Sensor-based robot deployment algorithms

Abstract — 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 such 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 algorithms that may not be adaptive to uncertain dynamic environments. We address these challenges by showing that algorithms for a variety of deployment scenarios in uncertain 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 work without a detailed model of the environment. To illustrate the richness of the framework, we discuss two applications, namely source seeking with realistic stochastic wireless connectivity constraints, and coverage with heterogeneous sensors. I

A Dynamic Game Model of Collective Choice in Multi-Agent Systems

Inspired by successful biological collective decision mechanisms such as honey bees searching for a new colony or the collective navigation of fish schools, we consider a mean field games (MFG)-like scenario where a large number of agents have to make a choice among a set of different potential target destinations. Each individual both influences and is influenced by the group's decision, as well as the mean trajectory of all the agents. The model can be interpreted as a stylized version of opinion crystallization in an election for example. The agents' biases are dictated first by their initial spatial position and, in a subsequent generalization of the model, by a combination of initial position and a priori individual preference. The agents have linear dynamics and are coupled through a modified form of quadratic cost. Fixed point based finite population equilibrium conditions are identified and associated existence conditions are established. In general multiple equilibria may exist and the agents need to know all initial conditions to compute them precisely. However, as the number of agents increases sufficiently, we show that 1) the computed fixed point equilibria qualify as epsilon Nash equilibria, 2) agents no longer require all initial conditions to compute the equilibria but rather can do so based on a representative probability distribution of these conditions now viewed as random variables. Numerical results are reported

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