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Trajectory Planning for CubeSat Short-Time-Scale Proximity Operations

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This paper considers motion planning for small satellites such as CubeSats performing proximity operations in a several meters range of a target object. The main goal is to develop a principled methodology for handling the coupled effects of orbital dynamics, rotational and translational rigid-body dynamics, underactuation and control bounds, and obstacle avoidance constraints. The proposed approach is based on constructing a reduced-order parameterization of the dynamics through dynamics inversion and differential flatness, and on efficient global optimization over a finite-dimensional reduced representation. Two simulated scenarios, a satellite reconfiguration maneuver and asteroid surface sampling, are developed to illustrate the approach. In addition, a simple two-dimensional experimental testbed consisting of an air-bearing table and two CubeSat engineering models is developed for partial testing and integration of the proposed methods.


  • [1] Underwood C. and Pellegrino S., “Autonomous Assembly of a Reconfigurable Space Telescope (AAReST) for Astronomy and Earth Observation,” Eighth IAA Symposium on Small Satellites for Earth Observation, 2011. Google Scholar

  • [2] Scharf D. P., Hadaegh F. Y. and Kang B., “Survey of Spacecraft Formation Flying Guidance,” Proceedings of the International Symposium Formation Flying, 2002, pp. 2976–2985. Google Scholar

  • [3] Scharf D. P., Hadaegh F. Y. and Ploen S. R., “Survey of Spacecraft Formation Flying Guidance and Control (Part 1): Guidance,” Proceedings of the 2003 American Control Conference, Vol. 2, 2003, pp. 1733–1739. Google Scholar

  • [4] Acikmese B., Scharf D. P., Murray E. and Hadaegh F. Y., “Convex Guidance Algorithm for Formation Reconfiguration,” Proceedings of the 2003 American Control Conference, 2003. Google Scholar

  • [5] Sultan C., Seereram S. and Mehra R. K., “Deep Space Formation Flying Spacecraft Path Planning,” International Journal of Robotics Research, Vol. 26, No. 4, April 2007, pp. 405–430. doi: IJRREL 0278-3649 CrossrefGoogle Scholar

  • [6] Richards A., Schouwenaars T., How J. P. and Feron E., “Spacecraft Trajectory Planning with Avoidance Constraints Using Mixed-Integer Linear Programming,” Journal of Guidance, Control, and Dynamics, Vol. 25, No. 4, July–Aug. 2002, pp. 755–764. doi: JGCDDT 0162-3192 LinkGoogle Scholar

  • [7] Frazzoli E., “Quasi-Random Algorithms for Real-Time Spacecraft Motion Planning and Coordination,” Acta Astronautica, Vol. 53, Nos. 4–10, 2003, pp. 485–495. doi: AASTCF 0094-5765 CrossrefGoogle Scholar

  • [8] Phillips J. M., Kavraki L. E. and Bedrosian N., “Probabilistic Optimization Applied to Spacecraft Rendezvous and Docking,” 13th American Astronomical Society/AIAA—Space Flight Mechanics Meeting, Feb. 2003. Google Scholar

  • [9] Breger L. and How J. P., “Safe Trajectories for Autonomous Rendezvous of Spacecraft,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 5, 2008, pp. 1478–1489. doi: JGCDDT 0162-3192 LinkGoogle Scholar

  • [10] Scharf D. P., Hadaegh F. Y., Rahman Z. H., Shields J. F. and Singh G., “Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer,” International Symposium on Formation Flying Missions and Technologies, 2004. Google Scholar

  • [11] Aoude G. S., How J. P. and Miller D. W., “Reconfiguration Maneuver Experiments Using the SPHERES Testbed Onboard the ISS,” Proceedings of the Third International Symposium on Formation Flying, Missions and Technologies, 2008. Google Scholar

  • [12] Saenz-Otero A. and Miller D. W., “Spheres: A Platform for Formation-Flight Research,” Proceedings of SPIE, Vol. 5899, No. 1, 2005, pp. 230–240. Google Scholar

  • [13] Tweddle B. E., Saenz-Otero A. and Miller D. W., “Design and Development of a Visual Navigation Testbed for Spacecraft Proximity Operations,” AIAA SPACE 2009 Conference and Exposition, 2009. Google Scholar

  • [14] Miller D. W., Mohan S. and Budinoff J., “Assembly of a Large Modular Optical Telescope (ALMOST),” SPIE Space Telescopes and Instrumentation, 2008. Google Scholar

  • [15] Faiz N., Agrawal S. and Murray R. M., “Differentially Flat Systems with Inequality Constraints: An Approach to Real-Time Feasible Trajectory Generation,” Journal of Guidance, Control, and Dynamics, Vol. 24, No. 2, 2001, pp. 219–227. doi: JGCDDT 0162-3192 LinkGoogle Scholar

  • [16] Murray R. M., Rathinam M. and Sluis W. M., “Differential Flatness of Mechanical Control Systems,” Proceedings ASME International Congress and Exposition, 1995. Google Scholar

  • [17] Van Nieuwstadt M. J. and Murray R. M., “Real Time Trajectory Generation for Differentially Flat Systems,” International Journal of Robust and Nonlinear Control, Vol. 8, No. 11, 1998, pp. 995–1020. doi: IJRCEA 1099-1239 CrossrefGoogle Scholar

  • [18] Tsiotras P., “Feasible Trajectory Generation for Underactuated Spacecraft Using Differential Flatness,” AAS/AIAA Astrodynamics Specialist Conference, 1999, pp. 16–18. Google Scholar

  • [19] Louembet C., “Collision Avoidance in Low Thrust Rendezvous Guidance Using Flatness and Positive B-Splines,” American Control Conference, 2011, pp. 456–461. Google Scholar

  • [20] Bullo F. and Lynch K. M., “Kinematic Controllability for Decoupled Trajectory Planning in Underactuated Mechanical Systems,” IEEE Transactions on Robotics and Automation, Vol. 17, No. 4, 2001, pp. 402–412. doi: IRAUEZ 1042-296X CrossrefGoogle Scholar

  • [21] Frazzoli E., Dahleh M. A. and Feron E., “Maneuver-Based Motion Planning for Nonlinear Systems with Symmetries,” IEEE Transactions on Robotics, Vol. 21, No. 6, Dec. 2005, pp. 1077–1091. doi: IRAUEZ 1042-296X CrossrefGoogle Scholar

  • [22] Mueller J., Hofer R. and Ziemer J., “Survey of Propulsion Technologies Applicable to CubeSats,” Jet Propulsion Lab. TR, 2010. Google Scholar

  • [23] Hinkley D. A., “Picosatellites at the Aerospace Corporation,” Small Satellites: Past, Present, and Future, edited by Helvajian H. and Janson S. W., No. 20, 2009, pp. 635–674. Google Scholar

  • [24] Janson S., Huang A., Hansen W. and Helvajian H., “Development of an Inspector Satellite Propulsion Module Using Photostructurable Glass/Ceramic Materials,” AIAA Conference on Micro-/Nanotechnologies, 2004. Google Scholar

  • [25] Schmuland D. T., Masse R. K. and Sota C. G., “Hydrazine Propulsion Module for CubeSats,” Small Satellite Conference, 2011. Google Scholar

  • [26] Wirz R. and Conversano R., “CubeSat Lunar Mission Using a Miniature Ion Thruster,” 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA Paper  2011-6083, 2011. AbstractGoogle Scholar

  • [27] Kobilarov M., “Cross-Entropy Motion Planning,” International Journal of Robotics Research, Vol. 31, No. 7, 2012, pp. 855–871. doi: IJRREL 0278-3649 CrossrefGoogle Scholar

  • [28] Vallado D., Fundamentals of Astrodynamics and Applications, Primis, 1997. Google Scholar

  • [29] Gottschalk S., Lin M. C. and Manocha D., “OBBTree: A Hierarchical Structure for Rapid Interference Detection,” Eurographics/ACM SIGGRAPH Symposium on Computer Animation, New York, Vol. 30, 1996, pp. 171–180. Google Scholar

  • [30] Frazzoli E., Dahleh M. A. and Feron E., “Trajectory Tracking Control Design for Autonomous Helicopters Using a Backstepping Algorithm,” Proceedings of the American Control Conference, June 2000, pp. 4102–4107. Google Scholar

  • [31] Kobilarov M. and Marsden J., “Discrete Geometric Optimal Control on Lie Groups,” IEEE Transactions on Robotics, Vol. 27, No. 4, 2011, pp. 641–655. doi: IRAUEZ 1042-296X CrossrefGoogle Scholar

  • [32] Hairer E., Lubich C. and Wanner G., Geometric Numerical Integration, Springer Series in Computational Mathematics, Springer–Verlag, New York, Vol. 31, 2006. Google Scholar

  • [33] Garcia I. and How J. P., “Trajectory Optimization for Satellite Reconfiguration Maneuvers with Position and Attitude Constraints,” American Control Conference, 2005, pp. 889–894. Google Scholar

  • [34] Karaman S. and Frazzoli E., “Sampling-Based Algorithms for Optimal Motion Planning,” International Journal of Robotics Research, Vol. 30, No. 7, 2011, pp. 846–894. IJRREL 0278-3649 CrossrefGoogle Scholar

  • [35] Rubenstein R. Y. and Kroese D. P., Simulation and the Monte Carlo Method, Wiley, Hoboken, NJ, 2008. Google Scholar

  • [36] Figueiredo M. A. F. and Jain A. K., “Unsupervised Learning of Finite Mixture Models,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, No. 3, 2002, pp. 381–396. doi: ITPIDJ 0162-8828 CrossrefGoogle Scholar

  • [37] Kubota T., Sawai S., Hashimoto T., Kawaguchi J. and Fujiwara A., “Robotics Technology for Asteroid Sample Return Mission Muses-c,” Proceedings of the Sixth International Symposium on Artificial Intelligence and Robotics and Automation in Space: I-SAIRAS, 2001, pp. 31–38. Google Scholar

  • [38] “Dawn,” NASA/Jet Propulsion Lab., [retrieved 01 April 2012]. Google Scholar