Formation control of a group of micro aerial vehicles (MAVs)

Coordinated motion of Unmanned Aerial Vehicles (UAVs) has been a growing research interest in the last decade. In this paper we propose a coordination model that makes use of virtual springs and dampers to generate reference trajectories for a group of quadrotors. Virtual forces exerted on each vehicle are produced by using projected distances between the quadrotors. Several coordinated task scenarios are presented and the performance of the proposed method is verified by simulations

Consensus optimization on manifolds

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO(n) and the Grassmann manifold Grass(p,n) are treated as original examples. A link is also drawn with the many existing results on the circle

Global phase-locking in finite populations of phase-coupled oscillators

We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.Comment: 31 pages; to appear in SIAM journal of dynamical systems (SIADS

Synchronization with partial state coupling on SO(n)

This paper studies autonomous synchronization of k agents whose states evolve on SO(n), but which are only coupled through the action of their states on one "reference vector" in Rn for each link. Thus each link conveys only partial state information at each time, and to reach synchronization agents must combine this information over time or throughout the network. A natural gradient coupling law for synchronization is proposed. Extensive convergence analysis of the coupled agents is provided, both for fixed and time-varying reference vectors. The case of SO(3) with fixed reference vectors is discussed in more detail. For comparison, we also treat the equivalent setting in Rn, i.e. with states in Rn and connected agents comparing scalar product of their states with a reference vector.Comment: to be submitted to SIAM Journal on Control and Optimizatio

Spatially-distributed coverage optimization and control with limited-range interactions

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.Comment: 31 pages, some figures left out because of size limits. Complete preprint version available at http://motion.csl.uiuc.ed