Distributed Formation Maneuver Control of Multiagent Systems Over Directed Graphs

Abstract

This paper studies the problem of integrated distributed network localization and formation maneuver control. We develop an integrated relative-measurement-based scheme, which only uses relative positions, distances, bearings, angles, ratio-of-distances, or their combination to achieve distributed network localization and formation maneuver control in R d (d ≥ 2). By exploring the localizability and invariance of the target formation, the scale, rotation, and translation of the formation can be controlled simultaneously by only tuning the leaders' positions, i.e., the followers do not need to know parameters of the scale, rotation, and translation of the target formation. The proposed method can globally drive the formation errors to zero in finite time over multi-layer d+1-rooted graphs. A simulation example is given to illustrate the theoretical results.

Distributed observer based event‐triggered affine formation maneuver control for underactuated surface vessels with positive minimum inter‐event times

“…Obviously, the above relation also holds in cases when one of ‖ ‖ e p,i ‖ ‖ is equal to zero or both ‖ ‖ e 𝜂,i ‖ ‖ = 0, ‖ ‖ e v,i ‖ ‖ = 0. Recalling (23), the following relation can be derived:…”

“…. Furthermore, according to relations (23), we can infer that the observation errors z1f and z2f are all bounded to the residual set…”

“…17,18 Under the methodology of containment maneuver control, the follower group can converge to the convex hull spanned by multiple leaders, such that the number of planned reference trajectories can be reduced. Apart from these results, recently, tremendous theories involving bearing based methods, [19][20][21] displacement based methods, 22,23 complex Laplacians, 24 and stress matrices 25,26 have been developed by academic communities to address the network localizability for multiagent systems under the formation maneuver transformation. Based on the invariance of the stress matrix to any affine transformations of the target formation, a new concept of affine formation maneuver control was further developed by Zhao, 27 making stress matrix based methods become a powerful tool for general formation maneuvering.…”

Stabilizing and Maneuvering Angle Rigid Multiagent Formations With Double-Integrator Agent Dynamics

“…The inequalities in Assumption 1 is used to guarantee the single-integrator angle rigid formation locally stable [18,Theorem 8]. Compared to [21], [24], the construction of angle rigid formations is based on the Type-II vertex addition operation [18,Definition 7], under which the inter-agent communication is avoided in the control design and the number of constraints is minimized.…”

“…(2) For the formation stabilization control law, only local velocity and direction measurements are needed. Compared to the stabilization of double-integrator formations using relative position measurements [21], [22], no distance measurements are required in our formation stabilization control law. For the formation maneuvering law, in addition to the measurements mentioned in the stabilization case, we require only one agent, to measure its relative position with respect to a reference agent.…”