Region of Attraction Estimation for Free-Floating LQR Controllers

The ever increasing amount of space debris poses great risks for the aerospace industry. Especially collision of two high mass resident space objects (RSOs) could greatly complicate and impede operations of existing satellites and future spacecraft launches. Removing such objects from functional orbits therefore has a high priority. Currently, there are many concepts on how active debris removal (ADR) could be achieved, however the problem is yet to be solved. Many approaches to ADR suggest docking and detumbling of the object that is to be removed. These steps are to be performed autonomously and require not only for novel docking hardware but also highly elaborate and robust control algorithms. A promising concept for such a controller is inspired by the notion of Rapidly Exploring Random Trees (RRT). It involves generating a lookup table by growing a sparse tree of nodes that branches throughout relevant regions of the nonlinear state space of the system. Each node represents a state and contains information that can be used to synthesize an optimal feedback policy using Linear Quadratic Regulators (LQR). In order to retain a sparse tree representation, states that are not part of the tree but in the vicinity of one of its nodes are stabilized using the same linear feedback policy of the nearest node in the tree. If a state can not be stabilized using an existing policy, that is, it is not contained within the Region of Attraction of the closed loop system, a new branch has to be added to the tree. Hence, being able to estimate the RoA of the closed loop system is necessary to grow the tree. Within this work an algorithm shall be developed that can asses the RoA within a LQR-Tree based controller that can be used to detumble a RSO. Furthermore tests onboard ELISSA, a free floating testbed located at the Institute for Space Systems at the TU Braunschweig shall demonstrate and verify the proper functioning of this control approach.