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In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called [alpha]-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or [alpha]-agents, and virtual agents associated with [alpha]-agents called [beta]- and [gamma]-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms. Index Terms--Consensus theory, distributed control, dynamic graphs, mobile sensor networks, networked autonomous vehicles, self-assembly of networks, self-organizing systems, swarms.

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results. Index Terms--Algebraic graph theory, consensus problems, digraph theory, graph Laplacians, networks of autonomous agents, networks with time-delays, switching systems.

Trajectory tracking and configuration stabilization for the vertical takeoff and landing (VTOL) aircraft has been so far considered in the literature only in the presence of a slight (or zero) input coupling (i.e., for a small [epsilon]). In this note, our main contribution is to address global configuration stabilization for the VTOL aircraft with a strong input coupling using a smooth static state feedback. In addition, the differentially flat outputs for the VTOL aircraft are automatically obtained as a by-product of applying a decoupling change of coordinates. Index Terms--Autonomous vehicles, backstepping, differential flatness, global stabilization, nonlinear control.

In this note, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms include three classes of cascade systems, namely, nonlinear systems in strict feedback form, feedforward form, and nontriangular quadratic form (to be defined). In each case, the transformation to cascade systems is provided in closed-form. We apply our results to the Acrobot, the Rotating Pendulum, and the Cart-Pole system. Index Terms--Cascade systems, nonlinear control, normal forms, symmetry, underactuated systems.