Control of spacecraft in proximity orbits

Formation flying of spacecraft and autonomous rendezvous and docking of spacecraft are two missions in which satellites operate in close proximity and their relative trajectories are critically important. Both classes of missions rely on accurate dynamics models for fuel minimization and observance of strict constraints for preventing collisions and achieving mission objectives. This thesis presents improvements to spacecraft dynamics modeling, orbit initialization procedures, and failsafe trajectory design that improve the feasibility and chances of success for future proximity operations. This includes the derivation of a new set of relative linearized orbital dynamics incorporating the effects of Earth's oblateness. These dynamics are embedded in a model predictive controller, enabling LP-based MPC formulations for large baseline formations in highly elliptic orbits. An initialization algorithm is developed that uses the new dynamics to optimize multiple objectives (drift and fuel usage minimization, geometry) over science-relevant time frames, improving previous J2-invariant initialization techniques which only considered infinite-horizon secular drift. The trajectory planning algorithm is used to design spacecraft rendezvous paths that observe realistic constraints on thruster usage and approach path. The paths are fuel-optimized and further constrained to be safe (i.e., avoid collisions) in the presence of many possible system failures, an enhancement over previous guaranteed-safe rendezvous methods, which did not minimize fuel use. The fuel costs of imposing safety as a constraint on trajectory design are determined to be low compared to standard approaches and a stochastic analysis demonstrates that both active and passive forms of the safe rendezvous algorithm substantially decrease the likelihood of system failures resulting in collisions. The effectiveness of the new controller/dynamics combination is demonstrated in high fidelity multi-week simulations. An optimized safe rendezvous trajectory was demonstrated on a hardware testbed aboard the International Space Station. Thesis Supervisor: Jonathan P. How Title: Associate Professor of Aeronautics and Astronautics

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