Parameterization of Fuel-Optimal Synchronous Approach Trajectories to Tumbling Targets

Docking with potentially tumbling Targets is a common element of many mission architectures, including on-orbit servicing and active debris removal. This paper studies synchronized docking trajectories as a way to ensure the Chaser satellite remains on the docking axis of the tumbling Target, thereby reducing collision risks and enabling persistent onboard sensing of the docking location. Chaser satellites have limited computational power available to them and the time allowed for the determination of a fuel optimal trajectory may be limited. Consequently, parameterized trajectories that approximate the fuel optimal trajectory while following synchronous approaches may be used to provide a computationally efficient means of determining near optimal trajectories to a tumbling Target. This paper presents a method of balancing the computation cost with the added fuel expenditure required for parameterization, including the selection of a parameterization scheme, the number of parameters in the parameterization, and a means of incorporating the dynamics of a tumbling satellite into the parameterization process. Comparisons of the parameterized trajectories are made with the fuel optimal trajectory, which is computed through the numerical propagation of Euler’s equations. Additionally, various tumble types are considered to demonstrate the efficacy of the presented computation scheme. With this parameterized trajectory determination method, Chaser satellites may perform terminal approach and docking maneuvers with both fuel and computational efficiency.

[1]  R. L. Robertson.  Guidance, flight mechanics and trajectory optimization. Volume 16 - Mission constraints and trajectory interfaces , 1968 .

[2]  R. Bevilacquaa,et al.  Online generation of quasi-optimal spacecraft rendezvous trajectories , 2008 .

[3]  Ioannis M. Rekleitis,et al.  Autonomous capture of a tumbling satellite , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[4]  Stephanie J. Thomas.  Generalized 3D Spacecraft Proximity Path Planning Using A , 2005 .

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

[6]  Gerd Hirzinger,et al.  Generating feasible trajectories for autonomous on-orbit grasping of spinning debris in a useful time , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[7]  Marcello Romano,et al.  Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers , 2018 .

[8]  Josué D. Muñoz,et al.  Rapid path-planning algorithms for autonomous proximity operations of satellites , 2011 .

[9]  M. W. Weeks,et al.  Optimal Trajectories for Spacecraft Rendezvous , 2007 .

[10]  John J. Leonard,et al.  Smoothing-based estimation of an inspector satellite trajectory relative to a passive object , 2017, 2017 IEEE Aerospace Conference.

[11]  Mark Charles Jackson.  A six degree of freedom, plume-fuel optimal trajectory planner for spacecraft proximity operations using an A* node search , 1994 .

[12]  D. Spencer,et al.  A Hybrid Stochastic Motion Planning Algorithm for Safe and Efficient, Close Proximity, Autonomous Spacecraft Missions , 2014 .

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

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

[15]  Robert M. Sanner,et al.  Variational Technique for Spacecraft Trajectory Planning , 2010 .

[16]  James R. Wertz,et al.  Autonomous On-board Orbit Control: Flight Results and Cost Reduction , 2001 .

[17]  Colin Robert McInnes.  Autonomous path planning for on-orbit servicing vehicles , 2000 .

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

[19]  James R. Wertz.  Autonomous Navigation and Autonomous Orbit Control in Planetary Orbits as a Means of Reducing Operations Cost , 2003 .

[20]  Roberto Lampariello,et al.  A Nonlinear Optimization Method to Provide Real-Time Feasible Reference Trajectories to Approach a Tumbling Target Satellite , 2016 .

[21]  Gabriel Urbain,et al.  INSPECT Sensor Suite for On-Orbit Inspection and Characterization with Extravehicular Activity Spacecraft , 2015 .

[22]  Eduardo F. Camacho,et al.  Trajectory Planning for Spacecraft Rendezvous with On / Off Thrusters , 2011 .

[23]  Angelo Miele,et al.  Guidance Trajectories for Spacecraft Rendezvous , 2007 .

[24]  Marcello Romano,et al.  Fast and Near-Optimal Guidance for Docking to Uncontrolled Spacecraft , 2017 .

[25]  Markus Wilde,et al.  Experimental Characterization of Inverse Dynamics Guidance in Docking with a Rotating Target , 2016 .

[26]  David Sternberg,et al.  Mapping a chaser satellite's feasibility space for soft docking , 2017, 2017 IEEE Aerospace Conference.

[27]  George A. Boyarko,et al.  Rapid Path-Planning Options for Autonomous Proximity Operations of Spacecraft , 2010 .