Equitable persistent coverage of non-convex environments with graph-based planning

In this article, we tackle the problem of persistently covering a complex non-convex environment with a team of robots. We consider scenarios where the coverage quality of the environment deteriorates with time, requiring every point to be constantly revisited. As a first step, our solution finds a partition of the environment where the amount of work for each robot, weighted by the importance of each point, is equal. This is achieved using a power diagram and finding an equitable partition through a provably correct distributed control law on the power weights. Compared with other existing partitioning methods, our solution considers a continuous environment formulation with non-convex obstacles. In the second step, each robot computes a graph that gathers sweep-like paths and covers its entire partition. At each planning time, the coverage error at the graph vertices is assigned as weights of the corresponding edges. Then, our solution is capable of efficiently finding the optimal open coverage path through the graph with respect to the coverage error per distance traversed. Simulation and experimental results are presented to support our proposal

Equitable Persistent Coverage of Non-Convex Environments with Graph-Based Planning

In this paper we tackle the problem of persistently covering a complex non-convex environment with a team of robots. We consider scenarios where the coverage quality of the environment deteriorates with time, requiring to constantly revisit every point. As a first step, our solution finds a partition of the environment where the amount of work for each robot, weighted by the importance of each point, is equal. This is achieved using a power diagram and finding an equitable partition through a provably correct distributed control law on the power weights. Compared to other existing partitioning methods, our solution considers a continuous environment formulation with non-convex obstacles. In the second step, each robot computes a graph that gathers sweep-like paths and covers its entire partition. At each planning time, the coverage error at the graph vertices is assigned as weights of the corresponding edges. Then, our solution is capable of efficiently finding the optimal open coverage path through the graph with respect to the coverage error per distance traversed. Simulation and experimental results are presented to support our proposal.Comment: This is the accepted version an already published manuscript. See journal reference for detail

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel

This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP). This intersection, once mapped, will then be used as a boundary within which a path will be planned for coverage to build a map of the Bathymetry. Methods for sequential updates to GP's are described allowing online fitting, prediction and hyper-parameter optimisation on a small embedded PC. New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage. These algorithms are tested both in simulation and in the field with a small twin hull differential thrust vessel built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field Robotic

Pattern Matching for sets of segments

In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and measures that relate to collections of orthogonal line segments in the plane. Such collections arise naturally from problems in mapping buildings and robot exploration. We propose a new measure of segment similarity called a \emph{coverage measure}, and present efficient algorithms for maximising this measure between sets of axis-parallel segments under translations. Our algorithms run in time O(n^3\polylog n) in the general case, and run in time O(n^2\polylog n) for the case when all segments are horizontal. In addition, we show that when restricted to translations that are only vertical, the Hausdorff distance between two sets of horizontal segments can be computed in time roughly O(n^{3/2}{\sl polylog}n). These algorithms form significant improvements over the general algorithm of Chew et al. that takes time $O(n^4 \log^2 n)$. In the second part of this paper we address the problem of matching polygonal chains. We study the well known \Frd, and present the first algorithm for computing the \Frd under general translations. Our methods also yield algorithms for computing a generalization of the \Fr distance, and we also present a simple approximation algorithm for the \Frd that runs in time O(n^2\polylog n).Comment: To appear in the 12 ACM Symposium on Discrete Algorithms, Jan 200