Skip to main content
Skip to article control options
No AccessFull-Length Paper

Automated Design of Multiphase Space Missions Using Hybrid Optimal Control

Published Online:https://doi.org/10.2514/1.58766

A modern space mission is assembled from multiple phases or events such as impulsive maneuvers, coast arcs, thrust arcs, and planetary flybys. Traditionally, a mission planner would resort to intuition and experience to develop a sequence of events for the multiphase mission and to find the space trajectory that minimizes propellant use by solving the associated continuous optimal control problem. This strategy, however, will most likely yield a suboptimal solution, as the problem is sophisticated for several reasons. For example, the number of events in the optimal mission structure is not known a priori, and the system equations of motion change depending on what event is current. In this work a framework for the automated design of multiphase space missions is presented using hybrid optimal control. The method developed uses two nested loops: an outer-loop that handles the discrete dynamics and finds the optimal mission structure in terms of the categorical variables, and an inner-loop that performs the optimization of the corresponding continuous-time dynamical system and obtains the required control history. Genetic algorithms and direct transcription with nonlinear programming are introduced as methods of solution for the outer-loop and inner-loop problems, respectively. Automation of the inner-loop, continuous optimal control problem solver required two new technologies. The first is a method for the automated construction of the nonlinear programming problems resulting from the use of a transcription method for systems with different structures, including different numbers of categorical events. The method assembles modules, consisting of parameters and constraints appropriate to each event, sequentially according to the given mission structure. The other new technology is for a robust initial guess generator required by the inner-loop nonlinear programming problem solver. The method, based on a real genetic algorithm, approximates optimal control histories by incorporating boundary conditions explicitly using a conditional penalty function. The solution of representative multiphase mission design problems shows the effectiveness of the methods developed.

References

  • [1] Vasile M., Ceriotti M., Radice G., Becerra V., Nasuto S. and Anderson J., “Global Trajectory Optimisation: Can We Prune the Solution Space when Considering Deep Space Manoeuvres? European Space Agency Final Rept. No.  06-4101c, 2008. Google Scholar

  • [2] Englander J., Conway B. A. and Williams T., “Automated Mission Planning via Evolutionary Algorithms,” Journal of Guidance, Control, and Dynamics, Vol. 35, No. 6, 2012, pp. 1878–1887. doi:https://doi.org/10.2514/1.54101 JGCDDT 0162-3192 LinkGoogle Scholar

  • [3] Gad A. and Abdelkhalik O., “Hidden Genes Genetic Algorithm for Multi-Gravity-Assist Trajectories Optimization,” Journal of Spacecraft and Rockets, Vol. 48, No. 4, 2011, pp. 629–641. doi:https://doi.org/10.2514/1.52642 JSCRAG 0022-4650 LinkGoogle Scholar

  • [4] Ceriotti M. and Vasile M., “Automated Multigravity Assist Trajectory Planning with a Modified Ant Colony Algorithm,” Journal of Aerospace Computing, Information, and Communication, Vol. 7, No. 9, 2010, pp. 261–293. doi:https://doi.org/10.2514/1.48448 1542-9423 LinkGoogle Scholar

  • [5] Ross I. M. and D’Souza C. N., “Hybrid Optimal Control Framework for Mission Planning,” Journal of Guidance, Control, and Dynamics, Vol. 28, No. 4, 2005, pp. 686–697. doi:https://doi.org/10.2514/1.8285 JGCDDT 0162-3192 LinkGoogle Scholar

  • [6] Goldberg D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison–Wesley, Reading, MA, 1989, pp. 6–14. Google Scholar

  • [7] Enright P. J. and Conway B. A., “Discrete Approximations to Optimal Trajectories Using Direct Transcription and Nonlinear Programming,” Journal of Guidance, Control, and Dynamics, Vol. 15, No. 4, 1992, pp. 994–1002. doi:https://doi.org/10.2514/3.20934 JGCDDT 0162-3192 LinkGoogle Scholar

  • [8] Battin R. H., An Introduction to the Mathematics and Methods of Astrodynamics, AIAA, New York, NY, 1987, pp. 295–342. Google Scholar

  • [9] Chilan C. M. and Conway B. A., “Using Genetic Algorithms for the Construction of a Space Mission Automaton,” Paper 557, IEEE Congress on Evolutionary Computation, IEEE Publications, Piscataway, NY, 2009, pp. 2316–2323. CrossrefGoogle Scholar

  • [10] von Stryk O. and Glocker M., “Numerical Mixed-Integer Optimal Control and Motorized Traveling Salesmen Problems,” Journal European des Systemes Automatises, Vol. 35, No. 4, 2001, pp. 519–533. EJCOFU 0947-3580 Google Scholar

  • [11] Buss M., Glocker M., Hardt M., von Stryk O., Bulirsch R. and Schmidt G., “Nonlinear Hybrid Dynamical Systems: Modeling, Optimal Control, and Applications,” Lecture Notes in Control and Information Sciences, Vol. 279, 2002, pp. 311–335. CrossrefGoogle Scholar

  • [12] Chilan C. M. and Conway B. A., “A Space Mission Automaton Using Hybrid Optimal Control,” Advances in the Astronautical Sciences, Vol. 127, Univelt, San Diego, CA, 2007, pp. 259–276. Google Scholar

  • [13] Lawden D. F., Optimal Trajectories for Space Navigation, Butterworths, London, 1963, pp. 54–69. Google Scholar

  • [14] Rauwolf G. A. and Coverstone–Carroll V. L., “Near-Optimal Low-Thrust Orbit Transfers Generated by a Genetic Algorithm,” Journal of Spacecraft and Rockets, Vol. 33, No. 6, 1996, pp. 859–862. doi:https://doi.org/10.2514/3.26850 JSCRAG 0022-4650 LinkGoogle Scholar

  • [15] Coverstone–Carrol V., “Near-Optimal Low-Thrust Trajectories via Micro-Genetic Algorithms,” Journal of Guidance, Control, and Dynamics, Vol. 20, No. 1, 1997, pp. 196–198. doi:https://doi.org/10.2514/2.4020 JGCDDT 0162-3192 LinkGoogle Scholar

  • [16] Vasile M., Minisci E. and Locatelli M., “Analysis of Some Global Optimization Algorithms for Space Trajectory Design,” Journal of Spacecraft and Rockets, Vol. 47, No. 2, 2010, pp. 334–344. doi:https://doi.org/10.2514/1.45742 JSCRAG 0022-4650 LinkGoogle Scholar

  • [17] Bryson A. E. and Ho Y. C., Applied Optimal Control, Hemisphere, New York, 1975, pp. 47–89. Google Scholar

  • [18] Hargraves C. R. and Paris S. W., “Direct Trajectory Optimization Using Nonlinear Programming and Collocation,” Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, 1987, pp. 338–342. doi:https://doi.org/10.2514/3.20223 JGCDDT 0162-3192 LinkGoogle Scholar

  • [19] Herman A. L. and Conway B. A., “Direct Optimization Using Collocation Based on High-Order Gauss-Lobatto Quadrature Rules,” Journal of Guidance, Control, and Dynamics, Vol. 19, No. 3, 1996, pp. 592–599. doi:https://doi.org/10.2514/3.21662 JGCDDT 0162-3192 LinkGoogle Scholar

  • [20] Gill P. E., Murray W. and Saunders M. A., User’s Guide SNOPT Version 7: Software for Large-Scale Nonlinear Programming, Stanford Univ., Stanford, CA, 2007. Google Scholar

  • [21] Conway B. A., Chilan C. M. and Wall B. J., “Evolutionary Principles Applied to Mission Planning Problems,” Celestial Mechanics and Dynamical Astronomy, Vol. 97, No. 2, 2007, pp. 73–86. doi:https://doi.org/10.1007/s10569-006-9052-7 CrossrefGoogle Scholar

  • [22] Prussing J. E. and Conway B. A., Orbital Mechanics, 2nd ed., Oxford Univ. Press, New York, NY, 2013, pp. 103–107. Google Scholar

  • [23] Schoenauer M. and Michalewics Z., “Evolutionary Computation at the Edge of Feasibility,” Lecture Notes in Computer Science, Vol. 1141, 1996, pp. 245–254. LNCSD9 0302-9743 CrossrefGoogle Scholar

  • [24] The MathWorks, Global Optimization Toolbox, http://www.mathworks.com/products/global-optimization/, 2012 [accessed 3 Dec. 2012]. Google Scholar

  • [25] Prussing J. E., “A Class of Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions,” The Journal of the Astronautical Sciences, Vol. 48, Nos. 2–3, 2000, pp. 131–148. Google Scholar

  • [26] Cantu–Paz E. and Goldberg D. E., “On the Scalability of Parallel Genetic Algorithms,” Evolutionary Computation, Vol. 7, No. 4, 1999, pp. 429–449. doi:https://doi.org/10.1162/evco.1999.7.4.429 EOCMEO 1063-6560 CrossrefGoogle Scholar

  • [27] Hudson J. S. and Scheeres D. J., “Reduction of Low-Thrust Continuous Controls for Trajectory Dynamics,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 3, 2009, pp. 780–787. doi:https://doi.org/10.2514/1.40619 JGCDDT 0162-3192 LinkGoogle Scholar

  • [28] Taheri E. and Abdelkhalik O., “Shape-Based Approximation of Constrained Low-Thrust Space Trajectories Using Fourier Series,” Journal of Spacecraft and Rockets, Vol. 49, No. 3, 2012, pp. 535–545. doi:https://doi.org/10.2514/1.A32099 JSCRAG 0022-4650 LinkGoogle Scholar

  • [29] Coello Coello C. A., “Constraint-Handling Using an Evolutionary Multiobjective Optimization Technique,” Civil Engineering and Environmental Systems, Vol. 17, No. 4, 2000, pp. 319–346. CrossrefGoogle Scholar

  • [30] TOMLAB Optimization, TOMLAB/SNOPT, http://tomopt.com/tomlab/products/snopt/, 2012 [accessed 3 Dec. 2012]. Google Scholar

  • [31] Prussing J. E. and Chiu J.-H., “Optimal Multiple-Impulse Time-Fixed Rendezvous Between Circular Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 9, No. 1, 1986, pp. 17–22. doi:https://doi.org/10.2514/3.20060 JGCDDT 0162-3192 LinkGoogle Scholar

  • [32] Colasurdo G. and Pastrone D., “Indirect Optimization Method for Impulsive Transfers,” AIAA Paper  1994-3762, 1994. LinkGoogle Scholar

  • [33] Prussing J. E., “Primer Vector Theory and Applications,” Spacecraft Trajectory Optimization, edited by Conway B. A., Cambridge Univ. Press, New York, 2010, pp. 16–36. CrossrefGoogle Scholar

  • [34] Chilan C. M., Automated Design of Multiphase Space Missions Using Hybrid Optimal Control, Ph.D. Thesis, Univ. of Illinois at Urbana-Champaign, Urbana, IL, 2009. Google Scholar

  • [35] Danby J. M. A., Fundamentals of Celestial Mechanics, Willmann–Bell, Richmond, VA, 1988, pp. 427–429. Google Scholar