Skip to main content

IMPORTANT NOTICE: The ARC website is being updated on Tuesday, May 28, 2024. ARC will be in a "Read Only" mode. Viewing and downloading content will be available but other functions are restricted. For further inquiries, please contact [email protected].

Skip to article control options
No AccessFull-Length Paper

Fast and Near-Optimal Guidance for Docking to Uncontrolled Spacecraft

Published Online:

This paper proposes a guidance scheme for autonomous docking between a controlled spacecraft and an uncontrolled tumbling target in circular orbit. The onboard trajectory planning consists of a direct optimization method based on the inversion of the system dynamics. The trajectory components of the controlled spacecraft are imposed by using polynomial functions. Some of the polynomial coefficients are constrained to satisfy path constraints, whereas the remaining coefficients are varied parameters to be optimized. The optimal control problem is converted into a nonlinear programming problem by inverting the system dynamics. The proposed guidance scheme, based on the closed-loop implementation of this optimization problem, is applied to several scenarios. The resulting trajectories closely match the solutions of the correspondent optimal control problems. The guidance scheme is shown to perform precise maneuvers in most maneuvering situations, even in the presence of orbital perturbations. The sensitivity analysis to system uncertainties shows that the guidance is sensitive to noise on the target angular velocity, being the critical disturbance for this type of maneuvers.


  • [1] Zimpfer D., Kachmar P. and Tuohy S., “Autonomous Rendezvous, Capture and In-Space Assembly: Past, Present and Future,” 1st Space Exploration Conference: Continuing the Voyage of Discovery, AIAA Paper  2005-2523, Jan.–Feb. 2005. doi: LinkGoogle Scholar

  • [2] Saleh J. H., Lamassoure E. and Hastings D. E., “Space Systems Flexibility Provided by On-Orbit Servicing: Part 1,” Journal of Spacecraft and Rockets, Vol. 39, No. 4, 2002, pp. 551–560. doi: LinkGoogle Scholar

  • [3] Hirzinger G., Landzettel K., Brunner B., Fischer M., Preusche C., Reintsema D., Albu-Schäffer A., Schreiber G. and Steinmetz B. M., “DLR’s Robotics Technologies for On-Orbit Servicing,” Advanced Robotics, Vol. 18, No. 2, pp. 139–174, 2004. doi: CrossrefGoogle Scholar

  • [4] Woffinden D. C. and Geller D. K., “Navigating the Road to Autonomous Orbital Rendezvous,” Journal of Spacecraft and Rockets, Vol. 44, No. 4, 2007, pp. 898–909. doi: LinkGoogle Scholar

  • [5] Oda M., “ETS-VII: Achievements, Troubles and Future,” Proceeding of the 6th International Symposium on Artificial Intelligence and Robotics and Automation in Space, Quebec, Canada, June 2001. Google Scholar

  • [6] Davis T. M. and Melanson D., “XSS-10 Microsatellite Flight Demonstration Program Results,” Proceedings of SPIE Conference on Spacecraft Platforms and Infrastructures, Vol. 5419, SPIE-International Soc. for Optical Engineering, Bellingham, WA, 2004, pp. 16–25. doi: Google Scholar

  • [7] Rumford T. E., “Demonstration of Autonomous Rendezvous Technology (DART) Project Summary,” Proceedings of the Society of Photo-Optical Instrumentation Engineers: Space Systems Technology and Operations, Vol. 5088, Aug. 2003, pp. 10–19. doi: Google Scholar

  • [8] Howard R. T. and Bryan T. C., “DART AVGS Flight Results,” Proceedings of the Society of Photo-Optical Instrumentation Engineers, Vol. 6555, Sensors and Systems for Space Applications, Bellingham, WA, May 2007, pp. 1–10. doi: Google Scholar

  • [9] Weismuller T. and Leinz M., “GN&C Technology Demonstrated by the Orbital Express Autonomous Rendezvous and Capture Sensor System,” Proceedings of the 29th AAS Guidance and Control Conference, American Astronautical Soc. Paper  06-016, 2006. Google Scholar

  • [10] D'Amico S., Ardaens J.-S., Gaias G., Benninghoff H., Schlepp B. and Jørgensen J. L., “Noncooperative Rendezvous Using Angles-Only Optical Navigation: System Design and Flight Results,” Journal of Guidance, Control, and Dynamics, Vol. 36, No. 6, 2013, pp. 1576–1595. doi: LinkGoogle Scholar

  • [11] Hartley E. N., Trodden P. A., Richards A. G. and Maciejowski J. M., “Model Predictive Control System Design and Implementation for Spacecraft Rendezvous,” Control Engineering Practice, Vol. 20, No. 7, pp. 695–713, 2012. doi: CrossrefGoogle Scholar

  • [12] Singh L., Bortolami S. and Page L., “Optimal Guidance and Thruster Control in Orbital Approach and Rendezvous for Docking Using Model Predictive Control,” AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA Paper  2010-7754, Aug. 2010. LinkGoogle Scholar

  • [13] Di Cairano S., Park H. and Kolmanovsky I., “Model Predictive Control Approach for Guidance of Spacecraft Rendezvous and Proximity Maneuvering,” International Journal of Robust and Nonlinear Control, Vol. 22, No. 12, 2012, pp. 1398–1427. doi: CrossrefGoogle Scholar

  • [14] Jacobsen S., Lee C., Zhu C. and Dubowsky S., “Planning of Safe Kinematic Trajectories for Free Flying Robots Approaching an Uncontrolled Spinning Satellite,” Proceedings of the ASME 27th Annual Biennial Mechanisms and Robotics Conference, American Soc. of Mechanical Engineers, Fairfield, NJ, 2002, pp. 1145–1151. doi: Google Scholar

  • [15] 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: LinkGoogle Scholar

  • [16] Nolet S., “Development of a Guidance, Navigation and Control Architecture and Validation Process Enabling Autonomous Docking to a Tumbling Satellite,” Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, 2007. Google Scholar

  • [17] Boyarko G., Yakimenko O. and Romano M., “Optimal Rendezvous Trajectories of a Controlled Spacecraft and a Tumbling Object,” Journal of Guidance, Control, and Dynamics, Vol. 34, No. 4, 2011, pp. 1239–1252. doi: LinkGoogle Scholar

  • [18] Boyarko G., “Spacecraft Guidance Strategies for Proximity Maneuvering and Close Approach with a Tumbling Object,” Ph.D. Dissertation, Dept. of Mechanical and Aerospace Engineering, Naval Postgraduate School, Monterey, CA, 2010. Google Scholar

  • [19] Lu P. and Liu X., “Autonomous Trajectory Planning for Rendezvous and Proximity Operations by Conic Optimization,” Journal of Guidance, Control, and Dynamics, Vol. 36, No. 2, 2013, pp. 375–389. doi: LinkGoogle Scholar

  • [20] Liu X. and Lu P., “Solving Nonconvex Optimal Control Problems by Convex Optimization,” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 3, 2014, pp. 750–765. doi: LinkGoogle Scholar

  • [21] Kobilarov M. and Pellegrino S., “Trajectory Planning for Cubesat Short-Time-Scale Proximity Operations,” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 2, 2014, pp. 566–579. doi: LinkGoogle Scholar

  • [22] Starek J. A., Acikmese B., Nesnas I. A. D. and Pavone M., Spacecraft Autonomy Challenges for Next Generation Space Missions, edited by Feron E., Vol. 460, Lecture Notes in Control and Information Sciences, Springer, Berlin, 2016, pp. 1–48. CrossrefGoogle Scholar

  • [23] Clohessy W. H. and Wiltshire R. S., “Terminal Guidance System for Satellite Rendezvous,” Journal of the Aerospace Sciences, Vol. 27, No. 9, 1960, pp. 653–674. LinkGoogle Scholar

  • [24] Wie B., Space Vehicle Dynamics and Control, AIAA Education Series, AIAA, Reston, VA, 1998, pp. 403–407. Google Scholar

  • [25] Ventura J., Romano M. and Walter U., “Performance Evaluation of the Inverse Dynamics Method for Optimal Spacecraft Reorientation,” Acta Astronautica, Vol. 110, May–June 2015, pp. 266–278. doi: CrossrefGoogle Scholar

  • [26] Shuster M. D., “A Survey of Attitude Representations,” Journal of Astronautical Sciences, Vol. 41, No. 4, 1993, pp. 439–517. Google Scholar

  • [27] Fehse W., Automated Rendezvous and Docking of Spacecraft, Cambridge Univ. Press, Cambridge, England, U.K., 2003, pp. 21–282, Chaps. 2–7. CrossrefGoogle Scholar

  • [28] Yakimenko O., “Direct Method for Rapid Prototyping of Near-Optimal Aircraft Trajectories,” Journal of Guidance, Control, and Dynamics, Vol. 23, No. 5, 2000, pp. 865–875. doi: LinkGoogle Scholar

  • [29] Liu H., Lai X. and Wu W., “Time-Optimal and Jerk-Continuous Trajectory Planning for Robot Manipulators with Kinematics Constraints,” Robotics and Computer-Integrated Manufacturing, Vol. 19, No. 2, 2013, pp. 309–317. doi: CrossrefGoogle Scholar

  • [30] Gill P. E., Murray W. and Saunders M. A., “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization,” SIAM Review, Vol. 47, No. 1, March 2005, pp. 99–131. doi: CrossrefGoogle Scholar

  • [31] Betts J. T. and Gablonsky J. M., “A Comparison of Interior Point and SQP Methods on Optimal Control Problems,” Boeing Phantom Works, Mathematics and Computing Technology, Rept.  M&CT-TECH-02-004, Seattle, WA, March 2002. Google Scholar

  • [32] Colodro F., Torralba A. and Laguna M., “Continuous-Time Sigma-Delta Modulator with an Embedded Pulsewidth Modulation,” IEEE Transaction on Circuits and Systems. , Vol. 55, No. 3, 2008, pp. 775–785. CrossrefGoogle Scholar

  • [33] Colodro F. and Torralba A., “Pulse-Width Modulation in Sigma-Delta Modulators,” Proceedings of 2010 IEEE International Symposium on Circuits and Systems, IEEE Publ., Piscataway, NJ, 2010, pp. 1081–1084. Google Scholar

  • [34] Holtz J., “Pulsewidth Modulation for Electronic Power Conversion,” Proceedings of the IEEE, Vol. 82, No. 9, 1994, pp. 1194–1214. Google Scholar

  • [35] Rupp T., Boge T., Kiehling R. and Sellmaier F., “Flight Dynamics Challenges of the German On-Orbit Servicing Mission DEOS,” 21st International Symposium on Space Flight Dynamics (ISSFD), French Space Agency, Toulouse, France, 2009. Google Scholar

  • [36] Virgili B. B., Lemmens S. and Krag H., “Investigation on Envisat Attitude Motion,” European Space Agency, Noordwijk, The Netherland, May 2014, [retrieved July 2014]. Google Scholar

  • [37] Envisat-1: Mission and System Summary,” European Space Agency, Noordwijk, The Netherlands, March 1998. Google Scholar

  • [38] Matlab Version 2013b User Manual, Mathworks, Natick, MA, 2013. Google Scholar

  • [39] Vallado D. A., Fundamentals of Astrodynamics and Applications, Microcosm Press, New York, 2007, Chap. 8. Google Scholar

  • [40] Kucharski D., et al., “Attitude and Spin Period of Space Debris Envisat Measured by Satellite Laser Ranging,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, No. 2, Dec. 2014, pp. 7651–7657. doi: CrossrefGoogle Scholar

  • [41] Patterson M. A. and Rao A. V., “GPOPS II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming,” ACM Transactions on Mathematical Software, Vol. 39, No. 3, 2013, pp. 1–41. doi: CrossrefGoogle Scholar

  • [42] Walter U., Astronautics: The Physics of Space Flight, 2nd ed., Wiley, Weinheim, Germany, 2008, pp. 536–538, Chap. 15. Google Scholar

  • [43] Hillenbrand U. and Lampariello R., “Motion and Parameter Estimation of a Free-Floating Space Object from Range Data for Motion Prediction,” 8th International Symposium on Artificial Intelligence, Robotics, and Automation in Space (i-SAIRAS 2005), Sept. 2005. Google Scholar

  • [44] Woodman O. J., “An Introduction to Inertial Navigation,” Univ. of Cambridge, TR 696, Computer Lab., Cambridge, England, U.K., 2007. Google Scholar

  • [45] Tweddle B. E., “Computer Vision-Based Localization and Mapping of an Unknown, Uncooperative and Spinning Target for Spacecraft Proximity Operations,” Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, 2013. Google Scholar

  • [46] Yu F., He Z., Qiao B. and Yu X., “Stereo-Vision-Based Relative Pose Estimation for the Rendezvous and Docking on Noncooperative Satellites,” Mathematical Problems in Engineering, Vol. 2014, Nov. 2014, pp. 1–12. doi: CrossrefGoogle Scholar

  • [47] Christiansen S. and Nilson T., “Docking System Mechanism Utilized on Orbital Express Program,” Proceedings of the 39th Aerospace Mechanisms Symposium, Lockheed Martin Space Systems Company, Sunnyvale, CA, May 2008; NASA CP-2008-215252, pp. 207–219. Google Scholar

  • [48] Ventura J., Fleischner A. and Walter U., “Pose Tracking of a Noncooperative Spacecraft During Docking Maneuvers Using a Time-of-Flight Sensor,” AIAA Guidance, Navigation and Control Conference, AIAA Paper  2016-0875, Jan. 2016. LinkGoogle Scholar