Wireless Localization and Formation Control with Asynchronous Agents

The formation control of multi-agent systems has increasingly drawn attention for fulfilling numerous emerging applications and services. To achieve high-accuracy formation, the location awareness of all agents becomes an essential requirement. In this paper, we address the problem of network localization and formation control in a cooperative system with asynchronous agents. In particular, we formulate the joint localization and synchronization of agents as a statistical inference problem. The underlying probabilistic model is represented by a factor graph from which a message-passing algorithm is designed that computes approximations of the marginals of unknown variables, i.e. agents' locations and clock offsets. Due to the Euclidean-norm operator involved in their computation no parametric closed-form expressions of the messages exist. As a compromise, implemented message-passing methods therefore resort to approximations of these messages. Conventional methods rely either on a first-order Taylor expansion of the norm operation or on non-parametric representations, e.g. by means particle filters (PFs), to compute such approximations. However, the former approach suffers from poor performance while the latter one experiences high complexity. The proposed message-passing algorithm in this paper is parametric. Specifically, it passes Gaussian messages that can be essentially obtained by suitably augmenting the factor graph and applying on it a hybrid method for combining belief propagation and variational message passing. Subsequently, the agents can exploit the estimated locations for determining the control policy. Two types of control policy are designed based on the optimization of a generalized cost function. We show that the proposed scheme enjoys a reduced complexity for multi-agent localization while achieving the desired formation with excellent accuracy.