Closed-loop Acceleration Feedback

Historically, sensor noise has been a key factor in the analysis of system performance for formation flying spacecraft. Since most interesting formation missions require coordination between multiple spacecraft, knowledge of the relative states must be as accurate as possible. This knowledge is typically used to design a trajectory to meet specific criteria, such as minimizing fuel use or maintaining a desired formation geometry. The planning process depends on knowledge of the initial conditions of the spacecraft [1], and degrades with increasing error. Specifically, Tillerson showed that velocity error was the primary cause of poor performance, and that an error of just 2 mm/s can result in errors on the order of 30 m after just one orbit. At that time, the best navigation filters, using Carrier-Phase Differential GPS (CDGPS) signals achieved velocity accuracy on the order of 0.5 mm/s [2]. Since then, the state-of-the-art has improved significantly, with Leung and Montenbruck [3] demonstrating a filter that can estimate relative position and velocity to within 1.5 mm and 5 μm/s, respectively. While those numbers represent a best-case performance for real world operation, with these improvements, it is nonetheless important to understand how other sources of noise can affect formation flight. One such source is the incorrect implementation of a thruster burn. A common way of commanding a thruster burn is to specify the spacecraft’s desired change in velocity (∆V ). The propulsion system is then responsible for applying the desired ∆V to the spacecraft. For mission critical maneuvers, thruster burns must be done with precision. For example, for the Cassini Saturn Orbit Insertion (∆V ≈ 625 m/s), an algorithm that measured the energy change of the spacecraft was used. This energy change was monitored autonomously by Cassini during the burn, using realtime measurements from onboard accelerometers [4]. The insertion was successfully terminated when the desired energy change was reached, allowing Cassini to become the first spacecraft to orbit Saturn. This paper will discuss using accelerometers to improve performance by providing accurate measurements of applied ∆V . If knowledge of the initial state is accurate enough to determine a good plan, another key step is to accurately implement the plan. Considering the simple case of a single thruster pointing in the direction of motion, one option is to calculate the burn duration based on an idealized thruster model, and then execute