Edge State Kalman Filtering for Distributed Formation Control Systems

Abstract

Formation control problems consider a set of mobile agents with the underlying goal of attaining and maintaining a state where the relative positions of agents are stable in accordance with the desired configuration.
Navigation for formation control is typically achieved through localization in a global reference frame, e.g., via GNSS. However, when a global reference frame is not shared among agents, a relative navigation approach is required.
Distributed filtering for relative localization in formation control systems is a relatively unexplored field.
The absence of absolute positioning means motivates the need for a distributed filter that operates on the edges of the sensing graph of the multi-agent system.
In this thesis, a data model for relative formation control problems and two edge-based Kalman filters are proposed. The first filter is designed for an individual edge. The second is a filter designed via decoupling of the optimal global filter which allows for the joint estimation of adjacent edges. It is shown that the joint filter is optimal under the decoupling constraints.
Monte Carlo results show that when random environmental disturbances are correlated among agents, the joint filter outperforms the local edge filter in a mean square error sense.
Lastly, systems are considered where inter-agent communications are unavailable, leading to biased prediction steps of the Kalman filters. We aim to minimize this effect through the proposal of a local Wiener filter which predicts the control actions of neighboring agents.