Centroidal area-constrained partitioning for robotic networks

We consider the problem of optimal coverage with area constraints in a mobile multi-agent system. For a planar environment with an associated density function, this problem is equivalent to dividing the environment into optimal subregions such that each agent is responsible for the coverage of its own region. In this paper, we design a continuous-time distributed policy which allows a team of agents to achieve a convex area-constrained partition of a convex workspace. Our work is related to the classic Lloyd algorithm, and makes use of generalized Voronoi diagrams. We also discuss practical implementation for real mobile networks. Simulation methods are presented and discussed

Stochastic Sensor Scheduling via Distributed Convex Optimization

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last versio

Problem of uniform deployment on a line segment for second-order agents

Consideration was given to a special problem of controlling a formation of mobile agents, that of uniform deployment of several identical agents on a segment of the straight line. For the case of agents obeying the first-order dynamic model, this problem seems to be first formulated in 1997 by I.A. Wagner and A.M. Bruckstein as "row straightening." In the present paper, the straightening algorithm was generalized to a more interesting case where the agent dynamics obeys second-order differential equations or, stated differently, it is the agent's acceleration (or the force applied to it) that is the control

DARP: Divide Areas Algorithm for Optimal Multi-Robot Coverage Path Planning

This paper deals with the path planning problem of a team of mobile robots, in order to cover an area of interest, with prior-defined obstacles. For the single robot case, also known as single robot coverage path planning (CPP), an (n) optimal methodology has already been proposed and evaluated in the literature, where n is the grid size. The majority of existing algorithms for the multi-robot case (mCPP), utilize the aforementioned algorithm. Due to the complexity, however, of the mCPP, the best the existing mCPP algorithms can perform is at most 16 times the optimal solution, in terms of time needed for the robot team to accomplish the coverage task, while the time required for calculating the solution is polynomial. In the present paper, we propose a new algorithm which converges to the optimal solution, at least in cases where one exists. The proposed technique transforms the original integer programming problem (mCPP) into several single-robot problems (CPP), the solutions of which constitute the optimal mCPP solution, alleviating the original mCPP explosive combinatorial complexity. Although it is not possible to analytically derive bounds regarding the complexity of the proposed algorithm, extensive numerical analysis indicates that the complexity is bounded by polynomial curves for practically sized inputs. In the heart of the proposed approach lies the DARP algorithm, which divides the terrain into a number of equal areas each corresponding to a specific robot, so as to guarantee complete coverage, non-backtracking solution, minimum coverage path, while at the same time does not need any preparatory stage (video demonstration and standalone application are available on-line http://tinyurl.com/DARP-app)

Distributed Deployment Strategies for Improved Coverage in a Network of Mobile Sensors With Prioritized Sensing Field

Efficient deployment strategies are proposed for a mobile sensor network, where the coverage priority of different points in the field is specified by a given function. The multiplicatively weighted Voronoi (MW-Voronoi) diagram is utilized to find the coverage holes of the network for the case where the sensing ranges of different sensors are not the same. Under the proposed strategies, each sensor detects coverage holes within its MW-Voronoi region, and then moves in a proper direction to reduce their size. Since the coverage priority of the field is not uniform, the target location of each sensor is determined based on the weights of the vertices or the points inside the corresponding MW-Voronoi region. Simulations validate the theoretical results

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations

Cooperative Coverage Control of Multi-Agent Systems

In this dissertation, motion coordination strategies are proposed for multiple mobile agents over an environment. It is desired to perform surveillance and coverage of a given area using a Voronoi-based locational optimization framework. Efficient control laws are developed for the coordination of a group of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with double-integrator and non-holonomic dynamics. The autonomous vehicles aim to spread out over the environment while more focus is directed towards areas of higher interest. It is assumed that the so-called ``operation costs'' of different agents are not the same. The center multiplicatively-weighted Voronoi configuration is introduced, which is shown to be the optimal configuration for agents. A distributed control strategy is also provided which guarantees the convergence of the agents to this optimal configuration. To improve the cooperation performance and ensure safety in the presence of inter-agent communication delays, a spatial partition is used which takes the information about the delay into consideration to divide the field. The problem is also extended to the case when the sensing effectiveness of every agent varies during the mission, and a novel partition is proposed to address this variation of the problem. To avoid obstacles as well as collision between agents in the underlying coverage control problem, a distributed navigation-function-based controller is developed. The field is partitioned to the Voronoi cells first, and the agents are relocated under the proposed controller such that a pre-specified cost function is minimized while collision and obstacle avoidance is guaranteed. The coverage problem in uncertain environments is also investigated, where a number of search vehicles are deployed to explore the environment. Finally, the effectiveness of all proposed algorithms in this study is demonstrated by simulations and experiments on a real testbed