An algorithm to guide the capture of a tumbling resident space object by a spacecraft equipped with a robotic manipulator is presented. A solution to the guidance problem is found by solving a collection of convex programming problems. As convex programming offers deterministic convergence properties, this algorithm is suitable for onboard implementation and real-time use. A set of hardware-in-the-loop experiments substantiates this claim. To cast the guidance problem as a collection of convex programming problems, the capture maneuver is divided into two simultaneously occurring submaneuvers: a system-wide translation and an internal re-configuration. These two sub-maneuvers are optimized in two consecutive steps. A sequential convex programming procedure, overcoming the presence of non-convex constraints and nonlinear dynamics, is used on both optimization steps. A proof of convergence is offered for the system-wide translation, while a set of structured heuristics-trust regions-is used for the optimization of the internal re-configuration sub-maneuver. Videos of the numerically simulated and experimentally demonstrated maneuvers are included as supplementary material.

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In this paper, Model Predictive Control (MPC) approaches are applied to multiple obstacle avoidance maneuvers for spacecraft rendezvous and docking. For safe obstacle avoidance, keep-out constraints are introduced by bounding ellipsoids around obstacles. In a linear quadratic MPC (LQ-MPC) framework, the rotating hyperplane method is used to convexify the obstacle avoidance constraints. A new method using two hyperplanes for convexification of the constraints is also proposed to improve performance of the LQ-MPC approach. A nonlinear MPC (NMPC) approach that deals with the nonlinear obstacle constraints directly is also applied to solve the spacecraft proximity maneuvering problems by using the nonlinear programming solver IPOPT (Interior Point OPTimizer). Real-time implementation of the MPC solutions is analyzed and compared on a physical test bed using several test cases. Numerical simulations and experiments demonstrate the obstacle avoidance as well as real-time operation capabilities of the considered control approaches.

Ground-based experimental evaluations of emerging guidance, navigation, and control (GNC) approaches may be used to raise their technological readiness level and determine their performance and limitations on flight-equivalent hardware (i.e., sensors, actuators, and computational systems) [2].An experimental campaign to evaluate the performance of the model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD) guidance methods has been performed at the Naval Postgraduate School POSEI-DYN 1 air-bearing test bed [4]. The focus of this research is limited in scope to the guidance and control of the simulated spacecraft. The navigation problem is solved by the POSEIDYN test bed motion capture system, which, augmented by onboard sensors, is used to provide accurate navigation data. The test vehicles operating in the POSEI-DYN test bed float on top of a 4-by-4 m granite table and exhibit a drag-free and weightless motion on a plane [4]. These test vehicles are referred to as floating spacecraft simulators, or simply as FSS.A spacecraft docking problem is selected for the experimental evaluation of these two different control approaches. A keep-out zone, an entry cone, and a maximum force constraint are added to the docking scenario to evaluate the constraint handling abilities of the two different controllers. A linear-quadratic MPC (LQ-MPC) algorithm with a quadratic programming (QP) solver and an IDVD algorithm with a nonlinear programming (NLP) solver have been chosen for this comparative study. These two controllers have been implemented and, when executed in real-time on board the FSS, they are successful in 1 POSEIDYN stands for Proximity Operation of Spacecraft: Experimental hardware-In-the-loop DYNamic simulator Abstract An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a groundbased air-bearing test bed, using spacecraft simulators that float over a granite table.Keywords Rendezvous and proximity operations · Model predictive control · Inverse dynamics · Hardware-in-theloop

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