Trajectory Planning Under Time-Constrained Communication

In the present paper we address the problem of trajectory planning for scenarios in which some robot has to exchange information with other moving robots for at least a certain time, determined by the amount of information. We are particularly focused on scenarios where a team of robots must be deployed, reaching some locations to make observations of the environment. The information gathered by all the robots must be shared with an operation center (OP), thus some robots are devoted to retransmit to the OP the data of their teammates. We develop a trajectory planning method called Time-Constrained RRT (TC-RRT). It computes trajectories to reach the assigned primary goals, but subjected to the constraint determined by the need of communicating with another robot acting as moving relay, just during the time it takes to fulfill the data exchange. Against other methods in the literature, using this method it is not needed a task allocator to assign beforehand specific meeting points or areas for communication exchange, because the planner finds the best area to do it, simultaneously minimizing the time to reach the goal. Evaluation and limitations of the technique are presented for different system parameters

Optimal Consensus set for nD Fixed Width Annulus Fitting

International audienceThis paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. We present an algorithm, that provides the optimal solution(s) within a time complexity O(N n+1 log N) for dimension n, N being the number of points. Our algorithm guarantees optimal solution(s) and has lower complexity than previous known methods

Reconstructing point set order types from radial orderings

We consider the problem of reconstructing the combinatorial structure of a set of n points in the plane given partial information on the relative position of the points. This partial information consists of the radial ordering, for each of the n points, of the n – 1 other points around it. We show that this information is sufficient to reconstruct the chirotope, or labeled order type, of the point set, provided its convex hull has size at least four. Otherwise, we show that there can be as many as n – 1 distinct chirotopes that are compatible with the partial information, and this bound is tight. Our proofs yield polynomial-time reconstruction algorithms. These results provide additional theoretical insights on previously studied problems related to robot navigation and visibility-based reconstruction.SCOPUS: ar.kSCOPUS: ar.jinfo:eu-repo/semantics/publishe

Stabbing segments with rectilinear objects

We consider stabbing regions for a set S of n line segments in the plane, that is, regions in the plane that contain exactly one endpoint of each segment of S. Concretely, we provide efficient algorithms for reporting all combinatorially different stabbing regions for S for regions that can be described as the intersection of axis-parallel halfplanes; these are halfplanes, strips, quadrants, 3-sided rectangles, and rectangles. The running times are O(n) (for the halfplane case), O(n log n) (for strips, quadrants, and 3-sided rectangles), and O(n2 log n) (for rectangles)

Stabbing Circles for Sets of Segments in the Plane

Stabbing a set S of n segments in the plane by a line is a well-known problem. In this paper we consider the variation where the stabbing object is a circle instead of a line. We show that the problem is tightly connected to cluster Voronoi diagrams, in particular, the Hausdorff and the farthest-color Voronoi diagram. Based on these diagrams, we provide a method to compute all the combinatorially different stabbing circles for S, and the stabbing circles with maximum and minimum radius. We give conditions under which our method is fast. These conditions are satisfied if the segments in S are parallel, resulting in a Onlog2n) time algorithm. We also observe that the stabbing circle problem for S can be solved in optimal O(n2) time and space by reducing the problem to computing the stabbing planes for a set of segments in 3D.Postprint (published version