6,913 research outputs found

    A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles

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    Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side-by-side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices

    Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation

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    We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of Bernstein et al. (2000). We do the same with curvature-constrained shortest paths and their distances, establishing what we believe are the first approximation bounds for them

    Visual Monitoring for Multiple Points of Interest on a 2.5D Terrain using a UAV with Limited Field-of-View Constraint

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    Varying terrain conditions and limited field-of-view restricts the visibility of aerial robots while performing visual monitoring operations. In this paper, we study the multi-point monitoring problem on a 2.5D terrain using an unmanned aerial vehicle (UAV) with limited camera field-of-view. This problem is NP-Hard and hence we develop a two phase strategy to compute an approximate tour for the UAV. In the first phase, visibility regions on the flight plane are determined for each point of interest. In the second phase, a tour for the UAV to visit each visibility region is computed by casting the problem as an instance of the Traveling Salesman Problem with Neighbourhoods (TSPN). We design a constant-factor approximation algorithm for the TSPN instance. Further, we reduce the TSPN instance to an instance of the Generalized Traveling Salesman Problem (GTSP) and devise an ILP formulation to solve it. We present a comparative evaluation of solutions computed using a branch-and-cut implementation and an off-the-shelf GTSP tool -- GLNS, while varying the points of interest density, sampling resolution and camera field-of-view. We also show results from preliminary field experiments

    Reachability by Paths of Bounded Curvature in a Convex Polygon

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    Let BB be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let PP be a convex polygon with nn vertices. Given a starting configuration (a location and a direction of travel) for BB inside PP, we characterize the region of all points of PP that can be reached by BB, and show that it has complexity O(n)O(n). We give an O(n2)O(n^2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment

    The traveling salesman problem for lines and rays in the plane

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    In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of nn regions (neighborhoods) and we seek a shortest tour that visits each region. In the path variant, we seek a shortest path that visits each region. We present several linear-time approximation algorithms with improved ratios for these problems for two cases of neighborhoods that are (infinite) lines, and respectively, (half-infinite) rays. Along the way we derive a tight bound on the minimum perimeter of a rectangle enclosing an open curve of length LL.Comment: 10 pages, 5 figure

    On Optimal Polyline Simplification using the Hausdorff and Fr\'echet Distance

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    We revisit the classical polygonal line simplification problem and study it using the Hausdorff distance and Fr\'echet distance. Interestingly, no previous authors studied line simplification under these measures in its pure form, namely: for a given ε\varepsilon > 0, choose a minimum size subsequence of the vertices of the input such that the Hausdorff or Fr\'echet distance between the input and output polylines is at most ε\varepsilon. We analyze how the well-known Douglas-Peucker and Imai-Iri simplification algorithms perform compared to the optimum possible, also in the situation where the algorithms are given a considerably larger error threshold than ε\varepsilon. Furthermore, we show that computing an optimal simplification using the undirected Hausdorff distance is NP-hard. The same holds when using the directed Hausdorff distance from the input to the output polyline, whereas the reverse can be computed in polynomial time. Finally, to compute the optimal simplification from a polygonal line consisting of nn vertices under the Fr\'echet distance, we give an O(kn5)O(kn^5) time algorithm that requires O(kn2)O(kn^2) space, where kk is the output complexity of the simplification.Comment: Full version of the SoCG2018 pape

    SU(2) graph invariants, Regge actions and polytopes

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    We revisit the the large spin asymptotics of 15j symbols in terms of cosines of the 4d Euclidean Regge action, as derived by Barrett and collaborators using a saddle point approximation. We bring it closer to the perspective of area-angle Regge calculus and twisted geometries, and compute explicitly the Hessian and phase offsets. We then extend it to more general SU(2) graph invariants, showing that saddle points still exist and have a similar structure. For graphs dual to 4d polytopes we find again two distinct saddle points leading to a cosine asymptotic formula, however a conformal shape-mismatch is allowed by these configurations, and the asymptotic action is thus a generalisation of the Regge action. The allowed mismatch correspond to angle-matched twisted geometries, 3d polyhedral tessellations with adjacent faces matching areas and 2d angles, but not their diagonals. We study these geometries, identify the relevant subsets corresponding to 3d Regge data and flat polytope data, and discuss the corresponding Regge actions emerging in the asymptotics. Finally, we also provide the first numerical confirmation of the large spin asymptotics of the 15j symbol. We show that the agreement is accurate to the per cent level already at spins of order 10, and the next-to-leading order oscillates with the same frequency and same global phase.Comment: v2: Section added on the implications of our results for spin foam models of quantum gravity, few amendments, references updated. 36 pages, many figures and many footnotes v3: Comparison with more recent work added at the end of the conclusion

    On Triangluar Separation of Bichromatic Point Sets in Polygonal Environment

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    Let P\mathcal P be a simple polygonal environment with kk vertices in the plane. Assume that a set BB of bb blue points and a set RR of rr red points are distributed in P\mathcal P. We study the problem of computing triangles that separate the sets BB and RR, and fall in P\mathcal P. We call these triangles \emph{inscribed triangular separators}. We propose an output-sensitive algorithm to solve this problem in O(r(r+cB+k)+h)O(r \cdot (r+c_B+k)+h_\triangle) time, where cBc_B is the size of convex hull of BB, and hh_\triangle is the number of inscribed triangular separators. We also study the case where there does not exist any inscribed triangular separators. This may happen due to the tight distribution of red points around convex hull of BB while no red points are inside this hull. In this case we focus to compute a triangle that separates most of the blue points from the red points. We refer to these triangles as \emph{maximum triangular separators}. Assuming n=r+bn=r+b, we design a constant-factor approximation algorithm to compute such a separator in O(n4/3log3n)O(n^{4/3} \log^3 n) time. "Eligible for best student paper

    SLAM-Assisted Coverage Path Planning for Indoor LiDAR Mapping Systems

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    Applications involving autonomous navigation and planning of mobile agents can benefit greatly by employing online Simultaneous Localization and Mapping (SLAM) techniques, however, their proper implementation still warrants an efficient amalgamation with any offline path planning method that may be used for the particular application. In this paper, such a case of amalgamation is considered for a LiDAR-based indoor mapping system which presents itself as a 2D coverage path planning problem implemented along with online SLAM. This paper shows how classic offline Coverage Path Planning (CPP) can be altered for use with online SLAM by proposing two modifications: (i) performing convex decomposition of the polygonal coverage area to allow for an arbitrary choice of an initial point while still tracing the shortest coverage path and (ii) using a new approach to stitch together the different cells within the polygonal area to form a continuous coverage path. Furthermore, an alteration to the SLAM operation to suit the coverage path planning strategy is also made that evaluates navigation errors in terms of an area coverage cost function. The implementation results show how the combination of the two modified offline and online planning strategies allow for an improvement in the total area coverage by the mapping system - the modification thus presents an approach for modifying offline and online navigation strategies for robust operation

    Minimum Opaque Covers for Polygonal Regions

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    The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is the problem of finding, for a set S in Euclidean space, the minimum-length set F which intersects every straight line passing through S. In spite of its simplicity, the problem remains remarkably intractable. The aim of this paper is to establish a framework and fundamental results for minimum opaque covers where S is a polygonal region in two-dimensional space. We begin by giving some general results about opaque covers, and describe the close connection that the OCP has with the Point Goalie Problem. We then consider properties of graphical solutions to the OCP when S is a convex polygonal region in the plane
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