Near-optimal guidance and control for spacecraft collision avoidance maneuvers

This study presents a semi-analytic and sub-optimal guidance/control for a controlled/active spacecraft to avoid collision with other free/inactive space objects. The collision avoidance problem is formulated as a typical optimal feedback control problem with a penalty term incorporated into the performance index. The penalty function is designed such that its value increases sharply as a spacecraft approaches other space objects. The Pontryagin’s principle is used to form a two point boundary value problem for a standard Hamiltonian system, whose solution is obtained in terms of the generating functions which appear in the theory of canonical transformation. The resultant algorithm allows one to develop near-optimal guidance/control laws as truncated power series in feedback form and generate near-optimal trajectories without any initial guess or iterative process. This procedural advantage over typical direct optimization approaches comes at the expense of reasonable efforts of developing higher-order generating functions and empirically updating the design parameters of penalty function. Numerical examples demonstrate that the proposed algorithm successfully accomplishes collision avoidance by appropriately detouring other space objects or forbidden regions.

[1]  Mohamed Elsayed Aly Abd Elaziz Okasha,et al.  Autonomous multi satellites assembly in keplerian orbits , 2013 .

[2]  S. Ploen,et al.  A direct solution for fuel-optimal reactive collision avoidance of collaborating spacecraft , 2006, 2006 American Control Conference.

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

[4]  Pablo Pedregal,et al.  Mixed‐Integer Linear Programming , 2011 .

[5]  Cornel Sultan,et al.  Energy Suboptimal Collision-Free Reconfiguration for Spacecraft Formation Flying , 2006 .

[6]  C. McInnes,et al.  Autonomous rendezvous using artificial potential function guidance , 1995 .

[7]  Gary Slater,et al.  Collision Avoidance for Satellites in Formation Flight , 2004 .

[8]  D. Scheeres,et al.  Solving Relative Two-Point Boundary Value Problems: Spacecraft Formation Flight Transfers Application , 2004 .

[9]  Sangjin Lee,et al.  Approximate Analytical Solutions to Optimal Reconfiguration Problems in Perturbed Satellite Relative Motion , 2011 .

[10]  S. D. Fernandes Optimization of Low-Thrust Limited-Power Trajectories in a Noncentral Gravity Field—Transfers between Orbits with Small Eccentricities , 2009 .

[11]  William W. Hager,et al.  Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method , 2011, Comput. Optim. Appl..

[12]  Sang-Young Park,et al.  Optimal tracking and formation keeping near a general Keplerian orbit under nonlinear perturbations , 2014 .

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