Formation State Estimation and Control

An integrated approach to Guidance, Navigation and Control (GNC) of formation flying spacecraft was developed under the project. The design process considers a 3-spacecraft mission in a reference Geostationary Transfer Orbit (GTO). A detailed definition of the mission framework, in terms of GNC modes and corresponding science and technology requirements, was provided by DEIMOS Engenharia. This, together with an analysis of the dynamic environment of the mission, establishes the inputs to the design of a low-thrust optimal relative configuration that minimises the fuel consumption and overall complexity.

The obtained solution is assessed in detail by means of an analysis considering perturbations acting over a spacecraft in Earth GTO. The GNC closed loop uses the results of the mission analysis and design process as specifications. An algebraic closed-loop algorithm is proposed for the Guidance and Control (GC) subsystem, minimizing the propellant consumption and ensuring collision avoidance. Using Pontryagin’s Maximum Principle, the GC algorithm provides the optimal trajectories from the current state until the target state, as well as the optimal control inputs to follow these trajectories.

From the navigation standpoint, a formation flying s/c fleet endowed with relative distance sensors and RF communications can be considered to have two underlying networks: a communication network, where linked s/c communicate state estimates, and a measurement network, linking each s/c to all the s/c it measures the relative distances to. In general, a s/c measures distances and communicates them to any of its fleetmates. Nevertheless, it is desirable to reduce the number of measurements and especially the number of links in the communication network. The concept proposed in this work is to have each s/c measuring locally the distance to another fleet s/c (as expressed in the fleet measurements network), and transmitting its updated state estimates to another s/c (as expressed in the fleet communications network). The measurement network concerns the RF measurements of the distance with respect to another s/c. The communication network concerns the communication between pairs of s/c, in order to send/receive the full state estimate between two spacecraft of the fleet. The state estimates are considered as observations in the receiving s/c.

The Navigation algorithm is based, at each s/c, on an Extended Kalman Filter (EKF) for local measurements, and on a Covariance Intersection (CI) algorithm (plus the EKF prediction part) for the measurements communicated by its linked s/c in the communications network. The CI algorithm avoids the possible divergence of the EKF at the receiving s/c, due to correlation between measurements of the s/c in the fleet, by computing an upper bound for the covariance matrix of the fused variables. The price to pay is reduced estimation accuracy. Therefore, in the filtering step, the EKF is used when observations are measurements from the sensors, and the CI algorithm is applied whenever the observations are the state vector estimates from a s/c linked by the communications network.