Doctor of Philosophy (PhD)
Mechanical & Industrial Engineering
This research is devoted to the decentralized formation control of multi-agent systems in two- and three-dimensional space. Rigid graph theory is used to describe the interactions between the agents, and Lyapunov theory and input-to-state stability are the main tools for designing and analyzing the stability of the proposed formation controllers. Two formation problems are addressed in this work: formation acquisition, where the goal is for the agents to form and maintain a pre-defined geometric shape; and formation maneuvering, where the agents need to acquire a formation and move cohesively as a virtual rigid body.
In the first problem, we tackle the more challenging problem where the formation is dynamic, which is motivated by applications where the formation size and/or geometric shape needs to vary in time. We propose a control law that exponentially stabilizes the origin of the inter-agent distance error dynamics and ensures tracking of the desired, 3D time-varying formation. The control is first designed for the single-integrator agent model and then extended to the double-integrator model. We also show how the control for the single-integrator model can be augmented with an extra term to allow the dynamic formation to translate in space.
In the second problem, we consider that the maneuver can consist of full rigid-body motions (translation and rotation). We use the leader-follower concept and assign the leader agent to be in the convex hull of the formation shape to serve as the reference point for the swarm rotation. We design a controller that ensures the exponential stability of the inter-agent distance error while tracking the desired rigid-body motion of the formation. This control law is restricted to the single integrator model.
Whereas the first two problems use undirected graphs to model the agent interactions, in the third problem, we address the directed graph case. Directed graphs reduce the number of communication, sensing, and/or control channels of the multi-agent system. By exploiting the stability of interconnected systems, we show that the directed version of the common gradient descent control law asymptotically stabilizes the inter-agent distance error dynamics of minimally persistent formation graphs. The stability analysis begins with a (possibly cyclic) primitive formation that is grown consecutively by Henneberg-type insertions, resulting at each step in two interconnected nonlinear systems.
Computer simulations and experiments on wheeled mobile robot platform are presented throughout the dissertation to demonstrate the proposed control laws in action.
Zhang, Pengpeng, "Formation Control of Multi-Agent Systems by Using Rigid Graphs" (2018). LSU Doctoral Dissertations. 4559.
de Queiroz, Marcio
Available for download on Wednesday, April 02, 2025