Trajectory Control of a Spacecraft with a Robotic Manipulator on Two-Dimensional Plane Using Udwadia-Kalaba Equation

This paper presents a trajectory control of a chaser spacecraft modelled as the second order error dynamics equation assuming two-dimensional proximity operation between a chaser and a target spacecraft. Based on the second order dynamics, the chaser spacecraft is controlled to keep stand-off distance and relative orientation. Udwadia-Kalaba equation is applied to describe motion of the system and generate exact control commands based on the acceleration constraint equation of the motion. Taking into account the disturbance is derived by the robotic manipulator mounted on the chaser spacecraft, the control scheme enables to conduct the stand-off maneuver of two-dimensional trajectory. A numerical simulation about two-dimensional trajectory control of spacecraft is conducted to verify proximity operation between a chaser and a target spacecraft, which shows that the constraints of stand-off distance and relative orientation between two spacecrafts are properly satisfied even under the disturbance.