Centroidal Voronoi Configuration Research Articles

Optimized Dislocation of Mobile Sensor Networks on Large Marine Environments Using Voronoi Partitions

The real-time environmental surveillance of large areas requires the ability to dislocate sensor networks. Generally, the probability of the occurrence of a pollution event depends on the burden of possible sources operating in the areas to be monitored. This implies a challenge for devising optimal real-time dislocation of wireless sensor networks. This challenge involves both hardware solutions and algorithms optimizing the displacements of mobile sensor networks in large areas with a vast number of sources of pollutant factors based mainly on diffusion mechanisms. In this paper, we present theoretical and simulated results inherent to a Voronoi partition approach for the optimized dislocation of a set of mobile wireless sensors with circular (radial) sensing power on large areas. The optimal deployment was found to be a variation of the generalized centroidal Voronoi configuration, where the Voronoi configuration is event-driven, and the centroid set of the corresponding generalized Voronoi cells changes as a function of the pollution event. The initial localization of the pollution events is simulated with a Poisson distribution. Our results could improve the possibility of reducing the costs for real-time surveillance of large areas, and other environmental monitoring when wireless sensor networks are involved.

Model Predictive Coverage Control

Cooperative robotic problems often require coordination in space in order to complete a given task, important examples include search and rescue, operations in hazardous environments, and autonomous taxi deployment. Events can be quickly detected by partitioning the working environment and assigning one robot to each partition. However, a crucial factor that limits the effectiveness and usage of coverage algorithms is related to the ability of taking decisions in the presence of constraints. In this paper, we propose a coverage control algorithm that is capable of handling nonlinear dynamics, and state and input constraints. The proposed algorithm is based on a nonlinear tracking model predictive controller and is proven to converge to a centroidal Voronoi configuration. We also introduce a procedure to design the terminal ingredients of the model predictive controller. The effectiveness of the algorithm is then highlighted with a numerical simulation.

Centroidal Voronoi Partitioning using Virtual Nodes for MultiRobot Coverage

This paper addresses the problem of Voronoi partitioning using Centroidal Voronoi configuration for a multi-robotic coverage strategy known as Voronoi Partition based Coverage (VPC) algorithm. In VPC, the area to be covered is divided into Voronoi cells and each robot covers the corresponding cell. We use the concept of Centroidal Voronoi Configuration (CVC) to achieve a more uniform load distribution among the robots in terms of the area covered. Instead of the robots moving physically into the CVC, we introduce a concept of virtual nodes, which are deployed into CVC. Once the Voronoi partition is created based on the virtual nods, the robots cover the corresponding Voronoi cells. A gradient based control law has been used for deployment of the virtual nodes. Simulation results are provided to demonstrate the proposed deployment and partitioning scheme.

Optimal Deployment of Camera Mounted UAVs Performing Search

In this paper we address a problem of optimal deployment of camera mounted UAVs for a multi-robot search application. Here multiple UAVs carrying downward facing cameras are required to look for targets of interest in a search area. The lack of information about the presence or absence of targets is modeled as an uncertainty density distribution over the search area and this uncertainty is reduced as the information is gathered using the onboard cameras. The UAVs are required to get deployed so as to maximize the uncertainty reduction. We provide a model for search effectiveness of the camera and use it to formulate a strategy for optimal deployment of UAVs. It is shown that a centroidal Voronoi configuration, where each UAV (camera) is located at the centroid of the corresponding Voronoi cell is an optimal deployment. We provide simulation results to demonstrate that the proposed optimal deployment strategy successfully deploys the UAVs into centroidal Voronoi configuration, which maximizes the uncertainty reduction using cameras as search sensors.

Coverage Control of Unicycle Agents under Constant Speed Constraints

This paper studies the problem of optimal coverage control over a convex bounded region by a group of unicycle-type mobile agents with constant speeds. We further assume that the constant speeds for different agents may be non-identical. Thus, a unicycle is controlled solely via steering of its orientation in which a virtual centre is defined for each unicycle. A basic controller is proposed which asymptotically drive the virtual centres to a Centroidal Voronoi configuration, thus achieving the optimal coverage objective. At the Centroidal Voronoi configuration, each unicycle executes steady-state circular orbit about its virtual centre. To overcome a drawback of the basic controller that requires a careful selection of initial conditions, a modified switching controller is proposed which achieves a Centroidal Voronoi configuration for arbitrarily chosen initial conditions. Simulations for both the basic and modified controllers are presented for a five-unicycle group.

Distributed Receding Horizon Coverage Control for Multiple Mobile Robots

This paper presents a distributed coverage control scheme based on receding horizon control for the coordination of multiple mobile robots to cover an event. The mission space is modeled using a probability density function representing the probability of occurrence of events. The distributed scheme is generated by the decomposition of a single optimal coverage problem into distributed receding horizon coverage control problems, each of them associated with one robot. The distributed coverage scheme is proven to optimally stabilize robots at a centroidal Voronoi configuration, which is an optimal configuration to cover an event. The control scheme is tested in three simulation environments to illustrate its good performance at environments with any probability density function of events, as well as its ability to generalize to much larger groups of mobile robots.

Distributed Receding Horizon Coverage Control by Multiple Mobile Robots

This paper presents a distributed receding horizon coverage control algorithm to control a group of mobile robots having linear dynamics with the assumption that the robot dynamics are decoupled from each other. The objective of the coverage algorithm considered here is to maximize the detection of the occurrence of the events. First the authors introduce a centralized receding horizon coverage control and then they introduce a distributed version of it. To avoid the common disadvantages that are associated with the centralized approach, the problem is then decomposed into several RHCC problems, each associated with a particular robot, that are solved using distributed techniques. In order to solve each RHCC, each robot needs to know the trajectories of its neighbors during the optimization time interval. Since this information is not available, an algorithm is presented to estimate the trajectory of the neighboring robots. To minimize the estimation error, a compatibility constraint, which is also a key requirement in the closed-loop stability analysis, is considered. Moreover, the proof of the close-loop stability of this distributed version is provided and shows that the location of the robots will indeed converge to the centroids of a Voronoi partition. Simulation results validate the algorithm and the convergence of the robots to the centroidal Voronoi configuration.

Heterogeneous locational optimisation using a generalised Voronoi partition

In this paper a generalisation of the Voronoi partition is used for locational optimisation of facilities having different service capabilities and limited range or reach. The facilities can be stationary, such as base stations in a cellular network, hospitals, schools, etc., or mobile units, such as multiple unmanned aerial vehicles, automated guided vehicles, etc., carrying sensors, or mobile units carrying relief personnel and materials. An objective function for optimal deployment of the facilities is formulated, and its critical points are determined. The locally optimal deployment is shown to be a generalised centroidal Voronoi configuration in which the facilities are located at the centroids of the corresponding generalised Voronoi cells. The problem is formulated for more general mobile facilities, and formal results on the stability, convergence and spatial distribution of the proposed control laws responsible for the motion of the agents carrying facilities, under some constraints on the agents’ speed and limit on the sensor range, are provided. The theoretical results are supported with illustrative simulation results.

Performance of a class of multi-robot deploy and search strategies based on centroidal voronoi configurations

This article considers a class of deploy and search strategies for multi-robot systems and evaluates their performance. The application framework used is deployment of a system of autonomous mobile robots equipped with required sensors in a search space to gather information. The lack of information about the search space is modelled as an uncertainty density distribution. The agents are deployed to maximise single-step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for sequential deploy and search (SDS) and combined deploy and search (CDS) strategies. Completeness results are provided for both search strategies. The deployment strategy is analysed in the presence of constraints on robot speed and limit on sensor range for the convergence of trajectories with corresponding control laws responsible for the motion of robots. SDS and CDS strategies are compared with standard greedy and random search strategies on the basis of time taken to achieve reduction in the uncertainty density below a desired level. The simulation experiments reveal several important issues related to the dependence of the relative performances of the search strategies on parameters such as the number of robots, speed of robots and their sensor range limits.

A robust-adaptive fuzzy coverage control for robotic swarms

In this paper, a decentralized adaptive control scheme for multi-robot coverage is proposed. This control method is designed based on centroidal Voronoi configuration integrated with robust adaptive fuzzy control techniques. We consider simple single integrator mobile robots used for covering dynamical environments, where an adaptive fuzzy logic system is used to approximate the unknown parts of control law. A robust coverage criterion is used to attenuate the adaptive fuzzy approximation error and measurement noises to a prescribed level. Therefore, the robots motion is forced to obey solutions of a coverage optimization problem. The advantages of the proposed controller can be listed as robustness to external disturbances, computation uncertainties, and measurement noises, while applicability on dynamical environments. A Lyapunov-function based proof is given of robust stability, i.e. convergence to the optimal positions with bounded error. Finally, simulation results are demonstrated for a swarm coverage problem simultaneous with tracking mobile intruders.

Distributed Receding Horizon Formation Control by Multiple Mobile Robots Using Voronoi-Based Coverage

This paper presents a formation control algorithm for controlling a group of mobile robots, based on distributed receding horizon coverage control. The objective of the formation algorithm is to control multiple mobile robots such that they are arranged in pre-determined geometric patterns. To achieve the desired pattern, centroidal Voronoi configuration concept is used. The convergence requires simultaneous updates for all robots, and exchange of control trajectories between all neighboring agents at each update. Simulations results validate the algorithm and show how the proposed coverage-based formation algorithm, leads the robots to converge to the desired formations.

Automated Multi-Agent Search Using Centroidal Voronoi Configuration

This paper addresses the problem of automated multiagent search in an unknown environment. Autonomous agents equipped with sensors carry out a search operation in a search space, where the uncertainty, or lack of information about the environment, is known a priori as an uncertainty density distribution function. The agents are deployed in the search space to maximize single step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for the proposed sequential deploy and search strategy. It is shown that with the proposed control law the agent trajectories converge in a globally asymptotic manner to the centroidal Voronoi configuration. Simulation experiments are provided to validate the strategy.