An Autonomous Guidance Scheme For Orbital Rendezvous

Abstract

The word 'rendezvous' implies a pre-arranged meeting between two entities for a specific purpose. This term is used in the study of spacecraft operations, to describe a set of maneuvers performed by two spacecraft in order to achieve a match in position and velocity. The term 'orbital rendezvous' applies to rendezvous between spacecraft in earth-centered orbits. Considering its obvious scope for application in the assembly, maintenance and retrieval of earth satellites, the importance of orbital rendezvous towards maintaining a sustained presence in space can be easily appreciated. This particular study deals with the development of a guidance scheme for an orbital rendezvous operation, wherein only one of the spacecraft, called the chaser, is assumed to be provided with a capability to maneuver, while the other spacecraft, the target, is assumed to be thrust-free or passive. There is presently a lot of interest in autonomous trajectory planning and guidance schemes for orbital rendezvous missions. Autonomy here, refers to the absence of ground supervision and control over the on-board planning and guidance process, and is expected to result in greater mission flexibility and lower operating costs. The terms trajectory planning and guidance collectively refer to the optimization process used to determine minimum-fuel trajectories, and the means employed to make the spacecraft follow them, based on navigational updates. The challenge lies mainly in making the autonomous scheme real-time implementable, and at the same time compatible with the limited computational capabilities available on-board. It is well known that a large part of the computation times and costs, when determining optimal trajectories, are taken up by (1) the prediction of spacecraft motion using numerical integration schemes, and (2) the use of iterative numerical techniques to solve the non-linear, coupled system of equations obtained as boundary conditions in the trajectory optimization problem. There exists on the other hand, a wealth of results from analytical investigations into the motion of spacecraft, that can be profitably utilized by use of suitable assumptions, to reduce computation times and costs relating to trajectory prediction. The present thesis seeks to follow this course, while trying to ensure that the assumptions made do not influence in a negative manner the accuracy of the guidance scheme. The assumptions to be described below are based on the division of the total rendezvous maneuver into sub-phases. The trajectory optimization problems for the individual sub-phases are first considered independent of one another. A method is then found to combine the two sub-phases in an optimal manner.

The initial or the homing phase of the rendezvous maneuver, consists of an open-loop orbit transfer, intended to place the chaser within a 'window of proximity' spanning a few hundreds of kilometers, of the target. In order to avoid time consuming numerical integration of the non-homogeneous, non-linear central force-field equations of motion, an impulsive thrust model is assumed. A parametric optimization method is used to determine the location, orientation and magnitude of the impulses for a minimum-fuel rendezvous transfer, as it is well known that parametric optimization methods are robust compared to the more general functional optimization methods. A two-impulse transfer is selected, knowing that at least two-impulses are required for a rendezvous maneuver, and that methods are available if necessary, to obtain optimal multi-impulse trajectories from a two-impulse solution. The total characteristic velocity, a scalar cost function related to fuel-consumption, is minimized with respect to a set of independent variables. The variables chosen in this case to determine the rendezvous transfer are (1) the transfer angle θc defining an initial coast in the chaser orbit C by the chaser, (2) the transfer angle θs defining a coast by the target to the position of the second impulse in the target orbit S and (3) a parameter (say p ) that determines the shape of the transfer orbit T between the first and second impulses.