Sonia Martínez

Coverage control for mobile sensing networks

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks, where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions

This paper presents coordination algorithms for networks of mobile autonomous agents. The objective of the proposed algorithms is to achieve rendezvous, that is, agreement over the location of the agents in the network. We provide analysis and design results for multiagent networks in arbitrary dimensions under weak requirements on the switching and failing communication topology. The novel correctness proof relies on proximity graphs and their properties and on a general LaSalle invariance principle for nondeterministic discrete-time dynamical systems

Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms

This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms.Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises.Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation

Optimal sensor placement and motion coordination for target tracking

This work studies optimal sensor placement and motion coordination strategies for mobile sensor networks. For a target-tracking application with range sensors, we investigate the determinant of the Fisher Information Matrix and compute it in the 2D and 3D cases, characterizing the global minima in the 2D case. We propose motion coordination algorithms that steer the mobile sensor network to an optimal deployment and that are amenable to a decentralized implementation. Finally, our numerical simulations illustrate how the proposed algorithms lead to improved performance of an extended Kalman filter in a target-tracking scenario.

Motion Coordination with Distributed Information

Motion coordination is a remarkable phenomenon in biological systems and an extremely useful tool for groups of vehicles, mobile sensors, and embedded robotic systems. For many applications, teams of mobile autonomous agents need the ability to deploy over a region, assume a specified pattern, rendezvous at a common point, or move in a synchronized manner. The objective of this article is to illustrate the use of systems theory to analyze emergent behaviors in animal groups and to design autonomous and reliable robotic networks. We present and survey some recently developed theoretical tools for modeling, analysis, and design of motion coordination algorithms in both continuous and discrete time. We pay special attention to the distributed character of coordination algorithms, the characterization of their performance, and the development of design methodologies that provide mobile networks with provably correct cooperative strategies.

On Distributed Convex Optimization Under Inequality and Equality Constraints

We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorithms based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian and penalty functions. These algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slaters condition.

Storage Size Determination for Grid-Connected Photovoltaic Systems

In this paper, we study the problem of determining the size of battery storage used in grid-connected photovoltaic (PV) systems. In our setting, electricity is generated from PV and is used to supply the demand from loads. Excess electricity generated from the PV can be either sold back to the grid or stored in a battery, and electricity must be purchased from the electric grid if the PV generation and battery discharging cannot meet the demand. Due to the time-of-use electricity pricing and net metered PV systems, electricity can also be purchased from the grid when the price is low, and be sold back to the grid when the price is high. The objective is to minimize the cost associated with net power purchase from the electric grid and the battery capacity loss while at the same time satisfying the load and reducing the peak electricity purchase from the grid. Essentially, the objective function depends on the chosen battery size. We want to find a unique critical value (denoted as Crefc ) of the battery size such that the total cost remains the same if the battery size is larger than or equal to Crefc, and the cost is strictly larger if the battery size is smaller than Crefc. We obtain a criterion for evaluating the economic value of batteries compared to purchasing electricity from the grid, propose lower and upper bounds on Crefc, and introduce an efficient algorithm for calculating its value; these results are validated via simulations.

Brief paper: Discrete-time dynamic average consensus

We propose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set of reference inputs is that the maximum relative deviation between the nth-order differences of any two reference inputs be bounded for some integer n>=1.

Monitoring Environmental Boundaries With a Robotic Sensor Network

In this brief, we propose and analyze an algorithm to monitor an environmental boundary with mobile agents. The objective is to optimally approximate the boundary with a polygon. The mobile sensors rely only on sensed local information to position some interpolation points and define an approximating polygon. We design an algorithm that distributes the vertices of the approximating polygon uniformly along the boundary. The notion of uniform placement relies on a metric inspired by approximation theory for convex bodies. The algorithm is provably convergent for static boundaries and efficient for slowly-moving boundaries because of certain input-to-state stability properties.

Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithms correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.