Maneuvering spacecraft in the vicinity of other objects is a complex operation, especially when the objective is to rendezvous with another, target object in a docking mission. Most of the algorithms developed to control a space craft in such circumstances have serious drawbacks.
Most of the existing methods and systems do not, for instance, optimize the fuel cost of the maneuver, or minimize the time taken to perform the maneuver. Moreover, they cannot, in general, deal with having unanticipated additional objects in the vicinity. Nor can they deal with stayout zones that have to be avoided that may result from, for instance, the optical sensors on the target. Most of the existing methods cannot be used to orbit the target en-route to a rendezvous, which may be desired in order to inspect either the spacecraft or the target. The few algorithms that can deal with obstacles and stay out zones tend to be very computationally intensive, requiring offline calculation. They are, therefore, of limited use, especially if obstacles near the target change during the maneuver. This may happen, for example, if the target encounters unexpected additional targets.
Several methods have been developed for use by spacecraft for close maneuvering, rendezvous and docking missions. Four of these are discussed below.
Method 1. The glideslope algorithm is a popular method of approaching another spacecraft. In this method the range rate is kept proportional to the range. When the range is zero the range rate is zero. The initial range rate/range ratio can be any desired. This algorithm cannot deal with stayout zones or obstacles, thus these must be handled in an ad hoc fashion. In addition, it does not allow for orbiting the target.
Method 2. Another method is the rbar or vbar approach. Vbar is the axis along the velocity vector and rbar is the axis along the position vector to the Earth. Approaches are made along either of these axes. However, this method also does not account for stayout zones or obstacles. As with the glideslope algorithm, this method does not handle orbiting the target.
Method 3. A method developed by Miller that can handle trajectory constraints such as obstacles and stayout zones is parametric programming and model predictive control, which finds the optimal control inputs as a piecewise affine function of the states. Most computation is performed off-line thus reducing the on-line computation to a simple table lookup. The solution found off-line is an exact solution, the equivalent of solving an open-loop optimal control problem over a finite horizon at each time step. However, even though the computation is offline it still must be done on the flight processor. In addition, obstacles may change during the approach which means this computationally intensive procedure must in practice be done in real-time.
Method 4. Another method developed by Zhao and Yang employs a 4-dimensional search space with 3 spatial and 1 temporal coordinate. Obstacles and potential conflicts are represented by several basic shapes and linear combinations of these shapes. Mathematical conditions are developed for a given point as well as a trajectory segment between two points to be outside of an obstacle. The A* search technique is used to obtain trajectory solutions in which successor trajectory points are selected that both avoid obstacles and satisfy dynamic motion constraints of the vehicle. A linear combination of flight distance and time is optimized. This algorithm is able to generate flight trajectories rapidly and has the potential to be used in real-time. However, the used of simple geometric shapes as the basis for obstacles is a major limitation of this approach. In addition it has no provision for non-uniform node spacing and generation.