Ryan K. Williams

Constrained Interaction and Coordination in Proximity-Limited Multiagent Systems

In this paper, we consider the problem of controlling the interactions of a group of mobile agents, subject to a set of topological constraints. Assuming proximity-limited interagent communication, we leverage mobility, unlike prior work, to enable adjacent agents to interact discriminatively, i.e., to actively retain or reject communication links on the basis of constraint satisfaction. Specifically, we propose a distributed scheme that consists of hybrid controllers with discrete switching for link discrimination, coupled with attractive and repulsive potentials fields for mobility control, where constraint violation predicates form the basis for discernment. We analyze the application of constrained interaction to two canonical coordination objectives, i.e., aggregation and dispersion, with maximum and minimum node degree constraints, respectively. For each task, we propose predicates and control potentials, and examine the dynamical properties of the resulting hybrid systems. Simulation results demonstrate the correctness of our proposed methods and the ability of our framework to generate topology-aware coordinated behavior.

Route Swarm: Wireless Network Optimization through Mobility

In this paper, we demonstrate a novel hybrid architecture for coordinating networked robots in sensing and information routing applications. The proposed INformation and Sensing driven PhysIcally REconfigurable robotic network (INSPIRE), consists of a Physical Control Plane (PCP) which commands agent position, and an Information Control Plane (ICP) which regulates information flow towards communication/sensing objectives. We describe an instantiation where a mobile robotic network is dynamically reconfigured to ensure high quality routes between static wireless nodes, which act as source/destination pairs for information flow. We demonstrate our propositions through simulation under a realistic wireless network regime.

Evaluating Network Rigidity in Realistic Systems: Decentralization, Asynchronicity, and Parallelization

In this paper, we consider the problem of evaluating the rigidity of a planar network, while satisfying common objectives of real-world systems: decentralization, asynchronicity, and parallelization. The implications that rigidity has in fundamental multirobot problems, e.g., guaranteed formation stability and relative localizability, motivates this study. We propose the decentralization of the pebble game algorithm of Jacobs et al. , which is an O(n2) method that determines the generic rigidity of a planar network. Our decentralization is based on asynchronous messaging and distributed memory, coupled with auctions for electing leaders to arbitrate rigidity evaluation. Further, we provide a parallelization that takes inspiration from gossip algorithms to yield significantly reduced execution time and messaging. An analysis of the correctness, finite termination, and complexity is given, along with a simulated application in decentralized rigidity control. Finally, we provide Monte Carlo analysis in a Contiki networking environment, illustrating the real-world applicability of our methods, and yielding a bridge between rigidity theory and realistic interacting systems.

Distributed combinatorial rigidity control in multi-agent networks

In this paper, we propose a distributed control law to maintain the combinatorial rigidity of a multi-agent system in the plane, when interaction is proximity-limited. Motivated by the generic properties of rigidity as a function of the underlying network graph, local link addition and deletion rules are proposed that preserve combinatorial rigidity through agent mobility. Specifically, redundancy of network links over local sub-graphs allows the determination of topological transitions that preserve rigidity. It is shown that local redundancy of a network link is sufficient for global redundancy, and thus applying minimal communication, and computation that scales like O(n2), the generic topological rigidity of a network can be preserved.

Probabilistic spatial mapping and curve tracking in distributed multi-agent systems

In this paper we consider a probabilistic method for mapping a spatial process over a distributed multi-agent system and a coordinated level curve tracking algorithm for adaptive sampling. As opposed to assuming the independence of spatial features (e.g. an occupancy grid model), we adopt a novel model of spatial dependence based on the grid-structured Markov random field that exploits spatial structure to enhance mapping. The multi-agent Markov random field framework is utilized to distribute the model over the system and to decompose the problem of global inference into local belief propagation problems coupled with neighbor-wise inter-agent message passing. A Lyapunov stable control law for tracking level curves in the plane is derived and a method of gradient and Hessian estimation is presented for applying the control in a probabilistic map of the process. Simulation results over a real-world dataset with the goal of mapping a plume-like oceanographic process demonstrate the efficacy of the proposed algorithms. Scalability and complexity results suggest the feasibility of the approach in realistic multi-agent deployments.

Locally constrained connectivity control in mobile robot networks

In this paper, we consider the problem of controlling the connectivity of a network of mobile agents under local topology constraints and proximity-limited communication. The inverse iteration algorithm for spectral analysis is formulated in a distributed manner to allow each agent to estimate a component of global network connectivity, improving on the convergence rate issues of previous approaches. Potential-based controls drive the agents to maximize connectivity under local degree constraints, maintain established links to guarantee connectivity, and avoid collisions. To achieve constraint satisfaction we exploit a switched model of interaction that regulates link addition through symmetric, repulsive potentials between constraint violators, enforcing discernment in communication through spatial organization. Simulations of connectivity estimation as well as agent aggregation and leader-following applications demonstrate the ability of our proposed methods to generate connectivity maximizing, constraint-aware self organization.

Global connectivity control for spatially interacting multi-robot systems with unicycle kinematics

In this paper, we consider the problem of connectivity maintenance in multi-robot systems with unicycle kinematics. While previous work has approached this problem through local control techniques, we propose a solution which achieves global connectivity maintenance under nonholonomic constraints. In addition, our formulation only requires intermittent estimation of algebraic connectivity, and accommodates discontinuous spatial interactions among robots. Specifically, we extend a decision-based link maintenance framework to unicycle kinematics and discontinuous potential-based interaction, by exploiting techniques from nonsmooth analysis. Then, we couple this extension with an existing connectivity estimation technique which yields an estimate with tunable precision in finite time, achieving our result. To illustrate the correctness of our methods, we provide a brief simulation result that closes the paper.

Topology-constrained flocking in locally interacting mobile networks

In this paper, we consider the problem of controlling a network of locally interacting mobile agents, subject to a set of non-local topology constraints, towards a group flocking objective. As opposed to switching network links directly in the space of discrete graphs, yielding a divide in spatial configuration and communication topology, we regulate topology through mobility, enabling adjacent agents to retain or deny links spatially on the basis of constraint satisfaction. Specifically, we propose a distributed formulation consisting of a switching control and smooth potential fields for local link discrimination and flocking, coupled with consensus-based coordination over proposed topology changes, yielding transitions in communication that respect non-local constraints and correspond to agent configuration. An analysis of the interplay between the topology consensus and constraint composition, together with a Lyapunov-like convergence argument guarantees the flocking, collision avoidance, and constraint satisfaction properties of the system. Finally, simulations of a novel constrained coordination scenario highlight the correctness and applicability of our proposed methods.

Decentralized generic rigidity evaluation in interconnected systems

In this paper, we consider the problem of evaluating the generic rigidity of an interconnected system in the plane, without a priori knowledge of the networks topological properties. We propose the decentralization of the pebble game algorithm of Jacobs et. al., an O(n2) method that determines the generic rigidity of a planar network. Our decentralization is based on asynchronous inter-agent message-passing and a distributed memory architecture, coupled with consensus-based auctions for electing leaders in the system. We provide analysis of the asynchronous messaging structure and its interaction with leader election, and Monte Carlo simulations demonstrating complexity and correctness. Finally, a novel rigidity evaluation and control scenario in the accompanying media illustrates the applicability of our proposed algorithm.

Decentralized matroid optimization for topology constraints in multi-robot allocation problems

In this paper, we demonstrate how topological constraints, as well as other abstract constraints, can be integrated into task allocation by applying the combinatorial theory of matroids. By modeling problems as an intersection of matroid constraints, arbitrary combinatorial relationships can be achieved in the task allocation space. To illustrate the expressiveness of the framework, we model a novel task allocation problem that couples abstract per-robot constraints with a communication spanning tree constraint. As our problem is cast as a matroid intersection, provable optimality bounds with simple greedy algorithms follows immediately from theory. Next, we present a decentralized algorithm that applies auction methods to task allocation with matroid intersections. Simulations of task allocation for surveillance in urban environments demonstrate our results. Finally, Monte Carlo results are provided that indicate greedy task allocations can be highly competitive even with near-optimal solutions in practice.