Cooperative Rendezvous Between Active Autonomous Vehicles

Abstract

The rendezvous problem between autonomous vehicles is formulated as an optimal cooperative control problem with terminal constraints. Optimal control problems are often solved by seeking solutions which satisfy the first order necessary conditions for an optimum. Such an approach is based on a Hamiltonian formulation, which leads to a difficult two-point boundary-value problem. We propose a different approach in which the control history is found directly by a genetic algorithm search method. The main advantage of the method is that it does not require the development of a Hamiltonian formulation and consequently, it eliminates the need to deal with an adjoint problem, which leads to a difficult two-point boundary-value problem in nonlinear ordinary differential equations. This method has been applied to the solution of interception and rendezvous problems in an underwater environment, where the direction of the velocity vector is used as the control. We consider the effects of gravity, thrust and viscous drag and treat the rendezvous location as a terminal constraint. We then study cooperative rendezvous problems between spacecraft. We treat the case where the magnitude of the continuous low thrust vector is fixed and the direction of the thrust is used as the control. The spacecraft start from different points on an initial circular orbit and meet at a point on a circular orbit of larger radius, with the same final orbital velocity. The present genetic algorithm was developed to treat complex interception and rendezvous problems involving multiple vehicles.