Time-Optimal Low-Thrust Formation Maneuvering Using a Hybrid Linear/Nonlinear Controller

M AINTAINING two spacecraft in a formation with a conventional fuel-based propulsion system could be challenging in its own right. But this problem becomes more difficult when the propulsion system has limited capabilities or control actuation is available in only one or two axes and timeoptimal and fuel-optimal control is desired. Fortunately, for the spacecraft relative motion problem, because the relative equations of motion are coupled, motion in more than one direction can be controlled by control actuation in only one direction. In this Note, we formulate a hybrid linear/nonlinear controller that can efficiently maneuver a spacecraft formation by applying control only in the along-track direction. We also assume that the available control is very small in magnitude. This type of problem could be anticipated when dealing with low-thrust systems such as plasma thrusters, control with differential drag or solar radiation pressure, or any other system with very-low-thrust capability. One of the very early papers on underactuated control of a spacecraft formation with low-thrust capability by Leonard [1] presented an elegant algorithm to control a formation with only differential drag (assumed to be a constant and acting only in the along-track direction). Although the derived control was proven to be time-optimal control, it was not fuel-optimal. This was because differential drag was assumed to be a free resource with no need to economize it. However, for a spacecraft relying on expendables for control (plasmic thrusters), fuel economy would be highly desired. Some of the recent papers on this topic [2,3] also address the problem of spacecraft formation control with limited resources. The idea is to use linear or nonlinear controllers with a saturation function. The resultant controllers are robust and globally stable but not time-optimal. In the applied control field, the problem to control less frequently andmore efficiently ismore often an issue and elegant solutions exist for the same problem [4,5]. In this Note, we borrow some ideas discussed from [1,5] and apply them to the spacecraft formation-control problem. The result is a time-optimal controller that is easy to implement for underactuated formation control with limited resources. Although the controller is not proven to be fueloptimal, it is shown to consume less fuel than a conventional timeoptimal or a linear robust controller.