Distributed Algorithms for Stochastic Source Seeking With Mobile Robot Networks

Autonomous robot networks are an effective tool for monitoring large-scale environmental fields. This paper proposes distributed control strategies for localizing the source of a noisy signal, which could represent a physical quantity of interest such as magnetic force, heat, radio signal, or chemical concentration. We develop algorithms specific to two scenarios: one in which the sensors have a precise model of the signal formation process and one in which a signal model is not available. In the model-free scenario, a team of sensors is used to follow a stochastic gradient of the signal field. Our approach is distributed, robust to deformations in the group geometry, does not necessitate global localization, and is guaranteed to lead the sensors to a neighborhood of a local maximum of the field. In the model-based scenario, the sensors follow a stochastic gradient of the mutual information (MI) between their expected measurements and the expected source location in a distributed manner. The performance is demonstrated in simulation using a robot sensor network to localize the source of a wireless radio signal

Information Acquisition with Sensing Robots: Algorithms and Error Bounds

Utilizing the capabilities of configurable sensing systems requires addressing difficult information gathering problems. Near-optimal approaches exist for sensing systems without internal states. However, when it comes to optimizing the trajectories of mobile sensors the solutions are often greedy and rarely provide performance guarantees. Notably, under linear Gaussian assumptions, the problem becomes deterministic and can be solved off-line. Approaches based on submodularity have been applied by ignoring the sensor dynamics and greedily selecting informative locations in the environment. This paper presents a non-greedy algorithm with suboptimality guarantees, which does not rely on submodularity and takes the sensor dynamics into account. Our method performs provably better than the widely used greedy one. Coupled with linearization and model predictive control, it can be used to generate adaptive policies for mobile sensors with non-linear sensing models. Applications in gas concentration mapping and target tracking are presented.Comment: 9 pages (two-column); 2 figures; Manuscript submitted to the 2014 IEEE International Conference on Robotics and Automatio

Geometric Programming and Mechanism Design for Air Traffic Conflict Resolution

We develop certain extensions of optimization based conflict resolution methods in air traffic control. The problem considered concerns the scheduling of the crossing times of a set of aircraft through a metering fix, while maintaining aircraft separation. First, we show how to solve this combined path planning and scheduling problem using mixed integer geometric programming. Second, the objective function used to determine the aircraft ordering at the fix is not given a priori but needs to be obtained from the airlines, which are strategic profit maximizing agents and could lie about their true cost. In order to realign individual and global objectives, we study the use of the Clarke-Groves mechanism in this context, which aims at extracting the true utility functions from the airlines using side-payments to the FAA

Joint Metering and Conflict Resolution in Air Traffic Control

This paper describes a novel optimization-based approach to conflict resolution in air traffic control, based on geometric programming. The main advantage of the approach is that Geometric Programs (GPs) can also capture various metering directives issued by the traffic flow management level, in contrast to most recent methods focusing purely on aircraft separation issues. GPs can also account for some of the nonlinearities present in the formulations of conflict resolution problems, while incurring only a small penalty in computation time with respect to the fastest linear programming based approaches. Additional integer variables can be introduced to improve the quality of the obtained solutions and handle combinatorial choices, resulting in Mixed-Integer Geometric Programs (MIGPs). We present GPs and MIGPs to solve a variety of joint metering and separation scenarios, e.g. including miles-in-trail and minutes-in-trail restrictions through airspace fixes and boundaries. Simulation results demonstrate the efficiency of the approach

Adaptive Algorithms for Coverage Control and Space Partitioning in Mobile Robotic Networks

We consider deployment problems where a mobile robotic network must optimize its configuration in a distributed way in order to minimize a steady-state cost function that depends on the spatial distribution of certain probabilistic events of interest. Three classes of problems are discussed in detail: coverage control problems, spatial partitioning problems, and dynamic vehicle routing problems. Moreover, we assume that the event distribution is a priori unknown, and can only be progressively inferred from the observation of the location of the actual event occurrences. For each problem we present distributed stochastic gradient algorithms that optimize the performance objective. The stochastic gradient view simplifies and generalizes previously proposed solutions, and is applicable to new complex scenarios, for example adaptive coverage involving heterogeneous agents. Finally, our algorithms often take the form of simple distributed rules that could be implemented on resource-limited platforms

Adaptive Robot Deployment Algorithms

In robot deployment problems, the fundamental issue is to optimize a steady state performance measure that depends on the spatial configuration of a group of robots. For static deployment problems, a classical way of designing high- level feedback motion planners is to implement a gradient descent scheme on a suitably chosen objective function. This can lead to computationally expensive deployment algorithms that may not be adaptive to uncertain dynamic environments. We address this challenge by showing that algorithms for a variety of deployment scenarios in stochastic environments and with noisy sensor measurements can be designed as stochastic gradient descent algorithms, and their convergence properties analyzed via the theory of stochastic approximations. This approach yields often surprisingly simple algorithms that can accommodate complicated objective functions, and adapt to slow temporal variations in environmental parameters. To illustrate the richness of the framework, we discuss several applications, including searching for a field extrema, deployment with stochastic connectivity constraints, coverage, and vehicle routing scenarios

Large deviation principle at fixed time in Glauber evolutions

Abstract: We consider the evolution of an asymptotically decoupled probability measure ν on Ising spin configurations under a Glauber dynamics. We prove that for any t > 0, ν t is asymptotically decoupled and hence satisfies a large deviation principle with the relative entropy density as rate function

The Wireless Control Network: Synthesis and Robustness

We consider the problem of stabilizing a plant with a network of resource constrained wireless nodes. Traditional networked control schemes are designed with one of the nodes in the network acting as a dedicated controller, while the other nodes simply route information to and from the controller and the plant. We introduce the concept of a Wireless Control Network (WCN) where the entire network itself acts as the controller. Specifically, at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. We show that this causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We then provide a numerical design procedure to determine the appropriate linear combinations to be applied by each node so that the transmissions of the nodes closest to the actuators will stabilize the plant. We also show how our design procedure can be modified to maintain mean square stability under packet drops in the network