Spacecraft formation-flying using potential functions

A group of small spacecraft able to change their relative position and attitude through the use of the potential function method is discussed. The spacecraft shapes, sizes and manoeuvring capabilities are not identical, although all are assumed to manoeuvre using continuous thrusters. A hyperbolic form of the attractive potential function is used to reduce actuator effort by using natural orbital motion to approaching the goal configuration. A superquadric repulsive potential with 3D a rigid object representation is then used to provide an accurate representation of the shape of spacecraft in the potential function. As the spacecraft start away from their goal, a parabolic attractive potential is inefficient as the control force increases with distance from the goal. Using a hyperbolic attractive potential, the control force is independent of the distance to goal, ensuring smooth manoeuvring towards the goal with a bound actuator effort