Visibility-based coverage of mobile sensors in non-convex domains

The area coverage problem of mobile sensor networks has attracted much attention recently, as mobile sensors find many important applications in remote and hostile environments. However, the deployment of mobile sensors in a non-convex domain is nontrivial due to the more general shape of the domain and the attenuation of sensing capabilities caused by the boundary walls or obstacles. We consider the problem of exploration and coverage by mobile sensors in an unknown non-convex domain. We propose the definition of 'visibility-based Voronoi diagram' and extend the continuous-time Lloyd's method, which only works for convex domains, to deploy the mobile sensors in the unknown environments in a distributed manner. Our simulations show the effectiveness of the proposed algorithms. © 2011 IEEE.published_or_final_versionThe 8th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD2011), Qingdao, China, 28-30 June 2011. In Proceedings of the 8th ISVD, 2011, p. 105-11

DisCoverage: From Coverage to Distributed Multi-Robot Exploration

DisCoverage transfers the well-known solution to the coverage problem to the exploration problem. Essentially, DisCoverage solves the multi-robot exploration problem through a spatially distributed optimization problem. Our contribution is a new objective function for DisCoverage based on the centroidal search. Each robot continuously creates and optimizes the proposed objective function, obtaining a gradient-based control law that leads into unexplored regions. A proof of convergence is given as well as a simulation and a statistical evaluation demonstrating DisCoverage

Curvature-Independent Last-Iterate Convergence for Games on Riemannian Manifolds

Numerous applications in machine learning and data analytics can be formulated as equilibrium computation over Riemannian manifolds. Despite the extensive investigation of their Euclidean counterparts, the performance of Riemannian gradient-based algorithms remain opaque and poorly understood. We revisit the original scheme of Riemannian gradient descent (RGD) and analyze it under a geodesic monotonicity assumption, which includes the well-studied geodesically convex-concave min-max optimization problem as a special case. Our main contribution is to show that, despite the phenomenon of distance distortion, the RGD scheme, with a step size that is agnostic to the manifold's curvature, achieves a curvature-independent and linear last-iterate convergence rate in the geodesically strongly monotone setting. To the best of our knowledge, the possibility of curvature-independent rates and/or last-iterate convergence in the Riemannian setting has not been considered before

Cooperative Multi Agent Search and Coverage in Uncertain Environments

In this dissertation, the cooperative multi agent search and coverage problem in uncertain environments is investigated. Each agent individually plans its desired trajectory. The agents exchange their positions and their sensors’ measurement with their neighbouring agents through a communication channel in order to maintain the cooperation objective. Different aspects of multi agent search and coverage problem are investigated. Several models for uncertain environments are proposed and the updating rules for the probability maps are provided. Each of this models is appropriate for a specific type of problems. The cooperative search mission is first converted to a decentralized multi agent optimal path planning problem, using rolling horizon dynamic programming approach which is a mid-level controller. To make cooperation between agents possible, two approximation methods are proposed to modify the objective function of agents and to take into the account the decision of other agents. The simulation results show the proposed methods can considerably increase the performance of mission without significantly increasing the computation burden. This approach is then extended for the case with known communication delay between mobile agents. The simulation results show the proposed methods can compensate for the effect of known communication delay between mobile agents. A Voronoi-based search strategy for a team of mobile agents with limited range sensors is also proposed which combines both mid-level and low-level controllers. The strategy includes the short-term objective of maximizing the uncertainty reduction in the next step, the long-term objective of distributing the agents in the environment with minimum overlap in their sensory domain, and the collision avoidance constraint. The simulation results show the proposed control law can reduce the value of uncertainty in the environment below any desired threshold. For the search and coverage problem, we first introduce a framework that includes two types of agents; search agents and coverage agents. The problem is formulated such that the information about the position of the targets is updated by the search agents. The coverage agents use this information to concentrate around the more important areas in the environment. The proposed cooperative search method, along with a well-known Centroidal Voronoi Configuration method for coverage, is used to solve the problem. The effectiveness of the proposed algorithm is demonstrated by simulation and experiment. We then introduce the “limited turn rate Voronoi diagram” and formulate the search and coverage problem as a multi-objective optimization problem with different constraints which is able to consider practical issues like minimum fuel consumption, refueling, obstacle avoidance, and collision avoidance. In this approach, there is only one type of agents which performs both search and coverage tasks. The “multi agent search and coverage problem” is formulated such that the “multi agent search problem” and “multi agent coverage problem” are special cases of this problem. The simulation results show the effectiveness of the proposed method

Multi-robot Coverage and Redeployment Algorithms

In this thesis, we focus on two classes of multi-robot task allocation and deployment problems motivated by applications in ride-sourcing transportation networks and service robots: 1) coverage control with multiple robots, and 2) robots servicing tasks arriving sequentially over time. The first problem considers the deployment of multiple robots to cover a domain. The multi-robot problem consists of multiple robots with sensors on-board observing the spatially distributed events in an environment. The objective is to maximize the sensing quality of the events via optimally distributing the robots in the environment. This problem has been studied extensively in the literature and several algorithms have been proposed for different variants of this problem. However, there has been a lack of theoretical results on the quality of the solutions provided by these algorithms. In this thesis, we provide a new distributed multi-robot coverage algorithm with theoretical guarantees on the solution quality, run-time complexity, and communication complexity. The theoretical bound on the solution quality holds for on-board sensors where the sensing quality of the sensors is a sub-additive function of the distance to the event location in convex and non-convex environments. A natural extension of the multi-robot coverage control problem is considered in this thesis where each robot is equipped with a set of different sensors and observes different event types in the environment. Servicing a task in this problem corresponds to sensing an event occurring at a particular location and does not involve visiting the task location. Each event type has a different distribution over the domain. The robots are heterogeneous in that each robot is capable of sensing a subset of the event types. The objective is to deploy the robots into the domain to maximize the total coverage of the multiple event types. We propose a new formulation for the heterogeneous coverage problem. We provide a simple distributed algorithm to maximize the coverage. Then, we extend the result to the case where the event distribution is unknown before the deployment and provide a distributed algorithm and prove the convergence of the approach to a locally optimal solution. The third problem considers the deployment of a set of autonomous robots to efficiently service tasks that arrive sequentially in an environment over time. Each task is serviced when a robot visits the corresponding task location. Robots can then redeploy while waiting for the next task to arrive. The objective is to redeploy the robots taking into account the next N task arrivals. We seek to minimize a linear combination of the expected cost to service tasks and the redeployment cost between task arrivals. In the single robot case, we propose a one-stage greedy algorithm and prove its optimality. For multiple robots, the problem is NP-hard, and we propose two constant-factor approximation algorithms, one for the problem with a horizon of two task arrivals and the other for the infinite horizon when the redeployment cost is weighted more heavily than the service cost. Finally, we extend the second problem to scenarios where the robots are self-interested service units maximizing their payoff. The payoff of a robot is a linear combination of its relocation cost and its expected revenue from servicing the tasks in its vicinity. In this extension, the global objective is either to minimize the expected time or minimize the maximum time to respond to the tasks. We introduce two indirect control methods to relocate the self-interested service units: 1) an information sharing method, and 2) a method that incentivizes relocation with payments. We prove NP-hardness of finding the optimal controls and provide algorithms to find the near-optimal control. We quantify the performance of the proposed algorithms with analytical upper-bounds and real-world data from ride-sourcing applications