Adaptive dual control for spacecrafts rendezvous

This paper deals with some algorithms of finding optimal stochastic control for spacecraft rendezvous. Spacecraft rendezvous in the earth's gravitation field with nonlinear motion equations in discrete form are considered. The motion equations are defined with respect to coordinate systems connected to the spacecraft which is passive in the process of rendezvous. The corresponding relative coordinates measurement in the rendezvous process is done by using special equipment on the active spacecraft. A nonlinear system describing the rendezvous process is assumed to have the certainty equivalence property. Based on this assumption, an algorithm of the approximate solution of the optimal stochastic control is developed. The well-known Tse-Bar Shalom procedure is then used for finding the approximate adaptive dual control. Here the methods described in the case of spacecraft and space station rendezvous. The rendezvous occurs on the spacestation level are compared. Considering this problem, corresponding characteristics for both algorithms are found by using the simulation method. Finally, some improvements of these algorithms are suggested.