Docking Maneuver to a Tumbling Target

As the number of uncontrollable objects in low earth orbit is rising, the thread of collisions and thus the breakdown of working satellites becomes worth analyzing. Consequently, space debris removal becomes an issue. In this study an optimal docking maneuver of a service satellite to an uncontrolled tumbling target is modeled and solved numerically. After deriving the system dynamics, we introduce boundary conditions to ensure a safe and realizable maneuver and a general Bolza type cost functional to incorporate different optimization goals. In order to solve the resulting problem, we transform the dynamics to a set of diļ¬€erential algebraic equations which allow us to employ a direct optimization method while preserving the energy of the system.

The results have been obtained at the Chairs of Engineering Mathematics at the University of the Federal Armed Forces (http://www.unibw.de/lrt1/gerdts) and at the University of Bayreuth (http://www.ingenieurmathematik.uni-bayreuth.de). More details can be found in

Michael, J., Chudej, K., Gerdts, M., Pannek, J., Optimal Rendezvous Path Planning to an Uncontrolled Tumbling Target, Automatic Control in Aerospace, Volume 19, Issue 1, Pages 347-352, DOI 10.3182/20130902-5-DE-2040.00001

The following video shows an optimal docking maneuver of a service satellite to an uncontrolled tumbling target satellite: