Michael M. Zavlanos

Potential Fields for Maintaining Connectivity of Mobile Networks

The control of mobile networks of multiple agents raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In this paper, we consider the problem of controlling a network of agents so that the resulting motion always preserves the connectivity property of the network. In particular, the connectivity condition is translated to differentiable constraints on individual agent motion by considering the dynamics of the Laplacian matrix and its spectral properties. Artificial potential fields are then used to drive the agents to configurations away from the undesired space of disconnected networks while avoiding collisions with each other. We conclude by illustrating a class of interesting problems that can be achieved while preserving connectivity constraints.

Distributed Connectivity Control of Mobile Networks

Control of mobile networks raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In particular, in applications involving mobile sensor networks and multiagent systems, a great new challenge is the development of distributed motion algorithms that guarantee connectivity of the overall network. Motivated by the inherently discrete nature of graphs as combinatorial objects, we address this challenge using a key control decomposition. First, connectivity control of the network structure is performed in the discrete space of graphs and relies on local estimates of the network topology used, along with algebraic graph theory, to verify link deletions with respect to connectivity. Tie breaking, when multiple such link deletions can violate connectivity, is achieved by means of gossip algorithms and distributed market-based control. Second, motion control is performed in the continuous configuration space, where nearest-neighbor potential fields are used to maintain existing links in the network. Integration of the earlier controllers results in a distributed, multiagent, hybrid system, for which we show that the resulting motion always ensures connectivity of the network, while it reconfigures toward certain secondary objectives. Our approach can also account for communication time delays as well as collision avoidance and is illustrated in nontrivial computer simulations.

Graph-theoretic connectivity control of mobile robot networks

In this paper, we provide a theoretical framework for controlling graph connectivity in mobile robot networks. We discuss proximity-based communication models composed of disk-based or uniformly-fading-signal-strength communication links. A graph-theoretic definition of connectivity is provided, as well as an equivalent definition based on algebraic graph theory, which employs the adjacency and Laplacian matrices of the graph and their spectral properties. Based on these results, we discuss centralized and distributed algorithms to maintain, increase, and control connectivity in mobile robot networks. The various approaches discussed in this paper range from convex optimization and subgradient-descent algorithms, for the maximization of the algebraic connectivity of the network, to potential fields and hybrid systems that maintain communication links or control the network topology in a least restrictive manner. Common to these approaches is the use of mobility to control the topology of the underlying communication network. We discuss applications of connectivity control to multirobot rendezvous, flocking and formation control, where so far, network connectivity has been considered an assumption.

Flocking while preserving network connectivity

Coordinated motion of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as consensus seeking or flocking by a group of mobile agents, a great new challenge is the development of robust distributed motion algorithms that can always achieve the desired coordination. In this paper, we address this challenge by embedding the requirement for connectivity of the underlying communication network in the controller specifications. We employ double integrator models for the agents and design nearest neighbor control laws, based on potential fields, that serve a twofold objective. First, they contribute to velocity alignment in the system and second, they regulate switching among different network topologies so that the connectivity requirement is always met. Collision avoidance among neighboring agents is also ensured and under the assumption that the initial network is connected, the overall system is shown to asymptotically flock for all initial conditions. In particular, it is shown that flocking is achieved even in sparse communication networks where connectivity is more prone to failure. We conclude by illustrating a class of interesting problems that can be achieved while preserving connectivity.

Hybrid Control for Connectivity Preserving Flocking

In this technical note, we address the combined problem of motion and network topology control in a group of mobile agents with common objective the flocking behavior of the group. Instead of assuming network connectivity, we enforce it by means of distributed topology control that decides on both deletion and creation of communication links between agents, adapting the network to the groups spatial distribution. With this protocol ensuring network connectivity, a decentralized motion controller aligns agent velocity vectors and regulates inter-agent distances to maintain existing network links. The stability of the flocking controller is established in continuous time by means of an observability argument on a quadratic form of the graph Laplacian that exploits the time delay between link deletion and creation caused by the topology control protocol, which induces a dwell time between network switches.

Distributed multi-robot task assignment and formation control

Distributed task assignment for multiple agents raises fundamental and novel problems in control theory and robotics. A new challenge is the development of distributed algorithms that dynamically assign tasks to multiple agents, not relying on a priori assignment information. We address this challenge using market-based coordination protocols where the agents are able to bid for task assignment with the assumption that every agent has knowledge of the maximum number of agents that any given task can accommodate. We show that our approach always achieves the desired assignment of agents to tasks after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of discrete assignment problems. We verify our algorithm through both simulation and experimentation on a team of non-holonomic robots performing distributed formation stabilization and group splitting and merging.

Controlling Connectivity of Dynamic Graphs

The control of mobile networks of multiple agents raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In this paper, we consider the problem of controlling a network of agents so that the resulting motion always preserves various connectivity properties. In particular, we consider preserving k-hop connectivity, where agents are allowed to move while maintaining connections to agents that are no more than k-hops away. The connectivity constraint is translated to constrains on individual agent motion by considering the dynamics of the adjacency matrix and related constructs from algebraic graph theory. As special cases, we obtain motion constraints that can preserve the exact structure of the initial dynamic graph, or may simply preserve the usual notion connectivity while the structure of the graph changes over time. We conclude by illustrating various interesting problems that can be achieved while preserving connectivity constraints.

A distributed auction algorithm for the assignment problem

The assignment problem constitutes one of the fundamental problems in the context of linear programming. Besides its theoretical significance, its frequent appearance in the areas of distributed control and facility allocation, where the problems¿ size and the cost for global computation and information can be highly prohibitive, gives rise to the need for local solutions that dynamically assign distinct agents to distinct tasks, while maximizing the total assignment benefit. In this paper, we consider the linear assignment problem in the context of networked systems, where the main challenge is dealing with the lack of global information due to the limited communication capabilities of the agents. We address this challenge by means of a distributed auction algorithm, where the agents are able to bid for the task to which they wish to be assigned. The desired assignment relies on an appropriate selection of bids that determine the prices of the tasks and render them more or less attractive for the agents to bid for. Up to date pricing information, necessary for accurate bidding, can be obtained in a multi-hop fashion by means of local communication between adjacent agents. Our algorithm is an extension to the parallel auction algorithm proposed by Bertsekas et al to the case where only local information is available and it is shown to always converge to an assignment that maximizes the total assignment benefit within a linear approximation of the optimal one.

Distributed connectivity control of mobile networks

Control of mobile networks raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In particular, in applications involving mobile sensor networks and multi-agent systems, a great new challenge is the development of distributed motion algorithms that guarantee connectivity of the overall network. In this paper, we address this challenge using a novel control decomposition. First, motion control is performed in the continuous state space, where nearest neighbor potential fields are used to maintain existing links in the network. Second, distributed coordination protocols in the discrete graph space ensure connectivity of the switching network topology. Coordination is based on locally updated estimates of the abstract network topology by every agent as well as distributed auctions that enable tie breaking whenever simultaneous link deletions may violate connectivity. Integration of the overall system results in a distributed, multi- agent, hybrid system for which we show that, under certain secondary objectives on the agents and the assumption that the initial network is connected, the resulting motion always satisfies connectivity of the network. Our approach can also account for communication time delays in the network as well as collision avoidance, while its efficiency and scalability properties are illustrated in nontrivial computer simulations.

Dynamic Assignment in Distributed Motion Planning With Local Coordination

Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as coverage by mobile sensor networks or multiple target tracking, a great new challenge is the development of motion planning algorithms that dynamically assign targets or destinations to multiple homogeneous agents, not relying on any a priori assignment of agents to destinations. In this paper, we address this challenge using two novel ideas. First, distributed multidestination potential fields are developed that are able to drive every agent to any available destination. Second, nearest neighbor coordination protocols are developed ensuring that distinct agents are assigned to distinct destinations. Integration of the overall system results in a distributed, multiagent, hybrid system for which we show that the mutual exclusion property of the final assignment is guaranteed for almost all initial conditions. Furthermore, we show that our dynamic assignment algorithm will converge after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of purely discrete assignment problems. Our scalable approach is illustrated with nontrivial computer simulations.