On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces

We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension of the space and on the type of regions considered. For example, the logic with the interior-connectedness predicate (and without contact) is undecidable over polygons or regular closed sets in the Euclidean plane, NP-complete over regular closed sets in three-dimensional Euclidean space, and ExpTime-complete over polyhedra in three-dimensional Euclidean space.Comment: Accepted for publication in the IJCAI 2011 proceeding

Planification de pas pour robots humanoïdes : approches discrètes et continues

Dans cette thèse nous nous intéressons à deux types d'approches pour la planification de pas pour robots humanoïdes : d'une part les approches discrètes où le robot n'a qu'un nombre fini de pas possibles, et d'autre part les approches où le robot se base sur des zones de faisabilité continues. Nous étudions ces problèmes à la fois du point de vue théorique et pratique. En particulier nous décrivons deux méthodes originales, cohérentes et efficaces pour la planification de pas, l'une dans le cas discret (chapitre 5) et l'autre dans le cas continu (chapitre 6). Nous validons ces méthodes en simulation ainsi qu'avec plusieurs expériences sur le robot HRP-2. ABSTRACT : In this thesis we investigate two types of approaches for footstep planning for humanoid robots: on one hand the discrete approaches where the robot has only a finite set of possible steps, and on the other hand the approaches where the robot uses continuous feasibility regions. We study these problems both on a theoretical and practical level. In particular, we describe two original, coherent and efficient methods for footstep planning, one in the discrete case (chapter 5), and one in the continuous case (chapter 6). We validate these methods in simulation and with several experiments on the robot HRP-2

Reasoning about topological and cardinal direction relations between 2-dimensional spatial objects

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints

Reasoning about topological and cardinal direction relations between 2-dimensional spatial objects

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints

Qualitative Spatial and Temporal Reasoning based on And/Or Linear Programming An approach to partially grounded qualitative spatial reasoning

Acting intelligently in dynamic environments involves anticipating surrounding processes, for example to foresee a dangerous situation or acceptable social behavior. Knowledge about spatial configurations and how they develop over time enables intelligent robots to safely navigate by reasoning about possible actions. The seamless connection of high-level deliberative processes to perception and action selection remains a challenge though. Moreover, an integration should allow the robot to build awareness of these processes as in reality there will be misunderstandings a robot should be able to respond to. My aim is to verify that actions selected by the robot do not violate navigation or safety regulations and thereby endanger the robot or others. Navigation rules specified qualitatively allow an autonomous agent to consistently combine all rules applicable in a context. Within this thesis, I develop a formal, symbolic representation of right-of-way-rules based on a qualitative spatial representation. This cumulative dissertation consists of 5 peer-reviewed papers and 1 manuscript under review. The contribution of this thesis is an approach to represent navigation patterns based on qualitative spatio-temporal representation and the development of corresponding effective sound reasoning techniques. The approach is based on a spatial logic in the sense of Aiello, Pratt-Hartmann, and van Benthem. This logic has clear spatial and temporal semantics and I demonstrate how it allows various navigation rules and social conventions to be represented. I demonstrate the applicability of the developed method in three different areas, an autonomous robotic system in an industrial setting, an autonomous sailing boat, and a robot that should act politely by adhering to social conventions. In all three settings, the navigation behavior is specified by logic formulas. Temporal reasoning is performed via model checking. An important aspect is that a logic symbol, such as \emph{turn left}, comprises a family of movement behaviors rather than a single pre-specified movement command. This enables to incorporate the current spatial context, the possible changing kinematics of the robotic system, and so on without changing a single formula. Additionally, I show that the developed approach can be integrated into various robotic software architectures. Further, an answer to three long standing questions in the field of qualitative spatial reasoning is presented. Using generalized linear programming as a unifying basis for reasoning, one can jointly reason about relations from different qualitative calculi. Also, concrete entities (fixed points, regions fixed in shape and/or position, etc.) can be mixed with free variables. In addition, a realization of qualitative spatial description can be calculated, i.e., a specific instance/example. All three features are important for applications but cannot be handled by other techniques. I advocate the use of And/Or trees to facilitate efficient reasoning and I show the feasibility of my approach. Last but not least, I investigate a fourth question, how to integrate And/Or trees with linear temporal logic, to enable spatio-temporal reasoning

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Control for Localization and Visibility Maintenance of an Independent Agent using Robotic Teams

Given a non-cooperative agent, we seek to formulate a control strategy to enable a team of robots to localize and track the agent in a complex but known environment while maintaining a continuously optimized line-of-sight communication chain to a fixed base station. We focus on two aspects of the problem. First, we investigate the estimation of the agent\u27s location by using nonlinear sensing modalities, in particular that of range-only sensing, and formulate a control strategy based on improving this estimation using one or more robots working to independently gather information. Second, we develop methods to plan and sequence robot deployments that will establish and maintain line-of-sight chains for communication between the independent agent and the fixed base station using a minimum number of robots. These methods will lead to feedback control laws that can realize this plan and ensure proper navigation and collision avoidance

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book