Survey of orbital dynamics and control of space rendezvous

Abstract Rendezvous orbital dynamics and control (RODC) is a key technology for operating space rendezvous and docking missions. This paper surveys the studies on RODC. Firstly, the basic relative dynamics equation set is introduced and its improved versions are evaluated. Secondly, studies on rendezvous trajectory optimization are commented from three aspects: the linear rendezvous, the nonlinear two-body rendezvous, and the perturbed and constrained rendezvous. Thirdly, studies on relative navigation are briefly reviewed, and then close-range control methods including automated control, manual control, and telecontrol are analyzed. Fourthly, advances in rendezvous trajectory safety and robust analysis are surveyed, and their applications in trajectory optimization are discussed. Finally, conclusions are drawn and prospects of studies on RODC are presented.

[1]  Jesse Ross Gossner An Analytic Method of Propagating a Covariance Matrix to a Maneuver Condition for Linear Covariance Analysis during Rendezvous , 1991 .

[2]  Hexi Baoyin,et al.  Practical Techniques for Low-Thrust Trajectory Optimization with Homotopic Approach , 2012 .

[3]  Zongli Lin,et al.  Lyapunov Differential Equation Approach to Elliptical Orbital Rendezvous with Constrained Controls , 2011 .

[4]  JiSheng Li,et al.  Mathematical prototypes for collocating geostationary satellites , 2013 .

[5]  M. Guelman,et al.  Optimal Bounded Low-Thrust Rendezvous with Fixed Terminal-Approach Direction , 2001 .

[6]  J. D. Alexander,et al.  Apollo lunar rendezvous , 1970 .

[7]  Yuri Ulybyshev,et al.  Optimization of multi-mode rendezvous trajectories with constraints , 2008 .

[8]  Jean Albert Kechichian,et al.  Techniques of accurate analytic terminal rendezvous in near-circular orbit , 1992 .

[9]  Ya-zhong Luo,et al.  Hybrid Approach to Optimize a Rendezvous Phasing Strategy , 2007 .

[10]  Dmitry Sergeevich Roldugin,et al.  Six-impulse maneuvers for rendezvous of spacecraft in near-circular noncoplanar orbits , 2012 .

[11]  Guo-Jin Tang,et al.  Research on the strategy of angles-only relative navigation for autonomous rendezvous , 2011 .

[12]  Charles L. Karr,et al.  Genetic-algorithm-based fuzzy control of spacecraft autonomous rendezvous , 1997 .

[13]  John E. Prussing,et al.  OPTIMAL IMPULSIVE INTERCEPT WITH LOW-THRUST RENDEZVOUS RETURN , 1993 .

[14]  Xu Shi-jie A Fuzzy Controller for Terminal Approach of Autonomous Rendezvous and Docking with Non-Cooperative Target , 2006 .

[15]  Jian Li,et al.  Multiple-Revolution Solutions of the Transverse-Eccentricity-Based Lambert Problem , 2010 .

[16]  Guo-Jin Tang,et al.  Multi-Objective Optimization of Perturbed Impulsive Rendezvous Trajectories Using Physical Programming , 2008 .

[17]  Derek F Lawden,et al.  Optimal trajectories for space navigation , 1964 .

[18]  John L. Goodman,et al.  History of Space Shuttle Rendezvous and Proximity Operations , 2006 .

[19]  Oleg A. Yakimenko,et al.  Online generation of quasi-optimal spacecraft rendezvous trajectories , 2009 .

[20]  Li Yili,et al.  Precision analysis of long distance navigation of rendezvous , 2006 .

[21]  Thomas Carter,et al.  Fuel-optimal maneuvers of a spacecraft relative to a point in circular orbit , 1984 .

[22]  Huijun Gao,et al.  Multi-Objective Robust $H_{\infty}$ Control of Spacecraft Rendezvous , 2009, IEEE Transactions on Control Systems Technology.

[23]  Jin Zhang,et al.  Spacecraft long-duration phasing maneuver optimization using hybrid approach , 2012 .

[24]  Jing Zhang,et al.  Necessary and sufficient conditions of the rendezvous between a single spacecraft and three non-coplanar Walker constellation satellites , 2011 .

[25]  R. Melton Time-Explicit Representation of Relative Motion Between Elliptical Orbits , 2000 .

[26]  G. Duan,et al.  Circular orbital rendezvous with actuator saturation and delay: A parametric Lyapunov equation approach , 2012 .

[27]  Michael W. Weeks,et al.  On-Board Rendezvous Targeting for Orion , 2010 .

[28]  Timothy E. Rumford Demonstration of autonomous rendezvous technology (DART) project summary , 2003, SPIE Defense + Commercial Sensing.

[29]  Thomas Carter,et al.  Optimal power-limited rendezvous with thrust saturation , 1995 .

[30]  Richard Epenoy,et al.  Fuel Optimization for Continuous-Thrust Orbital Rendezvous with Collision Avoidance Constraint , 2011 .

[31]  D. J. Jezewski,et al.  An efficient method for calculating optimal free-space n-impulse trajectories. , 1968 .

[32]  Hari B. Hablani,et al.  Guidance and Relative Navigation for Autonomous Rendezvous in a Circular Orbit , 2002 .

[33]  Guo-Jin Tang,et al.  Optimization of multiple-impulse, multiple-revolution, rendezvous-phasing maneuvers , 2007 .

[34]  Guo-Jin Tang,et al.  Interactive optimization approach for optimal impulsive rendezvous using primer vector and evolutionary algorithms , 2010 .

[35]  Nikolay Petrov,et al.  Short profile for the human spacecraft Soyuz-TMA rendezvous mission to the ISS☆ , 2012 .

[36]  Frederick H. Lutze,et al.  Second-Order Relative Motion Equations , 2003 .

[37]  Hua Wang,et al.  Quantitative Performance for Spacecraft Rendezvous Trajectory Safety , 2011 .

[38]  T. Carter State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example , 1998 .

[39]  Yin Yan Safety Mode Design of Final Translation Trajectories of Space Rendezvous , 2004 .

[40]  Xue Dan Review of Relative Motion Description Methods for Satellite Formation Flying , 2008 .

[41]  Thomas Carter,et al.  Optimal Power-Limited Rendezvous with Upper and Lower Bounds on Thrust , 1996 .

[42]  K. Alfriend,et al.  State Transition Matrix of Relative Motion for the Perturbed Noncircular Reference Orbit , 2003 .

[43]  Jonathan P. How,et al.  Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming , 2002 .

[44]  Ying Nan,et al.  A survey of numerical algorithms for trajectory optimization of flight vehicles , 2012, Science China Technological Sciences.

[45]  Yoshiaki Ohkami,et al.  Autonomous rendezvous and docking by engineering test satellite VII: a challenge of Japan in guidance, navigation and control—Breakwell memorial lecture☆ , 2003 .

[46]  S. Vadali,et al.  Near-optimal feedback rendezvous in elliptic orbits accounting for nonlinear differential gravity , 2007 .

[47]  Ilya Kolmanovsky,et al.  Model Predictive Control approach for guidance of spacecraft rendezvous and proximity maneuvering , 2012 .

[48]  Jonathan P. How,et al.  Safe Trajectories for Autonomous Rendezvous of Spacecraft , 2006 .

[49]  Cao Xibin,et al.  Monocular Vision-based Two-stage Iterative Algorithm for Relative Position and Attitude Estimation of Docking Spacecraft , 2010 .

[50]  Guo-Jin Tang,et al.  Hybrid planning for LEO long-duration multi-spacecraft rendezvous mission , 2012 .

[51]  JianYong Zhou,et al.  A new approach for teleoperation rendezvous and docking with time delay , 2012 .

[52]  Zhou Jianping A Review of Tiangong-1/Shenzhou-8 Rendezvous and Docking Mission , 2012 .

[53]  D. Jezewski,et al.  Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization , 1980 .

[54]  Tang Guo-jin,et al.  Collision Probability Based Optimal Collision Avoidance Maneuver in Rendezvous and Docking , 2008 .

[55]  Christopher D. Karlgaard,et al.  Adaptive Nonlinear Huber-Based Navigation for Rendezvous in Elliptical Orbit , 2011 .

[56]  David K. Geller,et al.  Relative Angles-Only Navigation and Pose Estimation for Autonomous Orbital Rendezvous , 2006 .

[57]  Colin R. McInnes,et al.  Safety Constrained Free-Flyer Path Planning at the International Space Station , 2000 .

[58]  Blair F. Thompson Engineering Notes Enhancing Lambert Targeting Methods to Accommodate 180-Degree Orbital Transfers , 2011 .

[59]  Jin Zhang,et al.  Error analysis for rendezvous phasing orbital control using design of experiments , 2012 .

[60]  Zhou Jian-ping,et al.  Multi-objective interplanetary trajectory optimization combining low-thrust propulsion and gravity-assist maneuvers , 2012 .

[61]  Ya-zhong Luo,et al.  Optimization of multiple-impulse minimum-time rendezvous with impulse constraints using a hybrid genetic algorithm , 2006 .

[62]  E. E. Prust,et al.  A survey of rendezvous trajectory planning , 1992 .

[63]  Zhen Yang,et al.  Robust optimization of nonlinear impulsive rendezvous with uncertainty , 2014 .

[64]  Zhou Zhicheng A Review of On-Orbit Life-Time Extension Technologies for GEO Satellites , 2012 .

[65]  Guo-Jin Tang,et al.  Orbital rendezvous mission planning using mixed integer nonlinear programming , 2011 .

[66]  O. Yakimenko,et al.  Optimal Rendezvous Trajectories of a Controlled Spacecraft and a Tumbling Object , 2011 .

[67]  Pradipto Ghosh,et al.  Particle Swarm Optimization of Multiple-Burn Rendezvous Trajectories , 2012 .

[68]  Guo-Jin Tang,et al.  Optimal Multi-Objective Nonlinear Impulsive Rendezvous , 2007 .

[69]  XU Shi-jie Relative Navigation for Non-cooperative Spacecraft Based on Second Step Multiple Model Estimation , 2008 .

[70]  Cao Xi-bin Guidance algorithms for near distance rendezvous of on-orbit-servicing spacecraft under constraints , 2006 .

[71]  Wigbert Fehse,et al.  Automated Rendezvous and Docking of Spacecraft , 2003 .

[72]  Hexi Baoyin,et al.  Optimal four-impulse rendezvous between coplanar elliptical orbits , 2011 .

[73]  H. London,et al.  SECOND APPROXIMATION TO THE SOLUTION OF THE RENDEZVOUS EQUATIONS , 1963 .

[74]  Y. Lei,et al.  Optimal Multi-Objective Linearized Impulsive Rendezvous , 2007 .

[75]  Thomas Carter,et al.  Necessary and Sufficient Conditions for Optimal Impulsive Rendezvous with Linear Equations of Motion , 2000 .

[76]  M. Handelsman,et al.  Primer Vector on Fixed-Time Impulsive Trajectories , 1967 .

[77]  Panagiotis Tsiotras,et al.  Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions , 2003 .

[78]  David K. Geller,et al.  Optimal Orbital Rendezvous Maneuvering for Angles-Only Navigation , 2009 .

[79]  Jin Zhang,et al.  Rendezvous-Phasing Errors Propagation Using Quasi-linearization Method , 2010 .

[80]  E. van Kampen,et al.  Optimization of Time-Open Constrained Lambert Rendezvous Using Interval Analysis , 2013 .

[81]  Guang-Ren Duan,et al.  Robust H∞ control of spacecraft rendezvous on elliptical orbit , 2012, J. Frankl. Inst..

[82]  Don J. Pearson The glideslope approach , 1989 .

[83]  Di Zhou,et al.  A second-order solution to the two-point boundary value problem for rendezvous in eccentric orbits , 2010 .

[84]  Zhang Weijin Shenzhou-8 Spacecraft Guidance Navigation and Control System and Flight Result Evaluation for Rendezvous and Docking , 2011 .

[85]  K. Yamanaka,et al.  New State Transition Matrix for Relative Motion on an Arbitrary Elliptical Orbit , 2002 .

[86]  Guo-Jin Tang,et al.  Optimization of perturbed and constrained fuel-optimal impulsive rendezvous using a hybrid approach , 2006 .

[87]  Xiuyun Meng,et al.  Suboptimal Power-Limited Rendezvous with Fixed Docking Direction and Collision Avoidance , 2013 .

[88]  Katsuhiko Yamada,et al.  New State Transition Matrix for Formation Flying in J2-Perturbed Elliptic Orbits , 2012 .

[89]  Katsuhiko Yamada,et al.  Guidance and navigation system design of R-bar approach for rendezvous and docking , 1998 .

[90]  R. Sedwick,et al.  High-Fidelity Linearized J Model for Satellite Formation Flight , 2002 .

[91]  Xie Yongchun A CCD Optical Sensor Based New Binocular Vision Measurement Algorithm for Rendezvous and Docking , 2011 .

[92]  I. Michael Ross Linearized Dynamic Equations for Spacecraft Subject to J Perturbations , 2003 .

[93]  Daniel J. Scheeres,et al.  Solving Optimal Continuous Thrust Rendezvous Problems with Generating Functions , 2005 .

[94]  Guo-Jin Tang,et al.  Optimal multi-objective trajectory design based on close-looped control for autonomous rendezvous , 2011 .

[95]  Jiang Zicheng A Survey of Teleoperator Rendezvous and Docking Technology , 2011 .

[96]  John E. Prussing Simple proof of the global optimality of the Hohmann transfer , 1992 .

[97]  Steven P. Hughes,et al.  A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem , 2002 .

[98]  David K. Geller,et al.  Linear Covariance Techniques for Orbital Rendezvous Analysis and Autonomous Onboard Mission Planning , 2005 .

[99]  J. Longuski,et al.  Analytical solutions for the relative motion of spacecraft subject to Lorentz-force perturbations , 2011 .

[100]  John E. Prussing,et al.  Optimal Multiple-Impulse Direct Ascent Fixed-Time Rendezvous , 1974 .

[101]  Huijun Gao,et al.  An impulse control approach to spacecraft autonomous rendezvous based on genetic algorithms , 2012, Neurocomputing.

[102]  Chi Zhu,et al.  Planning of Safe Kinematic Trajectories for Free Flying Robots Approaching an Uncontrolled Spinning Satellite , 2002 .

[103]  Frederick H. Lutze,et al.  Neural Network Control of Space Vehicle Intercept and Rendezvous Maneuvers , 1998 .

[104]  Daniele Mortari,et al.  Constrained Multiple-Revolution Lambert's Problem , 2010 .

[105]  J. A. Chamberlin,et al.  Gemini rendezvous program , 1964 .

[106]  Ya-zhong Luo,et al.  Optimal robust linearized impulsive rendezvous , 2007 .

[107]  Russell P. Patera Method for Calculating Collision Probability Between a Satellite and a Space Tether , 2002 .

[108]  W. H. Clohessy,et al.  Terminal Guidance System for Satellite Rendezvous , 2012 .

[109]  WeiRen Wu,et al.  Investigation on the development of deep space exploration , 2012 .

[110]  Alberto Novelli,et al.  The ATV "Jules Verne" supplies the ISS , 2008 .

[111]  Ya-zhong Luo,et al.  Spacecraft optimal rendezvous controller design using simulated annealing , 2005 .

[112]  A. Ichikawa,et al.  Orbital Rendezvous and Flyaround Based on Null Controllability with Vanishing Energy , 2007 .