Satellite Formation Flying (SFF) is a key technology for several future missions, since, with respect to a single spacecraft, it allows better performances, new capabilities, more flexibility and robustness to failure and cost reduction. Despite these benefits, however, this new concept poses several signicant design challenges and requires new technologies. The Guidance, Navigation and Control (GNC) system is a key element in the SFF concept since it must be reliable in coordinating all the satellites fying in formation during each mission phase, guaranteeing formation integrity and preventing from formation evaporation, and, at the same time, efficient in using the limited on board resources. Model Predictive Control (MPC), also referred to as Receding Horizon Control, is a modern optimal control technique that seems to be suitable for these purposes because of its three main features: model-based control scheme, constraints handling ability and replanning nature.
The final aim of my Ph.D. activities was to develop and test MPC strategies for SFF applications. This task was accomplished by means of both computer simulations and experimental tests conducted on both the MIT Synchronized Position Hold Engage & Reorient Experimental Satellites (SPHERES) testbed and the SFF Hardware Simulator under development at the Center of Studies and Activities for Space "Giuseppe Colombo" (CISAS), University of Padova.
MPC capabilities were first tested in computer simulations in carrying out a formation acquisition maneuver for two space vehicles, taking into account two scenarios: a Leader-Follower (LF) formation and Projected Circular Orbit (PCO) formation. The performances of the MPC-based controller were compared with those of a Linear Quadratic Regulator (LQR) based controller in the presence of active constraints on the maximum control acceleration, evaluating also the effects of the gravitational harmonics J2 and J3 and atmospheric drag perturbations on the proposed maneuvers. Simulation results of both scenarios showed that, with similar performances in tracking the same reference state trajectory in terms of settling time, the MPC controller is more efficient (less delta-v requirement) than the LQR controller also in the perturbed cases, allowing a delta-v requirement reduction by 40% in the LF formation scenario and by 30% in the PCO formation scenario.
The next activity concerned the development of some guidance and control strategies for a Collision-Avoidance scenario in which a free-flying chief spacecraft follows temporary off-nominal conditions and a controlled deputy spacecraft performs a collision avoidance maneuver. The proposed strategy consists on a first Separation Guidance that, using a computationally simple, deterministic and closed-form algorithm, takes charge of avoiding a predicted collision. When some safe conditions on the relative state vector (position and velocity) are met, a subsequent Nominal Guidance takes over. Genetic Algorithms are used to compute a pair of reference state trajectories in order to place the deputy spacecraft in a bounded safe or "parking" trajectory, while minimizing the propellant consumption and avoiding the formation evaporation. The performances of a LQR and a MPC in tracking these reference trajectories were compared, showing how a MPC controller can reduces the total delta-v requirement by 5 - 10% with respect to a LQR controller.
MPC capabilities were then evaluated on the MIT SPHERES testbed in simulating the close-proximity phase of the rendez-vous and capture maneuver for the Mars Orbital Sample Return (MOSR) scenario. Better performances of MPC with respect to PD in executing this maneuver were conrmed both in a Matlab simulator and in the MIT SPHERES software simulator, with a total delta-v requirement reduction by 10-15 %. The proposed MPC control strategy was then tested using the SPHERES Flat Floor facility at the MIT Space System Laboratory.
The last part of my research activities was devoted to the SFF Hardware Simulator of the University of Padova. My contributions to this project dealt with: (a) conclusion of the designing, building and testing of the five main subsystems of the hardware simulator; (b) software development for the hardware simulator and its Matlab software simulator; (c) preparatory experimental activities aimed at characterizing the thrust force performed by the on board thrusters and estimating the hardware simulator inertia properties; and (d) test of attitude control maneuvers with the use of predictive controllers.
In particular, three main tests were carried out with the hardware simulator moving at one degree of freedom about the yaw axis. The first one aimed at tuning a Kalman Filter to properly estimate the yaw axis angular velocity using a double-integrator as dynamic model and angular position measurements provided by the yaw quadrature encoder. With the use of a simple Kalman Filter, the yaw angular position and velocity could be estimated with an error less than 0.1 ° and 0.1°/s, respectively. In the second test, an explicit MPC was used to perform a 170° slew maneuver of the hardware simulator attitude module about the yaw axis. The final target angular position was reached with an error less than 0.5° in 20 s. In the third test, a 3 degrees of freedom attitude reference trajectory was first computed using pseudospectral optimization methods for a repointing maneuver with active constraints on the attitude trajectory. The state trajectory was then projected along the satellite z-Body axis and tracked in the hardware simulator using an explicit MPC. Experimental results showed that with an explicit MPC the reference trajectories can be tracked with an error less that 1.5° for the angular position and less than 1°/s for the angular velocity, both in dynamic conditions. The final target state was reached with an error less than the estimation accuracy.
The SFF Hardware Simulator is a ground-based testbed for the development and verification of GNC algorithms that in the present configuration allows the development and testing of advanced controls for attitude motion and in its final form will enable the derivation of control strategies for
Formation Flight and Automated Rendezvous and Docking
