Spacecraft Constrained Maneuver Planning Using Positively Invariant Constraint Admissible Sets

The paper considers spacecraft motion planning based on the use of safe positively invariant sets. In this approach, a connectivity graph is constructed between a set of forced equilibria, forming a virtual net that is centered around a nominal orbital position. The connectivity between two equilibria is determined based on safe positively invariant sets in order to guarantee that transitions between equilibria can be effected while spacecraft actuator limits are adhered to and debris collisions are avoided. A graph search algorithm is implemented to find the shortest path around the debris. Simulation results are presented that illustrate this approach.

[1]  Noelia Sanchez-ortiz,et al.  Collision avoidance manoeuvres during spacecraft mission lifetime: Risk reduction and required ΔV , 2006 .

[2]  Gloria J. Wiens,et al.  A new method of guidance control for autonomous rendezvous in a cluttered space environment , 2007 .

[3]  Roberto Kawakami Harrop Galvão,et al.  On the use of mixed‐integer linear programming for predictive control with avoidance constraints , 2009 .

[4]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[5]  Elmer G. Gilbert,et al.  Growth distances: new measures for object separation and penetration , 1996, IEEE Trans. Robotics Autom..

[6]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[7]  Yuri Ulybyshev.  Trajectory Optimization for Spacecraft Proximity Operations with Constraints , 2011 .

[8]  Nedjeljko Frančula.  The National Academies Press , 2013 .

[9]  Nick Martinson,et al.  Obstacle avoidance guidance and control algorithm for spacecraft maneuvers , 2009 .

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

[11]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[12]  A. Stephen Morse,et al.  Control Using Logic-Based Switching , 1997 .

[13]  A. Mayne.  Parametric Optimization: Singularities, Pathfollowing and Jumps , 1990 .

[14]  Chris Ranieri,et al.  Path-Constrained Trajectory Optimization for Proximity Operations , 2008 .

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

[16]  Stefano Di Cairano,et al.  Linear quadratic model predictive control approach to spacecraft rendezvous and docking , 2011 .

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

[18]  Ilya Kolmanovsky,et al.  Multimode regulators for systems with state & control constraints and disturbance inputs , 1997 .

[19]  Dinh Quoc Tran,et al.  Adjoint-Based Predictor-Corrector Sequential Convex Programming for Parametric Nonlinear Optimization , 2012, SIAM J. Optim..

[20]  J. Mueller.  Onboard Planning of Collision Avoidance Maneuvers Using Robust Optimization , 2009 .

[22]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[23]  Joseph B. Mueller,et al.  Avoidance maneuver planning incorporating station-keeping constraints and automatic relaxation , 2010 .