This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.
Motivated by current challenges in data-intensive sensor networks, we formulate a coverage optimization problem for mobile visual sensors as a (constrained) repeated multi-player game. Each visual sensor tries to optimize its own coverage while minimizing the processing cost. We present two distributed learning algorithms where each sensor only remembers its own utility values and actions played during the last plays. These algorithms are proven to be convergent in probability to the set of (constrained) Nash equilibria and global optima of certain coverage performance metric, respectively.
This paper presents a distributed multi-layer ring barrier coverage algorithm. In order to achieve single-layer ring barrier coverage, a distributed single-layer ring barrier coverage algorithm that maximises the probability of monitoring is proposed. Considering the security risks of single-layer barrier coverage, a distributed adjustment mechanism between multiple layers of barriers is designed and combined with the single-layer ring barrier coverage algorithm to propose a distributed multi-layer ring barrier coverage algorithm. Furthermore, we present a theoretical analysis of the proposed …
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns. In this paper, a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified. For these systems global stability results hold if the "secant" criterion is satisfied. In the linear case, it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic Lya…
This paper addresses the sweep coverage problem of multi-agent systems in uncertain regions. A new formulation of distributed sweep coverage is proposed to cooperatively complete the workload in the uncertain region. Specifically, each agent takes part in partitioning the whole region while sweeping its own subregion. In addition, the partition operation is carried out to balance the workload in subregions. The trajectories of partition points of agents form the boundaries between adjacent sub-regions. Moreover, it is proved that multi-agent system with the proposed control algorithm is input-…
This paper addresses the coverage control problem of multi-agent systems in the uncertain environment. With the aid of Voronoi partition, a distributed coverage control formulation of multi-agent system is proposed to complete the workload in uncertain environments. Driven by the gradient of thermal field, each agent is able to move around for clearing the workload on its own subregion. Theoretical analysis is conducted to ensure the completion of workload in finite time. Finally, numerical simulations are carried out to demonstrate the effectiveness and advantages of the proposed coverage con…
We consider the class of spatially decaying systems, where the underlying dynamics are spatially decaying and the sensing and controls are spatially distributed. This class of systems arise in various applications where there is a notion of spatial distance with respect to which couplings between the subsystems can be quantified using a class of coupling weight functions. We exploit spatial decay property of the underlying dynamics of the system to introduce a class of sparsity and spatial localization measures for spatially distributed systems. We develop a new methodology based on concepts o…
We analyze a differential game with spatially distributed controls to study a multiregional transboundary pollution problem. The dynamics of the state variable (pollution stock) is defined by a two dimensional parabolic partial differential equation. The control variables (emissions) are spatially distributed variables. The model allows for a, possibly large, number of agents with predetermined geographical relationships. For a special functional form previously used in the literature of transboundary pollution dynamic games we analytically characterize the feedback Nash equilibrium. We show t…
We derive gain-tuning rules for the positive and negative spatial-feedback loops of a spatially-distributed filter to change the resolution of its spatial band-pass characteristic accordingly to a wavelet zoom, while preserving temporal stability. The filter design is inspired by the canonical spatial feedback structure of the primary visual cortex and is motivated by understanding attentional control of visual resolution. Besides biology, our control-theoretical design strategy is relevant for the development of neuromorphic multiresolution distributed sensors through the feedback interconnec…
It is always a challenging task to service sudden events in non-convex and uncertain environments, and multi-agent coverage control provides a powerful theoretical framework to investigate the deployment problem of mobile robotic networks for minimizing the cost of handling random events. Inspired by the divide-and-conquer methodology, this paper proposes a novel coverage formulation to control multi-agent systems in the non-convex region while equalizing the workload among subregions. Thereby, a distributed coverage controller is designed to drive each agent towards the desired configurations…
We extend modern Walrasian economics, and in particular the results on Cournot convergence and dynamics, by focusing on renewable resources in a spatial setting. Building on the harvesting model of Behringer and Upmann (2014) we endogenize prices and investigate the two cases of durable and non-durable renewable commodities. We find that endogenizing prices is sufficient to prevent the full exploitation result and look at how competition affects not only the stock but also the temporal incentives for exploitation. We derive convergence results in static and dynamic settings which suggest that …
A k-order coverage control problem is studied where a network of agents must deploy over a desired area. The objective is to deploy all the agents in a decentralized manner such that a certain coverage performance metric of the network is maximized. Unlike many prior works that consider multi-agent deployment, we explicitly consider applications where more than one agent may be required to service an event that randomly occurs anywhere in the domain. The proposed method ensures the distributed agents autonomously cover the area while simultaneously relaxing the requirement of constant communic…
IITB-Monash Research Academy（IITB-莫纳什研究学院）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；Monash University（莫纳什大学）
This paper is concerned with the deployment of multiple mobile robots in order to autonomously cover a region Q. The region to be covered is described using a density function which may not be apriori known. In this paper, we pose the coverage problem as an optimization problem over some space of functions on Q. In particular, we look at L 2 -distance based coverage algorithm and derive adaptive control laws for the same. We also propose a modified adaptive control law incorporating consensus for better parameter convergence. We implement the algorithms on real differential drive robots with b…
We use the continuation and bifurcation package pde2path to numerically analyze infinite time horizon optimal control problems for parabolic systems of PDEs. The basic idea is a two step approach to the canonical systems, derived from Pontryagin's maximum principle. First we find branches of steady or time-periodic states of the canonical systems, i.e., canonical steady states (CSS) respectively canonical periodic states (CPS), and then use these results to compute time-dependent canonical paths connecting to a CSS or a CPS with the so called saddle point property. This is a (high dimensional)…
This paper discusses the effect of sequential conflict resolution maneuvers of an infinite aircraft flow through a finite control volume. Aircraft flow models are utilized to simulate traffic flows and determine stability. Pseudo-random flow geometry is considered to determine airspace stability in a more random airspace, where aircraft flows are spread over a given positive width. The use of this aircraft flow model generates a more realistic flow geometry. A set of upper bounds on the maximal aircraft deviation during conflict resolution is derived. Also with this flow geometry it is proven …
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.
École Polytechnique de Montréal（蒙特利尔综合理工学院）；University of Pennsylvania（宾夕法尼亚大学）
This paper considers 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. Moreover, it is assumed that the event location distribution is a priori unknown, and can only be progressively inferred from the observation of the actual event occurrences. Three classes of problems are discussed in detail: coverage control problems, spatial partitioning problems, and dynamic vehicle routing problems. In each case, dis…
This paper re-visits a multi-agent deployment problem where agents are restricted from requesting information from other agents as well as sending acknowledgments when information is received. These communication constraints relax the assumptions of instantaneous communication and synchronous actions by agents (request and response actions). In this paper, we propose a fully asynchronous communication aware solution to the multi-agent deployment problem that uses an event-triggered broadcasting strategy. Unlike all existing triggered solutions, our event-triggered broadcasting algorithm relies…
We consider the problem of determining the optimal composition of a heterogeneous multi-agent team for coverage problems by including costs associated with different agents and subject to an upper bound on the maximal allowable number of agents. We formulate a resource allocation problem without introducing additional non-convexities to the original problem. We develop a distributed Projected Gradient Ascent (PGA) algorithm to solve the optimal team composition problem. To deal with non-convexity, we initialize the algorithm using a greedy method and exploit the submodularity and curvature pro…
p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at the numerical solution of optimal control (OC) problems with an infinite time horizon for parabolic systems of PDE over 1D or 2D spatial domains. The basic idea is to treat the OC problem via the associated canonical system in two steps. First we use pde2path to find branches of stationary solutions of the canonical system, also called canonical steady states (CSS). In a second step we use the results and the spatial discretization of the first step to calculate the objective values of time-dependent canonical paths endi…
