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Computing short-time aircraft maneuvers using direct methods. (English. Russian original) Zbl 1267.93118
J. Comput. Syst. Sci. Int. 49, No. 3, 481-513 (2010); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upravl. 2010, No. 3, 145-176 (2010).
Summary: This paper analyzes the applicability of direct methods to design optimal short-term spatial maneuvers for an unmanned vehicle in a faster than real-time scale. It starts by introducing different basic control schemes, which employ online trajectory generation. Next, it presents and analyzes the results obtained through two recently developed direct transcription (collocation) methods: the Gauss pseudospectral method and the Legendre-Gauss-Lobatto pseudospectral method. The achieved results are further compared with those found through the Pontryagin’s Maximum (Minimum) Principle, and the paper continues by providing another set of direct method simulations incorporating more realistic boundary conditions. Finally, the results obtained using the third direct method, based on inverse dynamics in the virtual domain, are presented and discussed.

MSC:
93C85 Automated systems (robots, etc.) in control theory
49M30 Other numerical methods in calculus of variations (MSC2010)
49K15 Optimality conditions for problems involving ordinary differential equations
93B60 Eigenvalue problems
Software:
DIDO; MAD; Matlab; TOMLAB
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References:
[1] I. Kaminer, O. Yakimenko, V. Dobrokhodov, et al., ”Coordinated Path Following for Time-Critical Missions of Multiple UAVs via L1 Adaptive Output Feed-back Controllers”, in Proceedings of AIAA Guidance, Navigation and Control Conference, American Institute of Aeronautics and Astronautics, Hilton Head, 2007).
[2] V. T. Taranenko, Experience of Employing Ritz’s, Poincare’s, and Lyapunov’s Methods for Solving Flight Dynamics Problems (Air Force Engineering Academy, Moscow, 1968).
[3] V. T. Taranenko and V. G. Momdzhi, Direct Method of Calculus of Variations in Boundary Problems of Flight Dynamics (Maschinostroenie, Moscow, 1986).
[4] B. Geiger, J. Horn, A. DeLullo, et al., ”Optimal Path Planning of UAVs Using Direct Collocation with Nonlinear Programming”, in Proceedings AIAA Guidance, Navigation and Control Conference (American Institute of Aeronautics and Astronautics, Keystone, 2006).
[5] B. Geiger, J. Horn, G. Sinsley, et al., ”Flight Testing a Real Time Implementation of a UAV Path Planner Using Direct Collocation”, in Proceedings of AIAA Guidance, Navigation and Control Conference (American Institute of Aeronautics and Astronautics, Hilton Head, 2007).
[6] O. A. Yakimenko, ”Direct Methods for Rapid Prototyping of Near-Optimal Aircraft Trajectories”, J. Guidance, Control, and Dynamics 23(5), 865–875.
[7] D. A. Benson, G. T. Huntington, T. P. Thorvaldsen, et al., ”Direct Trajectory Optimization and Costate Estimation via An Orthogonal Collocation Method”, J. Guidance, Control, and Dynamics 29(6), 1435–1440 (2006). · doi:10.2514/1.20478
[8] F. Fahroo and I. M. Ross, ”Costate Estimation by a Legendre Pseudospectral Method”, J. Guidance, Control, and Dynamics 24(2), 270–277 (2001). · doi:10.2514/2.4709
[9] F. Fahroo and I. M. Ross, ”Direct Trajectory Optimization by a Chebyshev Pseudospectral Method”, J. Guidance, Control, and Dynamics 25(1), 160–166 (2002). · doi:10.2514/2.4862
[10] I. M. Ross and F. Fahroo, ”Pseudospectral Knotting Methods for Solving Nonsmooth Optimal Control Problems”, J. Guidance, Control, and Dynamics 27(3), 397–405 (2004). · doi:10.2514/1.3426
[11] G. T. Huntington, D. A. Benson, and A. V. Rao, ”A Comparison of Accuracy and Computational Efficiency of Three Pseudospectral Methods”, in Proceedings of AIAA Guidance, Navigation and Control Conference (American Institute of Aeronautics and Astronautics, Hilton Head, 2007).
[12] A. V. Rao, User’s Manual for GPOCS Version 1.1 (University of Florida, Gainesville, 2007).
[13] I. M. Ross, User’s Manual for DIDO: A MATLAB Application Package for Solving Optimal Control Problems (TOMLAB Optimization, Pullman, 2004).
[14] L. S. Pontryagin, V. Boltyanskii, R. Gamkrelidze, et al., The Mathematical Theory of Optimal Processes (Pergamon, New York, 1964).
[15] A. E. Bryson, Jr., Dynamic Optimization(Addison Wesley, Menlo Park, 1999).
[16] D. Kirk, Optimal Control Theory: An Introduction (Dover, New York, 2004).
[17] A. I. Neljubov, Mathematical Methods of Calculation of Combat, Takeoff/Climbing, and Landing Approach Maneuvers for An Aircraft with a 2-D Thrust Vectoring (Air Force Engineering Academy, Moscow, 1986).
[18] O. Yakimenko and N. Slegers, ”Using Direct Methods for Terminal Guidance of Autonomous Aerial Delivery Systems,” in Proceedings of European Control Conference, Budapest, Hungary, 2009.
[19] O. A. Yakimenko, ”Real-Time Computation of Spatial and Flat Obstacle Avoidance Trajectories for UUVs,” in Proceedings of 2nd IFAC Workshop on Navigation, Guidance and Control of Underwater Vehicles (NGCUVO08), Killaloe, Ireland, 2008.
[20] J. Lukacs and O. Yakimenko, ”Trajectory-Shaping Guidance for Interception of Ballistic Missiles During the Boost Phase”, Journal of Guidance, Control, and Dynamics 31(5), 1524–1531 (2008). · doi:10.2514/1.32262
[21] B. Eikenberry, O. Yakimenko, and M. Romano, ”A Vision Based Navigation Among Multiple Flocking Robots: Modeling and Simulation”, in Proceedings of AIAA Modeling and Simulation Technologies Conference (American Institute of Aeronautics and Astronautics, Keystone, 2006).
[22] R. Bevilacqua, M. Romano, and O. Yakimenko, ”Online Generation of Quasi-Optimal Spacecraft Rendezvous Trajectories”, Acta Astronaut. 64(2–3), 345–358 (2009). · doi:10.1016/j.actaastro.2008.08.001
[23] J. F. Whidborne, I. D. Cowling, and O. A. Yakimenko, ”A Direct Method for UAV Guidance and Control,” in Proceedings of 23rd International Unmanned Air Vehicle Systems (UAVS) Conference, Bristol. UK, University of Bristol, Bristol, 2008.
[24] A. E. Bryson, Jr. and Y-C. Ho, Applied Optimal Control: Optimization, Estimation, and Control, (Taylor and Franc, Levittown, 1975).
[25] S. A. Forth, ”An Efficient Overloaded Implementation of Forward Mode Automatic Differentiation in MATLAB”, ACM Trans. Math. Software 32(2), 195–222 (2006). · Zbl 1365.65053 · doi:10.1145/1141885.1141888
[26] S. A. Forth and M. M. Edvall, User Guide for MAD- a Matlab Automatic Differentiation Toolbox TOMLAB/MAD Version, 4, The Forward Mode (TOMLAB Optimization, Pullman, 2007).
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