Autonomous Trajectory Planning for Rendezvous and Proximity Operations by Conic Optimization

Autonomous rendezvous and proximity operations of spacecraft require the capability of onboard planning and executing highly constrained trajectories without ground support. This paper presents a general and rigorous methodology and algorithmic procedure toward this goal with a target vehicle that can be in an arbitrary orbit. The rendezvous and proximity operations problem is formulated as a nonlinear optimal control problem, subject to various state and control inequality constraints and equality constraints on interior points and terminal conditions. By a lossless relaxation technique, a relaxed problem is formed, the solution of which is proven to be equivalent to that of the original rendezvous and proximity operations problem. The relaxed problem is then solved by a novel successive solution process, in which the solutions of a sequence of constrained subproblems with linear, time-varying dynamics are sought. After discretization, each of these problems becomes a second-order cone programming proble...

[1]  Stephen P. Boyd,et al.  Applications of second-order cone programming , 1998 .

[2]  Behçet Açikmese,et al.  Lossless convexification of a class of optimal control problems with non-convex control constraints , 2011, Autom..

[3]  Stephen J. Wright.  Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

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

[5]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[6]  B. Tibken,et al.  An iterative method for the finite-time bilinear-quadratic control problem , 1988 .

[7]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

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

[9]  Stephen J. Wright,et al.  Primal-Dual Interior-Point Methods , 1997 .

[10]  T. Carter,et al.  Fuel-Optimal Rendezvous Near a Point in General Keplerian Orbit , 1987 .

[11]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[12]  Ping Lu,et al.  Rapid Optimal Multiburn Ascent Planning and Guidance , 2007 .

[13]  Behcet Acikmese,et al.  Minimum-Landing-Error Powered-Descent Guidance for Mars Landing Using Convex Optimization , 2010 .

[14]  Erling D. Andersen,et al.  On implementing a primal-dual interior-point method for conic quadratic optimization , 2003, Math. Program..

[15]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[16]  J. Stoer,et al.  Topics in Integration , 1980 .

[17]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[18]  Jack P. Brazzel,et al.  Challenges of Orion Rendezvous Development , 2007 .

[19]  Stephen P. Banks,et al.  Approximate Optimal Control and Stability of Nonlinear Finite- and Infinite-Dimensional Systems , 2000, Ann. Oper. Res..

[20]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[21]  D. J. Jezewski,et al.  An optimal, analytic solution to the linear- gravity, constant-thrust trajectory problem , 1971 .

[22]  Christopher D'Souza,et al.  Orion Rendezvous, Proximity Operations, and Docking Design and Analysis , 2007 .

[23]  Behcet Acikmese,et al.  Convex programming approach to powered descent guidance for mars landing , 2007 .

[24]  Behçet Açikmese,et al.  Lossless Convexification of Nonconvex Control Bound and Pointing Constraints of the Soft Landing Optimal Control Problem , 2013, IEEE Transactions on Control Systems Technology.

[25]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[26]  David K. Geller,et al.  Navigating the Road to Autonomous Orbital Rendezvous , 2007 .

[27]  Gong-You Tang,et al.  Suboptimal control for nonlinear systems: a successive approximation approach , 2005, Syst. Control. Lett..

[28]  L. Berkovitz.  Convexity and Optimization in Rn , 2001 .

[29]  Vladimir A. Chobotov,et al.  Orbital Mechanics, Third Edition , 2002 .

[30]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

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

[32]  Z. Gajic,et al.  The successive approximation procedure for finite-time optimal control of bilinear systems , 1994, IEEE Trans. Autom. Control..

[33]  Behcet Acikmese,et al.  A model predictive control technique with guaranteed resolvability and required thruster silent times for small-body proximity operations , 2006 .

[34]  John L. Goodman,et al.  History of Space Shuttle Rendezvous , 2011 .

[35]  T. Ström.  On Logarithmic Norms , 1975 .