Trajectory Reproduction Algorithm in Application to an On-Orbit Docking Maneuver with Tumbling Target

The paper presents a new algorithm for a trajectory planning problem. As a result, we obtain a control function which drives the system along the prescribed trajectory. This algorithm is embedded into an Endogenous Configuration Space Approach. The instantaneous map of the nonholonomic system allows us to construct a system of nonlinear functional equations which solution is a demanded control function. In order to solve the mentioned system of equations, the large scale root-finding algorithm is employed. The new trajectory reproduction algorithm is applied to solve the problem of an on-orbit servicing, namely a docking maneuver of a free-floating space manipulator with a tumbling target. The efficiency of the proposed approach is presented with a series of numerical experiments.