arXiv subjects

Jonathan Crespo

Publications and source records attributed to Jonathan Crespo.

4 recordsLinked to original sources

arXiv2026

Reasoning Systems for Semantic Navigation in Mobile Robots

Semantic navigation is the navigation paradigm in which environmental semantic concepts and their relationships are taken into account to plan the route of a mobile robot. This paradigm facilitates the interaction with humans and the understanding of human environments in terms of navigation goals and tasks. At the high level, a semantic navigation system requires two main components: a semantic representation of the environment, and a reasoner system. This paper is focused on develop a model of the environment using semantic concepts. This paper presents two solutions for the semantic navigation paradigm. Both systems implement an ontological model. Whilst the first one uses a relational database, the second one is based on KnowRob. Both systems have been integrated in a semantic navigator. We compare both systems at the qualitative and quantitative levels, and present an implementation on a mobile robot as a proof of concept.

cs.RO↗

arXiv2017

Measured quantum groupoids on a finite basis and equivariant Kasparov theory

In this article, we generalize to the case of measured quantum groupoids on a finite basis some important results concerning equivariant Kasparov theory for actions of locally compact quantum groups [S. Baaj and G. Skandalis, 1989, 1993]. To every pair $(A,B)$ of C*-algebras continuously acted upon by a regular measured quantum groupoid on a finite basis $\cal G$, we associate a $\cal G$-equivariant Kasparov theory group ${\sf KK}_{\cal G}(A,B)$. The Kasparov product generalizes to this setting. By applying recent results concerning actions of regular measured quantum groupoids on a finite basis [S. Baaj and J. C., 2015; J. C., 2017], we obtain two canonical homomorphisms $J_{\cal G}:{\sf KK}_{\cal G}(A,B)\rightarrow{\sf KK}_{\widehat{\cal G}}(A\rtimes{\cal G},B\rtimes{\cal G})$ and $J_{\widehat{\cal G}}:{\sf KK}_{\widehat{\cal G}}(A,B)\rightarrow{\sf KK}_{\cal G}(A\rtimes\widehat{\cal G},B\rtimes\widehat{\cal G})$ inverse of each other through the Morita equivalence coming from a version of the Takesaki-Takai duality theorem [S. Baaj and J. C., 2015; J. C., 2017]. We investigate in detail the case of colinking measured quantum groupoids. In particular, if $\mathbb{G}_1$ and $\mathbb{G}_2$ are two monoidally equivalent regular locally compact quantum groups, we obtain a new proof of the canonical equivalence of the associated equivariant Kasparov categories [S. Baaj and J. C., 2015].

math.OA↗

arXiv2017

Actions of measured quantum groupoids on a finite basis

In this article, we generalize to the case of measured quantum groupoids on a finite basis some important results concerning actions of locally compact quantum groups on C*-algebras [S. Baaj, G. Skandalis and S. Vaes, 2003]. Let $\cal G$ be a measured quantum groupoid on a finite basis. We prove that if $\cal G$ is regular, then any weakly continuous action of $\cal G$ on a C*-algebra is necessarily strongly continuous. Following [S. Baaj and G. Skandalis, 1989], we introduce and investigate a notion of $\cal G$-equivariant Hilbert C$^*$-modules. By applying the previous results and a version of the Takesaki-Takai duality theorem obtained in [S. Baaj and J. C., 2015] for actions of $\cal G$, we obtain a canonical equivariant Morita equivalence between a given $\cal G$-C$^*$-algebra $A$ and the double crossed product $(A\rtimes{\cal G})\rtimes\widehat{\cal G}$.

math.OA↗

arXiv2015

\'Equivalence mono\"idale de groupes quantiques et K-th\'eorie bivariante

In this article, we generalize to the case of regular locally compact quantum groups, two important results concerning actions of compact quantum groups. Let $G_1$ and $G_2$ be two monoidally equivalent regular locally compact quantum groups in the sense of De Commer. We introduce an induction procedure and we build an equivalence of the categories ${A}^{G_1}$ and ${A}^{G_2}$ consisting of continuous actions of $G_1$ and $G_2$ on $C^*$-algebras. As an application of this result, we derive a canonical equivalence of the categories ${KK}^{G_1}$ and ${KK}^{G_2}$. We introduce and investigate a notion of actions on $C^*$-algebras of measured quantum groupoids on a finite basis. The proof of the equivalence between ${KK}^{G_1}$ and ${KK}^{G_2}$ relies on a version of the Takesaki-Takai duality theorem for continuous actions on $C^*$-algebras of measured quantum groupoids on a finite basis.

math.OA↗