Doctor of Philosophy (PhD)


Department of Mechanical & Industrial Engineering

Document Type



In this study, we tackle two well-known problems in distance-based formation control of multi-agent systems. The first problem – flip ambiguities – occurs due to the existence of multiple equilibrium points in the closed-loop inter-agent distance dynamics. We first introduce a simple solution for avoiding such ambiguities in 2D formations that are sequentially grown via triangulations. The proposed control system consists of a low-level control law in the form of the standard distance-based controller and a high-level switching scheme that steers the formation to the region of attraction of the desired formation. The control system ensures convergence to the desired formation for all initial conditions, except for the collocated and collinear cases. Experimental results are presented to demonstrate the formation control in action. Next, we show how the same switched control approach can be extended to avoid ambiguities in 3D formations comprised of tetrahedra. Here, the allowable initial conditions also exclude coplanar cases. Simulations are used to demonstrate that the proposed formation control system can lead to faster formation acquisition and less control effort than a recently proposed formation controller. We then address the flip ambiguity issue in 2D with a formation controller based on minimally globally rigid graphs. The method involves embedding the 2D formation in 3D and introducing virtual 3D body coordinates frames for the agents. For an N-agent system, we show that by translating N − 3 virtual frames along the z-axis (perpendicular to the formation plane), the rigidity matrix has full row rank. As a result, a typical Lyapunov stability analysis can be used to prove exponential convergence to the desired formation shape for all generic initial positions as well as when N − 3 agents are initially collocated or collinear. An experiment is included to show the benefit of using distancex based formation control with minimally globally rigid graphs over the standard minimally rigid graph case. The second problem is avoiding static obstacles while a group of nonholonomic mobile agents maneuvers in an unknown 2D environment. We merge the distance-based formation controller with the so-called vector field histogram method such that the agents temporarily separate into subsets of the full formation for obstacle avoidance purposes, thus facilitating subsequent reassembly. The overall control system is decentralized, since it only requires on-board sensors for inter-robot relative positioning and obstacle detection. We illustrate the proposed control via simulations for two typical obstacle avoidance scenarios.



Committee Chair

de Queiroz, Marcio.

Available for download on Saturday, March 27, 2027