On the Sub-Low Contact Velocity Control of Rendezvous Docking for Smart World

In order to avoid damages caused by high-speed collision during the rendezvous and docking process, the contact velocity between two spacecrafts has to be as low as possible. But in practice, it is very difficult to find the minimum value of contact velocity because of the complicated function involved. The only method to find the minimum of a function is by differentiating. However, this method is used to solve the problem of minimum speed, which is not only complicated in operation but also difficult to eliminate in the local minimum. Moreover, space applications should also consider the limitation of operation speed. For this reason, this paper proposes a method to find the sub-low relative speed, and derives the control law of rendezvous and docking.