Direction-only Distributed Formation Control and Pose Localization in Multi-Agent Systems

Abstract

A fundamental task in distributed algorithms over networked multi-agent systems (MASs), including distributed control and estimation, is designing local interaction rules and control protocols for the individual agents so that the system achieves a system-level objective. This thesis studies three problems in networked systems, namely, distributed formation control based on orientation estimation, network pose localization and control using direction-only measurements, and discrete-time matrix-weighted consensus.

In the first part, we first present distributed algorithms to estimate the global orientations of the agents' local coordinate frames using relative orientations between the agents, with asymptotic, finite-time, and fixed-time stability properties, respectively. Based on the orientation estimation, various distributed coordination control schemes are then proposed for achieving the desired formation and formation maneuvering of multiple mobile agents. Direction-only formation control protocols are also presented for infinitesimal bearing rigid networks to stabilize the desired formation in finite-time and fixed time, respectively.

The second part explores a network pose localization strategy based exclusively on direction measurements between the agents in twin-leader follower networks in $\mb{R}^3$. In particular, we propose position and orientation localization algorithms, implemented through differential equations, which simultaneously compute poses of all followers by using locally measured directional vectors and angular velocities, and actual pose knowledge of some leader agents. Direction-only network orientation alignment law is also presented for a type of two-leader follower networks with only inter-agent direction measurements and direction measurements to some landmarks of the first two agents. Under the proposed alignment scheme, the orientations of the agents converge asymptotically (and semi-globally exponentially fast) to a constant unknown orientation.

In the last part, we investigate discrete-time consensus of multi-agent networks over undirected and connected graphs, whose edges are weighted by non-negative definite matrices, under various scenarios. If the network has symmetric matrix-weights, we show that a consensus is achieved if the agents' step sizes are sufficiently small and the interaction graph has a positive spanning tree. When the network graph is time-varying, joint connectedness condition of the network graph is sufficient for the agents to reach a consensus. In a special case of consensus with non-symmetric matrix weights, under certain conditions, the agents are shown to achieve a consensus.