D path planning algorithms,” Journal of Control Science and Engineering, vol. 2016, 2016.
[4]  Muren, J. Wu, L. Zhou, Z. Du, and Y. Lv, “Mixed steepest descent algorithm for the traveling salesman problem and application in air logistics,” Transportation Research Part E: Logistics and Transportation Review, vol. 126, pp. 87–102, Jun. 2019, doi: 10.1016/j.tre.2019.04.004.
[5]  J. T. Betts, “Survey of numerical methods for trajectory optimization,” Journal of guidance, control, and dynamics, vol. 21, no. 2, pp. 193–207, 1998.
[6]  M. Norsell, “Multistage trajectory optimization with radar range constraints,” Journal of aircraft, vol. 42, no. 4, pp. 849–857, 2005.
[7]  A. L. Herman and D. B. Spencer, “Optimal, low-thrust earth-orbit transfers using higher-order collocation methods,” Journal of Guidance, Control, and Dynamics, vol. 25, no. 1, pp. 40–47, 2002.
[8]  K. Horie and B. A. Conway, “Optimal aeroassisted orbital interception,” Journal of guidance, control, and dynamics, vol. 22, no. 5, pp. 625–631, 1999.
[9]  G. Moon and Y. Kim, “Flight path optimization passing through waypoints for autonomous flight control systems,” Engineering Optimization, vol. 37, no. 7, pp. 755–774, 2005.
[10]         C. F. Lin and L. L. Tsai, “Analytical solution of optimal trajectory-shaping guidance,” Journal of Guidance, Control, and Dynamics, vol. 10, no. 1, pp. 60–66, Jan. 1987, doi: 10.2514/3.20181.
[11]         M. N. Rao, “Analytical solution of optimal trajectory-shaping guidance,” Journal of Guidance, Control, and Dynamics, vol. 12, no. 4, pp. 600–601, Jul. 1989, doi: 10.2514/3.20451.
[12]         B. M. Shippey, “Trajectory optimization using collocation and evolutionary programming for constrained nonlinear dynamical systems,” The University of Texas at Arlington, 2008.
[13]         A. L. Yanesi, “Three-Dimensional Constrained Optimal Motion Planning and its Robust Tracking Control Design for a Six-Degree-of-Freedom Quadrotor-Helicopter for Urban Traffic Purposes,” Tehran, 2014.
[14]         R. Bordalba, T. Schoels, L. Ros, J. M. Porta, and M. Diehl, “Direct Collocation Methods for Trajectory Optimization in Constrained Robotic Systems,” IEEE Transactions on Robotics, pp. 1–20, 2022, doi: 10.1109/TRO.2022.3193776.
[15]         A. Angelopoulos et al., “Drone Brush: Mixed Reality Drone Path Planning,” in 2022 17th ACM/IEEE International Conference on Human-Robot Interaction (HRI), Mar. 2022, pp. 678–682. doi: 10.1109/HRI53351.2022.9889504.
[16]         M. T. R. Khan, M. Muhammad Saad, Y. Ru, J. Seo, and D. Kim, “Aspects of unmanned aerial vehicles path planning: Overview and applications,” International Journal of Communication Systems, vol. 34, no. 10, Jul. 2021, doi: 10.1002/dac.4827.
[17]         S.-H. Kim, G. E. G. Padilla, K.-J. Kim, and K.-H. Yu, “Flight Path Planning for a Solar Powered UAV in Wind Fields Using Direct Collocation,” IEEE Trans Aerosp Electron Syst, vol. 56, no. 2, pp. 1094–1105, Apr. 2020, doi: 10.1109/TAES.2019.2926654.
[18]         C. Balas, “Modelling and linear control of a quadrotor,” Cranfield University, MSc Thesis, vol. 2007, 2006.
[19]         A. Lavaei and M. A. A. Atashgah, “Optimal 3D trajectory generation in delivering missions under urban constraints for a flying robot,” Intelligent Service Robots, vol. 10, no. 3, 2017, doi: 10.1007/s11370-017-0225-x.
[20]         P. Zarafshan, S. B. Moosavian, S. A. A. Moosavian, and M. Bahrami, “Optimal control of an aerial robot,” in 2008 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2008, pp. 1284–1289.
[21]         M. Forkan, M. M. Rizvi, and M. A. M. Chowdhury, “Optimal path planning of Unmanned Aerial Vehicles (UAVs) for targets touring: Geometric and arc parameterization approaches,” Plos One, vol. 17, no. 10, p. e0276105, Oct. 2022, doi: 10.1371/journal.pone.0276105.
[22]         K. Chen, D. Zhang, K. Wang, Z. Shao, and L. T. Biegler, “Nonlinear homotopy interior-point algorithm for 6-DoF powered landing guidance,” Aerospace Sci Tech, vol. 127, p. 107707, Aug. 2022, doi: 10.1016/j.ast.2022.107707.