Dynamic programming for aligning sketch maps

Dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science in Geospatial TechnologiesSketch maps play an important role in communicating spatial knowledge, particularly in applications interested in identifying correspondences to metric maps for land tenure in rural communities. The interpretation of a sketch map is linked to the users’ spatial reasoning and the number of features included. Additionally, in order to make use of the information provided by sketch maps, the integration with information systems is needed but is convoluted. The process of identifying which element in the base map is being represented in the sketch map involves the use of correct descriptors and structures to manage them. In the past years, different methods to give a solution to the sketch matching problem employs iterative methods using static scores to create a subset of correspondences. In this thesis, we propose an implementation for the automatic aligning of the sketch to metric maps, based on dynamic programming techniques from reinforcement learning. Our solution is distinctive from other approaches as it searches for pair equivalences by exploring the environment of the search space and learning from positive rewards derived from a custom scoring system. Scores are used to evaluate the likeliness of a candidate pair to belong to the final solution, and the results are back up in a state-value function to recover the best subset states and recovering the highest scored combinations. Reinforcement learning algorithms are dynamic and robust solutions for finding the best solution in an ample search space. The proposed workflow improves the outcoming spatial configuration for the aligned features compared to previous approaches, specifically the Tabu Search

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

Reasoning about Qualitative Direction and Distance between Extended Objects using Answer Set Programming

In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a starting point and extend CDC with new sorts of constraints which involve defaults, preferences and negation. We call this extended version as nCDC. Then we further extend nCDC by augmenting qualitative distance relation and name this extension as nCDC+. For CDC, nCDC, nCDC+, we introduce an ASP-based general framework to solve consistency checking problems, address composition and inversion of qualitative spatial relations, infer unknown or missing relations between objects, and find a suitable configuration of objects which fulfills a given inquiry.Comment: In Proceedings ICLP 2019, arXiv:1909.0764

Connecting qualitative spatial and temporal representations by propositional closure

This paper establishes new relationships between existing qualitative spatial and temporal representations. Qualitative spatial and temporal representation (QSTR) is concerned with abstractions of infinite spatial and temporal domains, which represent configurations of objects using a finite vocabulary of relations, also called a qualitative calculus. Classically, reasoning in QSTR is based on constraints. An important task is to identify decision procedures that are able to handle constraints from a single calculus or from several calculi. In particular the latter aspect is a longstanding challenge due to the multitude of calculi proposed. In this paper we consider propositional closures of qualitative constraints which enable progress with respect to the longstanding challenge. Propositional closure allows one to establish several translations between distinct calculi. This enables joint reasoning and provides new insights into computational complexity of individual calculi. We conclude that the study of propositional languages instead of previously considered purely relational languages is a viable research direction for QSTR leading to expressive formalisms and practical algorithms

The complexity of reasoning with relative directions

© 2014 The Authors and IOS Press. Whether reasoning with relative directions can be performed in NP has been an open problem in qualitative spatial reasoning. Efficient reasoning with relative directions is essential, for example, in rule-compliant agent navigation. In this paper, we prove that reasoning with relative directions is ∃ℝ-complete. As a consequence, reasoning with relative directions is not in NP, unless NP=∃ℝ

Qualitative Reasoning about Relative Directions : Computational Complexity and Practical Algorithm

Qualitative spatial reasoning (QSR) enables cognitive agents to reason about space using abstract symbols. Among several aspects of space (e.g., topology, direction, distance) directional information is useful for agents navigating in space. Observers typically describe their environment by specifying the relative directions in which they see other objects or other people from their point of view. As such, qualitative reasoning about relative directions, i.e., determining whether a given statement involving relative directions is true, can be advantageously used for applications, for example, robot navigation, computer-aided design and geographical information systems. Unfortunately, despite the apparent importance of reasoning about relative directions, QSR-research so far could not provide efficient decision procedures for qualitative reasoning about relative directions. Accordingly, the question about how to devise an efficient decision procedure for qualitative reasoning about relative directions has meanwhile turned to the question about whether an efficient decision procedure exists at all. Answering the latter existential question, which requires a formal analysis of relative directions from a computational complexity point of view, has remained an open problem in the field of QSR. The present thesis solves the open problem by proving that there is no efficient decision procedure for qualitative reasoning about relative directions, even if only left or right relations are involved. This is surprising as it contradicts the early premise of QSR believed by many researchers in and outside the field, that is, abstracting from an infinite domain to a finite set of relations naturally leads to efficient reasoning. As a consequence of this rather negative result, efficient reasoning with any of the well-known relative direction calculi (OPRAm, DCC, DRA, LR) is impossible. Indeed, the present thesis shows that all the relative direction calculi belong to one and the same class of ∃R-complete problems, which are the problems that can be reduced to the NP-hard decision problem of the existential theory of the reals, and vice versa. Nevertheless, in practice, many interesting computationally hard AI problems can be tackled by means of approximative algorithms and heuristics. In the same vein, the present thesis shows that qualitative reasoning about relative directions can also be tackled with approximative algorithms. In the thesis we develop the qualitative calculus SVm which allows for a practical algorithm for qualitative reasoning about relative directions. SVm also provides an effective semi-decision procedure for the OPRAm calculus, the most versatile one among the relative direction calculi. In this thesis we substantiate the usefulness of SVm by applying it in the marine navigation domain

StarVars-effective reasoning about relative directions

Relative direction information is very commonly used. Observers typically describe their environment by specifying the relative directions in which they see other objects or other people from their point of view. Or they receive navigation instructions with respect to their point of view, for example, turn left at the next intersection. However, it is surprisingly hard to integrate relative direction information obtained from different observers, and to reconstruct a model of the environment or the locations of the observers based on this information. Despite intensive research, there is currently no algorithm that can effectively integrate this information: this problem is NP-hard, but not known to be in NP, even if we only use left and right relations. In this paper we present a novel qualitative representation, StarVars, that can solve these problems. It is an extension of the STAR calculus [Renz and Mitra, 2004]) by a VARiable interpretation of the orientation of observers. We show that reasoning in StarVars is in NP and present the first algorithm that allows us to effectively integrate relative direction information from different observers

StarVars - Effective Reasoning about Relative Directions

Relative direction information is very commonly used. Observers typically describe their environment by specifying the relative directions in which they see other objects or other people from their point of view. Or they receive navigation instructions w