A Nonlinear Optimization Method to Provide Real-Time Feasible Reference Trajectories to Approach a Tumbling Target Satellite

Abstract

We present a motion planning method based on nonlinear optimization to provide reference trajectories for a robotic spacecraft approaching a non-cooperative target satellite. We perform a first investigation of a planning method containing an offline and an online element which can be used to provide reference trajectories in a useful time. The method capabilities include identifying feasible solutions in the presence of a non-static obstacle space and the treatment of a Target satellite in any general tumbling state with angular velocities less than $5$ deg/s. We use a safety metric defined as the time-to-collision (ttc) with the Target satellite and show that the planning method can find the global minima for the defined problem within $50$ min. The approach maneuver is parametrized using a 6 degree of freedom (dof) task space which describes the final position of the grasping point on the Target satellite and the satellite's final angular velocity. First a global search composed of a coarse, randomized optimization plus a finer smoothing is performed, then the online algorithm interpolates between the pre-computed solutions and provides the reference trajectory to an on-board controller. An estimate for the offline computation times, up to 6 days for a sparse discretization, shows that in the presence of inertia uncertainties of the Target satellite, using parallelized optimization in an online global search can provide solutions on the order of minutes and is more attractive.