arXiv subjects

Michael Schröder

Publications and source records attributed to Michael Schröder.

16 recordsLinked to original sources

arXiv2025

Polygonal Obstacle Avoidance Combining Model Predictive Control and Fuzzy Logic

In practice, navigation of mobile robots in confined environments is often done using a spatially discrete cost-map to represent obstacles. Path following is a typical use case for model predictive control (MPC), but formulating constraints for obstacle avoidance is challenging in this case. Typically the cost and constraints of an MPC problem are defined as closed-form functions and typical solvers work best with continuously differentiable functions. This is contrary to spatially discrete occupancy grid maps, in which a grid's value defines the cost associated with occupancy. This paper presents a way to overcome this compatibility issue by re-formulating occupancy grid maps to continuously differentiable functions to be embedded into the MPC scheme as constraints. Each obstacle is defined as a polygon -- an intersection of half-spaces. Any half-space is a linear inequality representing one edge of a polygon. Using AND and OR operators, the combined set of all obstacles and therefore the obstacle avoidance constraints can be described. The key contribution of this paper is the use of fuzzy logic to re-formulate such constraints that include logical operators as inequality constraints which are compatible with standard MPC formulation. The resulting MPC-based trajectory planner is successfully tested in simulation. This concept is also applicable outside of navigation tasks to implement logical or verbal constraints in MPC.

cs.RO↗

arXiv2025

Trajectory Planning with Model Predictive Control for Obstacle Avoidance Considering Prediction Uncertainty

This paper introduces a novel trajectory planner for autonomous robots, specifically designed to enhance navigation by incorporating dynamic obstacle avoidance within the Robot Operating System 2 (ROS2) and Navigation 2 (Nav2) framework. The proposed method utilizes Model Predictive Control (MPC) with a focus on handling the uncertainties associated with the movement prediction of dynamic obstacles. Unlike existing Nav2 trajectory planners which primarily deal with static obstacles or react to the current position of dynamic obstacles, this planner predicts future obstacle positions using a stochastic Vector Auto-Regressive Model (VAR). The obstacles' future positions are represented by probability distributions, and collision avoidance is achieved through constraints based on the Mahalanobis distance, ensuring the robot avoids regions where obstacles are likely to be. This approach considers the robot's kinodynamic constraints, enabling it to track a reference path while adapting to real-time changes in the environment. The paper details the implementation, including obstacle prediction, tracking, and the construction of feasible sets for MPC. Simulation results in a Gazebo environment demonstrate the effectiveness of this method in scenarios where robots must navigate around each other, showing improved collision avoidance capabilities.

eess.SY↗

arXiv2023

An Exploratory Study of Ad Hoc Parsers in Python

Background: Ad hoc parsers are pieces of code that use common string functions like split, trim, or slice to effectively perform parsing. Whether it is handling command-line arguments, reading configuration files, parsing custom file formats, or any number of other minor string processing tasks, ad hoc parsing is ubiquitous -- yet poorly understood. Objective: This study aims to reveal the common syntactic and semantic characteristics of ad hoc parsing code in real world Python projects. Our goal is to understand the nature of ad hoc parsers in order to inform future program analysis efforts in this area. Method: We plan to conduct an exploratory study based on large-scale mining of open-source Python repositories from GitHub. We will use program slicing to identify program fragments related to ad hoc parsing and analyze these parsers and their surrounding contexts across 9 research questions using 25 initial syntactic and semantic metrics. Beyond descriptive statistics, we will attempt to identify common parsing patterns by cluster analysis.

cs.SE↗

arXiv2022

Grammars for Free: Toward Grammar Inference for Ad Hoc Parsers

Ad hoc parsers are everywhere: they appear any time a string is split, looped over, interpreted, transformed, or otherwise processed. Every ad hoc parser gives rise to a language: the possibly infinite set of input strings that the program accepts without going wrong. Any language can be described by a formal grammar: a finite set of rules that can generate all strings of that language. But programmers do not write grammars for ad hoc parsers -- even though they would be eminently useful. Grammars can serve as documentation, aid program comprehension, generate test inputs, and allow reasoning about language-theoretic security. We propose an automatic grammar inference system for ad hoc parsers that would enable all of these use cases, in addition to opening up new possibilities in mining software repositories and bi-directional parser synthesis.

cs.SE↗

arXiv2021

An Empirical Investigation of Command-Line Customization

The interactive command line, also known as the shell, is a prominent mechanism used extensively by a wide range of software professionals (engineers, system administrators, data scientists, etc.). Shell customizations can therefore provide insight into the tasks they repeatedly perform, how well the standard environment supports those tasks, and ways in which the environment could be productively extended or modified. To characterize the patterns and complexities of command-line customization, we mined the collective knowledge of command-line users by analyzing more than 2.2 million shell alias definitions found on GitHub. Shell aliases allow command-line users to customize their environment by defining arbitrarily complex command substitutions. Using inductive coding methods, we found three types of aliases that each enable a number of customization practices: Shortcuts (for nicknaming commands, abbreviating subcommands, and bookmarking locations), Modifications (for substituting commands, overriding defaults, colorizing output, and elevating privilege), and Scripts (for transforming data and chaining subcommands). We conjecture that identifying common customization practices can point to particular usability issues within command-line programs, and that a deeper understanding of these practices can support researchers and tool developers in designing better user experiences. In addition to our analysis, we provide an extensive reproducibility package in the form of a curated dataset together with well-documented computational notebooks enabling further knowledge discovery and a basis for learning approaches to improve command-line workflows.

cs.SE↗

arXiv2021

Improving Efficient Neural Ranking Models with Cross-Architecture Knowledge Distillation

Retrieval and ranking models are the backbone of many applications such as web search, open domain QA, or text-based recommender systems. The latency of neural ranking models at query time is largely dependent on the architecture and deliberate choices by their designers to trade-off effectiveness for higher efficiency. This focus on low query latency of a rising number of efficient ranking architectures make them feasible for production deployment. In machine learning an increasingly common approach to close the effectiveness gap of more efficient models is to apply knowledge distillation from a large teacher model to a smaller student model. We find that different ranking architectures tend to produce output scores in different magnitudes. Based on this finding, we propose a cross-architecture training procedure with a margin focused loss (Margin-MSE), that adapts knowledge distillation to the varying score output distributions of different BERT and non-BERT passage ranking architectures. We apply the teachable information as additional fine-grained labels to existing training triples of the MSMARCO-Passage collection. We evaluate our procedure of distilling knowledge from state-of-the-art concatenated BERT models to four different efficient architectures (TK, ColBERT, PreTT, and a BERT CLS dot product model). We show that across our evaluated architectures our Margin-MSE knowledge distillation significantly improves re-ranking effectiveness without compromising their efficiency. Additionally, we show our general distillation method to improve nearest neighbor based index retrieval with the BERT dot product model, offering competitive results with specialized and much more costly training methods. To benefit the community, we publish the teacher-score training files in a ready-to-use package.

cs.IR↗

arXiv2020

Fine-Grained Relevance Annotations for Multi-Task Document Ranking and Question Answering

There are many existing retrieval and question answering datasets. However, most of them either focus on ranked list evaluation or single-candidate question answering. This divide makes it challenging to properly evaluate approaches concerned with ranking documents and providing snippets or answers for a given query. In this work, we present FiRA: a novel dataset of Fine-Grained Relevance Annotations. We extend the ranked retrieval annotations of the Deep Learning track of TREC 2019 with passage and word level graded relevance annotations for all relevant documents. We use our newly created data to study the distribution of relevance in long documents, as well as the attention of annotators to specific positions of the text. As an example, we evaluate the recently introduced TKL document ranking model. We find that although TKL exhibits state-of-the-art retrieval results for long documents, it misses many relevant passages.

cs.IR↗

arXiv2013

On a Brownian excursion law, I: convolution representations

This paper studies Brownian motion subject to the occurrence of a minimal length excursion below a given excursion level. The law of this process is determined. The characterization is explicit and shows by a layer construction how the law is built up over time in terms of the laws of sums of a given set of independent random variables.

math.CA↗

arXiv2011

Patterson--Sullivan distributions in higher rank

For a compact locally symmetric space $\XG$ of non-positive curvature, we consider sequences of normalized joint eigenfunctions which belong to the principal spectrum of the algebra of invariant differential operators. Using an $h$-\psdiff\ calculus on $\XG$, we define and study lifted quantum limits as weak$^*$-limit points of Wigner distributions. The Helgason boundary values of the eigenfunctions allow us to construct Patterson--Sullivan distributions on the space of Weyl chambers. These distributions are asymptotic to lifted quantum limits and satisfy additional invariance properties, which makes them useful in the context of quantum ergodicity. Our results generalize results for compact hyperbolic surfaces obtained by Anantharaman and Zelditch.

math.SP↗

arXiv2002

On the integral of geometric Brownian motion

This paper studies the law of any power of the integral of geometric Brownian motion over any finite time interval. As its main results, two integral representations for this law are derived. This is by enhancing the Laplace transform ansatz of Yor (1992) with complex analytic methods, which is the main methodological contribution of the paper. The one of our integrals has a similar structure to that obtained by Yor, while the other is in terms of Hermite functions as those of Dufresne (2001). Performing or not performing a certain Girsanov transformation is identified as the source of these two forms of the laws. While our results specialize for exponents equal to 1 to those obtained by Yor, they yield on specialization representations for the exponent equal to minus 1 laws which are markedly different from those obtained by Dufresne.

math.PR↗

arXiv2002

Analytical ramifications of derivatives valuation: Asian options and special functions

Averaging problems are ubiquitous in Finance with the valuation of the so-called Asian options on arithmetic averages as their most conspicuous form. There is an abundance of numerical work on them, and their stochastic structure has been extensively studied by Yor and his school. However, the analytical structure of these problems is largely unstudied. Our philosophy now is that such valuation problems should be considered as an extension of the theory of special functions: they lead to new problems about new classes of special functions which should be studied in terms of and using of the methods of special functions and their theory. This is exemplified by deriving integral representations for the Black-Scholes prices based on Yor's Laplace transform ansatz to their valuation. They are obtained by analytic Laplace inversion using complex analytic methods. The analysis ultimately rests on the gamma function which in this sense is found to be at the base of Asian options. The results improve on those of Yor and have served us a as starting point for deriving first time benchmark prices for these options.

math.CA↗

arXiv2002

Brownian excursions an Parisian barrier options: a note

This note re-addresses the Paris barrier options proposed by Yor and collaborators and their valuation using the Laplace transform approach. The notion of Paris barrier options, based on excursion theory and using the Brownian meander, is extended such that their valuation is now possible at any point during their lifespan. The pertinent Laplace transforms are modified when necessary.

math.PR↗

arXiv2001

On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisited

The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial relevance of its results. First, we show that the Geman and Yor Laplace transform is not that of an Asian option price, as reported in Geman and Yor and other papers. We nonetheless show how the Geman and Yor Laplace transform can be used to obtain the price of an Asian option. Second, we find that following Geman and Yor these Laplace transfoms are available only if the risk-neutral drift is not less than half the squared volatility. Using complex analytic techniques, we lift this restriction, thus extending the financial applicability of the Laplace transform approach.

math.CA↗

arXiv2000

On the valuation of arithmetic-average Asian options: Laguerre series and Theta integrals

In a recent significant advance, using Laguerre series, the valuation of Asian options has been reduced by Dufresne to computing the negative moments of Yor's accumulation processes. For these he has given functional recursion rules whose probabilistic structure has been the object of intensive recent studies of Yor and co-workers. Stressing the role of Theta functions, this paper now solves these recursion rules and expresses these negative moments as linear combinations of certain Theta integrals. Using the Jacobi transformation formula, very rapidly and very stably convergent series for them are derived. In this way computable series for Black--Scholes price of the Asian option result which are numerically illustrated. Moreover, the Laguerre series approach of Dufresne is made rigorous, and extensions and modifications are discussed. The key for this is the analysis of the integrability and growth properties of Yor's 1992 Asia density, basic problems which seem to be addressed here for the first time.

math.CA↗

arXiv2000

On the valuation of Paris options: foundational results

This paper adresses the valuation of the Paris barrier options proposed by Yor, Jeanblanc-Picque, and Chesnay (Advances in Applied Probability, 29(1997), 165-184) using the Laplace transform approach. Based on suggestions by Pliska the notion of Paris options is extended such that their valuation is possible at any point during their lifespan. The Laplace transforms derived by Yor et al. are modified when necessary, and their basic analytic properties are discussed.

math.CA↗

arXiv2000

On the valuation of Asian options: integral representations

This paper derives integral representations for the Black-Scholes price of arithmetic-average Asian options. Their proof is by Laplace inverting the 1992 Laplace transform of Geman-Yor using complex analytic methods. The analysis ultimately rests on the gamma function which in this sense is at the base of Asian options. The results of Geman-Yor are corrected and their validitity is extended.

math.CV↗