On Practical Nearest Sub-Trajectory Queries under the Fr\'echet Distance

We study the problem of sub-trajectory nearest-neighbor queries on polygonal curves under the continuous Fr\'echet distance. Given an $n$ vertex trajectory $P$ and an $m$ vertex query trajectory $Q$, we seek to report a vertex-aligned sub-trajectory $P'$ of $P$ that is closest to $Q$, i.e. $P'$ must start and end on contiguous vertices of $P$. Since in real data $P$ typically contains a very large number of vertices, we focus on answering queries, without restrictions on $P$ or $Q$, using only precomputed structures of ${\mathcal{O}}(n)$ size. We use three baseline algorithms from straightforward extensions of known work, however they have impractical performance on realistic inputs. Therefore, we propose a new Hierarchical Simplification Tree data structure and an adaptive clustering based query algorithm that efficiently explores relevant parts of $P$. The core of our query methods is a novel greedy-backtracking algorithm that solves the Fr\'echet decision problem using ${\cal O}(n+m)$ space and ${\cal O}(nm)$ time in the worst case. Experiments on real and synthetic data show that our heuristic effectively prunes the search space and greatly reduces computations compared to baseline approaches.Comment: Added journal referenc

PPQ-Trajectory : spatio-temporal quantization for querying in large trajectory repositories

We present PPQ-trajectory, a spatio-temporal quantization based solution for querying large dynamic trajectory data. PPQ-trajectory includes a partition-wise predictive quantizer (PPQ) that generates an error-bounded codebook with autocorrelation and spatial proximity-based partitions. The codebook is indexed to run approximate and exact spatio-temporal queries over compressed trajectories. PPQ-trajectory includes a coordinate quadtree coding for the codebook with support for exact queries. An incremental temporal partition-based index is utilised to avoid full reconstruction of trajectories during queries. An extensive set of experimental results for spatio-temporal queries on real trajectory datasets is presented. PPQ-trajectory shows significant improvements over the alternatives with respect to several performance measures, including the accuracy of results when the summary is used directly to provide approximate query results, the spatial deviation with which spatio-temporal path queries can be answered when the summary is used as an index, and the time taken to construct the summary. Superior results on the quality of the summary and the compression ratio are also demonstrated

Safe human-robot interaction based on dynamic sphere-swept line bounding volumes

This paper presents a geometric representation for human operators and robotic manipulators, which cooperate in the development of flexible tasks. The main goal of this representation is the implementation of real-time proximity queries, which are used by safety strategies for avoiding dangerous collisions between humans and robotic manipulators. This representation is composed of a set of bounding volumes based on swept-sphere line primitives, which encapsulate their links more precisely than previous sphere-based models. The radius of each bounding volume does not only represent the size of the encapsulated link, but it also includes an estimation of its motion. The radii of these dynamic bounding volumes are obtained from an algorithm which computes the linear velocity of each link. This algorithm has been implemented for the development of a safety strategy in a real human–robot interaction task.This work is funded by the Spanish Ministry of Education and the Spanish Ministry of Science and Innovation through the projects DPI2005-06222 and DPI2008-02647 and the grant AP2005-1458

Efficient Configuration Space Construction and Optimization for Motion Planning

The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this paper, we survey some of our recent work on solving two important challenges related to configuration spaces