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Service robots need to show appropriate social behaviour in order to be deployed in social environments such as healthcare, education, retail, etc. Some of the main capabilities that robots should have are navigation and conversational skills. If the person is impatient, the person might want a robot to navigate faster and vice versa. Linguistic features that indicate politeness can provide social cues about a person's patient and impatient behaviour. The novelty presented in this paper is to dynamically incorporate politeness in robotic dialogue systems for navigation. Understanding the politeness in users' speech can be used to modulate the robot behaviour and responses. Therefore, we developed a dialogue system to navigate in an indoor environment, which produces different robot behaviours and responses based on users' intention and degree of politeness. We deploy and test our system with the Pepper robot that adapts to the changes in user's politeness., Comment: Proceedings of ICSR 2018

We study the characterisation of efficient and non-efficient families of Grover's algorithms according to the majorization principle. We develop a geometrical interpretation based on the parameters that appears on these algorithms. Using this interpretation we observe a step-by-step majorization in all efficient Grover's algorithms, whereas the non-efficient Grover's algorithms fail to abide by this majorization principle. These Majorization results are first obtained from numerical calculations. Motivated by these numerical results, we also obtained an analytical demonstration. Finally, the geometrical interpretation found for these parameters is used to obtain additional results of Grover's algorithms that improves our understanding of how they work., Comment: 10 pages, 17 figures

Understanding driving situations regardless the conditions of the traffic scene is a cornerstone on the path towards autonomous vehicles; however, despite common sensor setups already include complementary devices such as LiDAR or radar, most of the research on perception systems has traditionally focused on computer vision. We present a LiDAR-based 3D object detection pipeline entailing three stages. First, laser information is projected into a novel cell encoding for bird's eye view projection. Later, both object location on the plane and its heading are estimated through a convolutional neural network originally designed for image processing. Finally, 3D oriented detections are computed in a post-processing phase. Experiments on KITTI dataset show that the proposed framework achieves state-of-the-art results among comparable methods. Further tests with different LiDAR sensors in real scenarios assess the multi-device capabilities of the approach., Comment: Submittied to IEEE International Conference on Intelligent Transportation Systems 2018 (ITSC)

This paper establishes connections between the group-Fourier transform and the geometry of measures in the Heisenberg group. Firstly, it is shown that if the Fourier transform of a compactly supported, finite, Radon measure is square integrable, then the measure must have a square integrable density. If it's Fourier transform is integrable, the the measure must have a continuous density. In addition, an alternative formulation of the Fourier transform on the Heisenberg group is used to show that energies of measures can be computed via integrals on an appropriate frequency space. This in turns opens the possibility of using Fourier methods in the computation of Hausdorff dimension of sets.

Weighted fractional Poincar\'e-type inequalities are proved on John domains whenever the weights defined on the domain are depending on the distance to the boundary and to an arbitrary compact set in the boundary of the domain.

We classify closed, simply-connected cohomogeneity-one Alexandrov spaces in dimensions $5$, $6$ and $7$. We show that every closed, simply-connected smooth $n$-orbifold, $2\leq n\leq 7$ with a cohomogeneity one action is equivariantly homeomorphic to a smooth good orbifold of cohomogeneity one., Comment: 47 pages

We prove that sufficiently collapsed, closed and irreducible three-dimensional Alexandrov spaces are modeled on one of the eight three-dimensional Thurston geometries. This extends a result of Shioya and Yamaguchi, originally formulated for Riemannian manifolds, to the Alexandrov setting., Comment: We have added a proof of the fact that a closed collapsing Alexandrov 3-space cannot admit hyperbolic geometry (see Remark B). This improves our main Theorem (Theorem A) by ruling out the appearance of hyperbolic geometry. 24 pages, 3 Tables

Sensor setups consisting of a combination of 3D range scanner lasers and stereo vision systems are becoming a popular choice for on-board perception systems in vehicles; however, the combined use of both sources of information implies a tedious calibration process. We present a method for extrinsic calibration of lidar-stereo camera pairs without user intervention. Our calibration approach is aimed to cope with the constraints commonly found in automotive setups, such as low-resolution and specific sensor poses. To demonstrate the performance of our method, we also introduce a novel approach for the quantitative assessment of the calibration results, based on a simulation environment. Tests using real devices have been conducted as well, proving the usability of the system and the improvement over the existing approaches. Code is available at http://wiki.ros.org/velo2cam_calibration, Comment: Accepted to IEEE International Conference on Intelligent Transportation Systems 2017 (ITSC)

Track-before-detect (TBD) is a powerful approach that consists in providing the tracker with sensor measurements directly without pre-detection. Due to the measurement model non-linearities, online state estimation in TBD is most commonly solved via particle filtering. Existing particle filters for TBD do not incorporate measurement information in their proposal distribution. The Langevin Monte Carlo (LMC) is a sampling method whose proposal is able to exploit all available knowledge of the posterior (that is, both prior and measurement information). This letter synthesizes recent advances in LMC-based filtering to describe the Riemann-Langevin particle filter and introduces its novel application to TBD. The benefits of our approach are illustrated in a challenging low-noise scenario., Comment: Minor grammatical updates

Let $(M,g)$ be a smooth Riemannian manifold and $\mathsf{G}$ a compact Lie group acting on $M$ effectively and by isometries. It is well known that a lower bound of the sectional curvature of $(M,g)$ is again a bound for the curvature of the quotient space, which is an Alexandrov space of curvature bounded below. Moreover, the analogous stability property holds for metric foliations and submersions. The goal of the paper is to prove the corresponding stability properties for synthetic Ricci curvature lower bounds. Specifically, we show that such stability holds for quotients of $\mathsf{RCD}^{*}(K,N)$-spaces, under isomorphic compact group actions and more generally under metric-measure foliations and submetries. An $\mathsf{RCD}^{*}(K,N)$-space is a metric measure space with an upper dimension bound $N$ and weighted Ricci curvature bounded below by $K$ in a generalized sense. In particular, this shows that if $(M,g)$ has Ricci curvature bounded below by $K\in \mathbb{R}$ and dimension $N$, then the quotient space is an $\mathsf{RCD}^{*}(K,N)$-space. Additionally, we tackle the same problem for the $\mathsf{CD}/\mathsf{CD}^*$ and $\mathsf{MCP}$ curvature-dimension conditions. We provide as well geometric applications which include: A generalization of Kobayashi's Classification Theorem of homogenous manifolds to $\mathsf{RCD}^{*}(K,N)$-spaces with essential minimal dimension $n\leq N$; a structure theorem for $\mathsf{RCD}^{*}(K,N)$-spaces admitting actions by large (compact) groups; and geometric rigidity results for orbifolds such as Cheng's Maximal Diameter and Maximal Volume Rigidity Theorems. Finally, in two appendices we apply the methods of the paper to study quotients by isometric group actions of discrete spaces and of (super-)Ricci flows., Comment: 51 pages. Comments welcome!

We obtain a topological and equivariant classification of closed, connected three-dimensional Alexandrov spaces admitting a local isometric circle action. We show, in particular, that such spaces are homeomorphic to connected sums of some closed 3-manifold with a local circle action and finitely many copies of the suspension of the real projective plane., Comment: 23 pages, Final version to appear at the Kyoto Journal of Mathematics

The goal of this work is to show that the generalized Korn inequality that replaces the symmetric part of the differential matrix in the classical Korn inequality by its trace-free part is valid over John domains and weighted Sobolev spaces. The weights considered are nonnegative powers of the distance to the boundary., Comment: 17 pages

We show a weighted version of Korn inequality on bounded euclidean John domains, where the weights are nonnegative powers of the distance to the boundary. In this theorem, we also provide an estimate of the constant involved in the inequality which depends on the power that appears in the weight and a geometric condition that characterizes John domains. The proof uses a local-to-global argument based on a certain decomposition of functions. In addition, we prove the solvability in weighted Sobolev spaces of div(u)=f on the same class of domains. In this case, the weights are nonpositive powers of the distance to the boundary. The constant appearing in this problem is also estimated., Comment: 17 pages