Amirreza Rahmani

Controllability of Multi-Agent Systems from a Graph-Theoretic Perspective

In this work, we consider the controlled agreement problem for multi-agent networks, where a collection of agents take on leader roles while the remaining agents execute local, consensus-like protocols. Our aim is to identify reflections of graph-theoretic notions on system-theoretic properties of such systems. In particular, we show how the symmetry structure of the network, characterized in terms of its automorphism group, directly relates to the controllability of the corresponding multi-agent system. Moreover, we introduce network equitable partitions as a means by which such controllability characterizations can be extended to the multileader setting.

On the controlled agreement problem

Our work examines the controlled agreement problem over a network of interconnected dynamic units. The agreement protocol has recently been a focus of a large number of research work in systems and control community. Most of the existing work in this area, however, consider the uncontrolled agreement protocol. In this work, we consider the controlled agreement problem and introduce algebraic and graph theoretic conditions for its controllability. We then proceed to provide a graphical interpretation of these controllability conditions. In addition, we explore the role of anchored vertex position in the information structure to improve the convergence properties of the controlled agreement protocol

Pulling the Strings on Agreement: Anchoring, Controllability, and Graph Automorphisms

This work examines the controlled Laplacian (or agreement) over a network of interconnected dynamic units. This dynamics has recently been the focus of a large number of research work in the systems community. Most of the existing work in this area- however- consider the unforced agreement protocol. In the present paper, we consider the controlled version of this dynamics and introduce graph theoretic conditions for its system theoretic properties. In particular, we show how the symmetry structure of the network, characterized in terms of its automorphism group, relates to the network controllability. Some of the ramifications of such a characterization are then explored.

Agreement via the edge laplacian

This work explores the properties of the edge variant of the graph Laplacian in the context of the edge agreement problem. We show that the edge Laplacian, and its corresponding agreement protocol, provide a useful perspective on the well-known node agreement, or the consensus problem. Specifically, the dynamics induced by the edge Laplacian facilitates a better understanding of the role played by certain subgraphs, e.g., cycles and spanning trees, in the original agreement problem. We also point out a reduced order modeling of the edge agreement as parameterized by the spanning trees of the underlying graph.

Optimal Approach to Halo Orbit Control

Three-dimensional orbits in the vicinity of the collinear libration points of the Sun-Earth/Moon barycenter system are currently being considered for use with a number of missions planed for 2000 and beyond. Since such libration point trajectories are, in general, unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. In this paper, circular restricted three body problem is reviewed and a numerical method to control spacecrafts on periodic halo orbits around L1 and L2 collinear points of the Sun-Earth/Moon barycenter system is investigated. The control approach is based on the optimal control theory and implements variation of extremals technique to solve the resulting two point boundary value problem. The reference trajectory, halo orbit, is supposed to be given in the form of the Fourier series.

Optimal Balanced-Energy Formation Flying Maneuvers

Spacecraft formation flying has recently been proposed and examined in the space systems community as a promising alternative to monolithic and often large space structures. Optimal balanced-energy control of such distributed space systems potentially increases their lifetime and can serve as an important baseline in mission feasibility studies. In this paper, an optimal balanced-energy control strategy for two- and three- spacecraft distributed space systems is proposed. Along the way, we will delineate relevant mission scenarios in deep space, as well as those that operate in Earths gravitational sphere of influence. Simulation results demonstrating the ramifications of our theoretical analysis are also provided.

Multiple UAV deconfliction via navigation functions

Unmanned aerial vehicles (UAVs) offer an unprecedented set of capabilities for many civilian and military missions, including those pertaining to surveillance, monitoring, and detection. In fact, as UAVs continue to become less expensive and easy to operate, they have also become more capable in executing complex mission objectives. In the meantime, the higher levels of maneuverability and dynamic capability for UAVs have necessitated the design of efficient algorithms for conflict resolution among them when operating in close proximity of each other. In this paper, we consider a variant of multiple UAV collision avoidance referred to as the Deconfliction problem. We then proceed to develop a multiple UAV deconfliction algorithm via appropriate navigationor potentialfunctions. The proposed method combines conflict prediction and resolution, navigation, and control of the unmanned flying vehicles while respecting specific mission requirements. Refinements of the basic control module synthesized from the navigation function approach, in terms of augmenting it with a “moving target” and velocity control, are also discussed. A representative set of simulation scenarios concludes the paper.

Decentralized formation control via the edge Laplacian

Formation keeping strategies for groups of interconnected agents have recently been of great research interest in the systems community. In this work, we explore the utility of the edge variant of the graph Laplacian in the synthesis of formation keeping control laws. Along the way, we show a general duality relation between networked dynamic systems with measurement restrictions and those with control constraints. In both cases, it is shown that the closed loop error dynamics for the formation reduces to the edge agreement problem- which in turn-can be fully characterized via the spanning trees of the underlying interconnection topology.

On the Optimal Balanced-Energy Formation Flying Maneuvers

Spacecraft formation flying has received an enor- mous amount of attention over the past few years as a promising alternative to monolithic- and often large- space structures. Balanced optimal energy control of such distributed space systems guarantees maximum lifetime for these missions and hence is of great importance in mission feasibility studies. In this paper, an optimal control strategy for two and three spacecraft distributed space systems that are commanded to attain new relative coordinates, is proposed, guaranteeing balanced energy consumption among the spacecraft. We will delineate on the relevant mission scenarios both in deep space as well as in close proximity to a gravitational force field as in Earths orbit. Index Terms— Formation flying, balanced energy reconfig- urations, optimal control

Multilevel Coalition Formation Strategy for Suppression of Enemy Air Defenses Missions

This paper investigates the problem of how to form coalitions in teams of heterogeneous vehicles. In particular, a coordination strategy is designed for unmanned vehicles to autonomously carry out the suppression of enemy air defenses (SEAD) mission, which would benefit from a heterogeneous network of unmanned vehicles to search and destroy threats in an unexplored area. Inspiration for this work is drawn from natural systems, and we consider the alliance-forming behavior of bottlenose dolphins as a guiding example. A two-phased approach is taken to develop the bioinspired strategy. First, in the context of multi-agent systems, a mathematical model is produced that expressively captures the alliance-forming behavior. Next, this model is tailored to the suppression of enemy air defenses mission: the target application. Advantages of using this bioinspired approach are discussed and simulations are provided to demonstrate its operation.