[Paper Review] Higher order mobile coverage control with application to localization

Bomin Jiang, Zhiyong Sun+2 more|arXiv (Cornell University)|Mar 7, 2017

Distributed Control Multi-Agent Systems31 references3 citations

TL;DR

This paper proposes a distributed gradient-based control law for multi-agent mobile coverage using higher-order Voronoi partitions, where each region is monitored by multiple sensors. The method optimizes coverage performance by minimizing a function based on the maximum or sum of distances to multiple sensors, achieving local convergence and extending classical Lloyd algorithms to higher-order settings.

ABSTRACT

Most current results on coverage control using mobile sensors require that one partitioned cell is associated with precisely one sensor. In this paper, we consider a class of coverage control problems involving higher order Voronoi partitions, motivated by applications where more than one sensor is required to monitor and cover one cell. Such applications are frequent in scenarios requiring the sensors to localize targets. We introduce a framework depending on a coverage performance function incorporating higher order Voronoi cells and then design a gradient-based controller which allows the multi-sensor system to achieve a local equilibrium in a distributed manner. The convergence properties are studied and related to Lloyd algorithm. We study also the extension to coverage of a discrete set of points. In addition, we provide a number of real world scenarios where our framework can be applied. Simulation results are also provided to show the controller performance.

Motivation & Objective

• Address the lack of distributed control strategies for multi-sensor coverage where each region requires monitoring by more than one sensor.
• Formulate a coverage performance function based on higher-order Voronoi cells to model scenarios requiring cooperative sensing, such as target localization via triangulation.
• Design a distributed, gradient-based controller that enables mobile sensors to converge to a local equilibrium without centralized coordination.
• Extend classical Lloyd algorithm and k-means clustering to higher-order coverage problems, particularly for order-2 and higher-order cases.
• Demonstrate applicability to real-world problems such as bearing-only localization, time-difference-of-arrival, and bi-static radar deployment.

Proposed method

• Define a coverage performance function using higher-order Voronoi partitions, where each point in the region is associated with the k closest sensors.
• Introduce a performance metric based on the maximum distance from a target to its k nearest sensors, or a sum of such distances, to model sensing reliability.
• Derive a distributed gradient control law that updates each sensor’s position based on local information from neighboring sensors and the performance function.
• Establish convergence of the controller to a local equilibrium by relating the dynamics to a generalized Lloyd algorithm for higher-order partitions.
• Formulate the expected detection probability in bi-static radar systems as a function of sensor-to-target distances, and minimize the negative of this probability as the cost function.
• Generalize the k-means clustering framework to higher-order coverage by minimizing the sensor radius required for k-coverage of a region.

Experimental results

Research questions

• RQ1 How can a distributed control law be designed for mobile sensors to achieve optimal coverage when each region must be monitored by at least two or more sensors?
• RQ2 What is the relationship between the proposed higher-order coverage control and the classical Lloyd algorithm, and does it preserve convergence properties?
• RQ3 How can the performance of cooperative sensing systems—such as those using triangulation or time-difference-of-arrival—be modeled and optimized via higher-order Voronoi partitions?
• RQ4 What are the convergence characteristics of the gradient-based controller in higher-order coverage problems, and how do they compare to first-order coverage control?
• RQ5 Can the framework be extended to minimize the required sensor radius for k-coverage, and how does it relate to k-means clustering in higher-order settings?

Key findings

• The proposed distributed gradient controller converges to a local equilibrium in higher-order Voronoi-based coverage problems, extending the convergence properties of the classical Lloyd algorithm.
• The performance function based on the maximum distance to the k nearest sensors effectively models cooperative sensing reliability, particularly in bearing-only or time-difference-of-arrival localization scenarios.
• Simulation results demonstrate that the controller achieves stable and efficient coverage configurations, with convergence to a local minimum of the performance function.
• The framework successfully models bi-static radar deployment by minimizing the negative expected detection probability, showing that sensor placement can be optimized via gradient descent on a non-convex, non-smooth function.
• The paper establishes a formal connection between higher-order coverage control and generalized Lloyd maps, showing that the controller dynamics correspond to a descent on a higher-order energy function.
• The method generalizes k-means clustering to higher-order coverage by minimizing the required sensor radius to achieve k-coverage, providing a new perspective on distributed clustering in multi-agent systems.