Distance-Based Formation Control of Multi-Agent Systems

This Ph.D. dissertation studies the distance-based formation control of multi-agent systems. A new approach to the distance-based formation control problem is proposed in this thesis. We formulated distance-based formation in a nonlinear optimal control framework and used the state-dependent Riccati equation (SDRE) technique as the primary tool for solving the optimal control problem. In general, a distance-based formation can be undirected, where distance constraints between pairs of agents are actively controlled by both adjacent agents, or directed, where just one of the neighboring agents is responsible for maintaining the desired distance. This thesis presents both, undirected and directed formations, and provides extensive simulations to verify the theoretical results. For undirected topologies, we studied the formation control problem where we showed that the proposed control law results in the global asymptotic stability of the closed-loop system under certain conditions. The formation tracking problem was studied, and the uniform ultimate boundedness of the solutions is rigorously proven. The proposed method guarantees collision avoidance among neighboring agents and prevents depletion of the agents' energy. In the directed distance-based formation control case, we developed a distributed, hierarchical control scheme for a particular class of directed graphs, namely directed triangulated and trilateral Laman graphs. The proposed controller ensures the global asymptotic stability of the desired formation. Rigorous stability analyses are carried out in all cases. Moreover, we addressed the flip-ambiguity issue by using the signed area and signed volume constraints. Additionally, we introduced a performance index for a formation mission that can indicate the controller's overall performance. We also studied the distance-based formation control of nonlinear agents. We proposed a method that can guarantee asymptotic stability of the distance-based formation for a broad category of nonlinear systems. Furthermore, we studied a distance-based formation control of uncertain nonlinear agents. Based on the combination of integral sliding mode control (ISMC) theory with the SDRE method, we developed a robust optimal formation control scheme that guarantees asymptotic stability of the desired distance-based formation in the presence of bounded uncertainties. We have shown that the proposed controller can compensate for the effect of uncertainties in individual agents on the overall formation

Geometry of discrete and continuous bounded surfaces

We work on reconstructing discrete and continuous surfaces with boundaries using length constraints. First, for a bounded discrete surface, we discuss the rigidity and number of embeddings in three-dimensional space, modulo rigid transformations, for given real edge lengths. Our work mainly considers the maximal number of embeddings of rigid graphs in three-dimensional space for specific geometries (annulus, strip). We modify a commonly used semi-algebraic, geometrical formulation using Bézout\u27s theorem, from Euclidean distances corresponding to edge lengths. We suggest a simple way to construct a rigid graph having a finite upper bound. We also implement a generalization of counting embeddings for graphs by segmenting multiple rigid graphs in d-dimensional space. Our computational methodology uses vector and matrix operations and can work best with a relatively small number of points

Bearing rigidity theory and its applications for control and estimation of network systems: Life beyond distance rigidity

Distributed control and location estimation of multiagent systems have received tremendous research attention in recent years because of their potential across many application domains [1], [2]. The term agent can represent a sensor, autonomous vehicle, or any general dynamical system. Multiagent systems are attractive because of their robustness against system failure, ability to adapt to dynamic and uncertain environments, and economic advantages compared to the implementation of more expensive monolithic systems

Decentralized Formation Control with A Quadratic Lyapunov Function

In this paper, we investigate a decentralized formation control algorithm for an undirected formation control model. Unlike other formation control problems where only the shape of a configuration counts, we emphasize here also its Euclidean embedding. By following this decentralized formation control law, the agents will converge to certain equilibrium of the control system. In particular, we show that there is a quadratic Lyapunov function associated with the formation control system whose unique local (global) minimum point is the target configuration. In view of the fact that there exist multiple equilibria (in fact, a continuum of equilibria) of the formation control system, and hence there are solutions of the system which converge to some equilibria other than the target configuration, we apply simulated annealing, as a heuristic method, to the formation control law to fix this problem. Simulation results show that sample paths of the modified stochastic system approach the target configuration