Optimal steering for kinematic vehicles with applications to spatially distributed agents

The recent technological advances in the field of autonomous vehicles have resulted in a growing impetus for researchers to improve the current framework of mission planning and execution within both the military and civilian contexts. Many recent efforts towards this direction emphasize the importance of replacing the so-called monolithic paradigm, where a mission is planned, monitored, and controlled by a unique global decision maker, with a network centric paradigm, where the same mission related tasks are performed by networks of interacting decision makers (autonomous vehicles). The interest in applications involving teams of autonomous vehicles is expected to significantly grow in the near future as new paradigms for their use are constantly being proposed for a diverse spectrum of real world applications. One promising approach to extend available techniques for addressing problems involving a single autonomous vehicle to those involving teams of autonomous vehicles is to use the concept of Voronoi diagram as a means for reducing the complexity of the multi-vehicle problem. In particular, the Voronoi diagram provides a spatial partition of the environment the team of vehicles operate in, where each element of this partition is associated with a unique vehicle from the team. The partition induces, in turn, a graph abstraction of the operating space that is in a one-to-one correspondence with the network abstraction of the team of autonomous vehicles; a fact that can provide both conceptual and analytical advantages during mission planning and execution. In this dissertation, we propose the use of a new class of Voronoi-like partitioning schemes with respect to state-dependent proximity (pseudo-) metrics rather than the Euclidean distance or other generalized distance functions, which are typically used in the literature. An important nuance here is that, in contrast to the Euclidean distance, state-dependent metrics can succinctly capture system theoretic features of each vehicle from the team (e.g., vehicle kinematics), as well as the environment-vehicle interactions, which are induced, for example, by local winds/currents. We subsequently illustrate how the proposed concept of state-dependent Voronoi-like partition can induce local control schemes for problems involving networks of spatially distributed autonomous vehicles by examining different application scenarios.PhDCommittee Chair: Tsiotras Panagiotis; Committee Member: Egerstedt Magnus; Committee Member: Feron Eric; Committee Member: Haddad Wassim; Committee Member: Shamma Jef

Asymmetric Robot Motion Design for Pursuit-Evasion Games

Symmetric turning control is the typical design choice for most machines. However, historical examples of asymmetric machine design, as well as examples of asymmetry in nature, suggest that asymmetric turning may be a potential advantage in adversarial applications. For instance, aircraft of World Wars I and II were plagued by asymmetric turning controls as a result of gyroscopic forces from the rotating engine. Pilots of the time actually believed this to be a feature, not a bug, suggesting that the asymmetric turning improved strategic evasion and pursuit during battle. As autonomous robots become increasingly critical in military operations, it is imperative that we endow them with strategic designs for better performance. We seek to understand if asymmetric turning is an advantageous design. Using Karaman and Frazzoli's sample-based algorithm for pursuit-evasion games, software simulates robot motion planning in an asymmetric Dubins state space to observe how asymmetric turning influences agent success. We demonstrate mathematically that the Dubins interval path solutions are applicable to asymmetric Dubins vehicles, as both are utilized within the simulation. The Open Motion Planning Library (OMPL) is leveraged to implement the pursuit-evasion game algorithm. To simulate asymmetric action, agents are assigned varying degrees of asymmetric turning constraints, such that as one turn sharpens, the other broadens. Agents then compete in a pursuit-evasion game. Pursuit-evasion games are simulated across a range of asymmetric turning match-ups and agent starting positions. Results show that pursuer success increases as its asymmetry increases. Evader success remains constant, regardless of asymmetric turning influence. Furthermore, the advantages of asymmetric turning can be further augmented when considered in conjunction with relative agent starting position. The results of this research inform more intelligent machine design strategies for vehicles in dynamic spaces

Optimal ship navigation and algorithms for stochactic obstacle scenes

Tezin basılısı İstanbul Şehir Üniversitesi Kütüphanesi'ndedir.This thesis is comprised of two different but related sections. In the first section, we consider the optimal ship navigation problem wherein the goal is to find the shortest path between two given coordinates in the presence of obstacles subject to safety distance and turn-radius constraints. These obstacles can be debris, rock formations, small islands, ice blocks, other ships, or even an entire coastline. We present a graph-theoretic solution on an appropriately-weighted directed graph representation of the navigation area obtained via 8-adjacency integer lattice discretization and utilization of the A∗ algorithm. We explicitly account for the following three conditions as part of the turn-radius constraints: (1) the ship’s left and right turn radii are different, (2) ship’s speed reduces while turning, and (3) the ship needs to navigate a certain minimum number of lattice edges along a straight line before making any turns. The last constraint ensures that the navigation area can be discretized at any desired resolution. We illustrate our methodology on an ice navigation example involving a 100,000 DWT merchant ship and present a proof- of-concept by simulating the ship’s path in a full-mission ship handling simulator at Istanbul Technical University. In the second section, we consider the stochastic obstacle scene problem wherein an agent needs to traverse a spatial arrangement of possible-obstacles, and the status of the obstacles may be disambiguated en route at a cost. The goal is to find an algorithm that decides what and where to disambiguate en route so that the expected length of the traversal is minimized. We present a polynomial-time method for a graph-theoretical version of the problem when the associated graph is restricted to parallel avenues with fixed policies within the avenues. We show how previously proposed algorithms for the continuous space version can be adapted to a discrete setting. We propose a gener- alized framework encompassing these algorithms that uses penalty functions to guide the navigation in realtime. Within this framework, we introduce a new algorithm that provides near-optimal results within very short execution times. Our algorithms are illustrated via computational experiments involving synthetic data as well as an actual naval minefield data set. Keywords: Graph theory, shortest path, ship navigation, probabilistic path planning, stochastic dynamic programming, Markov decision process, Canadian traveler’s problemContents Declaration of Authorship ii Abstract iv ¨ Oz v Acknowledgments vii List of Figures x List of Tables xi 1 Optimal Ship Navigation with Safety Distance and Realistic Turn Con- straints 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 The Optimal Ship Navigation Problem . . . . . . . . . . . . . . . . . . . . 4 1.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4.1 Safety Distance Constraints . . . . . . . . . . . . . . . . . . . . . . 5 1.4.2 Lattice Discretization . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.3 Ship-Turn Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.4 The A∗ Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4.5 Smoothing the Optimal Path . . . . . . . . . . . . . . . . . . . . . 13 1.5 Ice Navigation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Simulator Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.7 Summary, Conclusions, and Future Research . . . . . . . . . . . . . . . . 18 2 Algorithms for Stochastic Obstacle Scenes 21 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 The Stochastic Obstacle Scene Problem: Continuous vs. Discrete Settings 23 2.2.1 Deciding Where to Disambiguate: Single Disk Case . . . . . . . . 23 2.2.2 Deciding Where to Disambiguate: Two Disks Case . . . . . . . . . 25 2.2.3 Discretization of the Continuous Setting: An Example . . . . . . . 27 2.3 Definition of the Stochastic Obstacle Scene Problem . . . . . . . . . . . . 27 2.3.1 Continuous SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Discrete SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.3 Discretized SOSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 A Polynomial Algorithm for Discrete SOSP on Parallel Graphs . . . . . . 29 2.5 Discrete Adaptation of the Simulated Risk Disambiguation Algorithm . . 30 2.5.1 Adaptation to Discrete SOSP . . . . . . . . . . . . . . . . . . . . . 30 2.5.2 Adaptation to Discretized SOSP . . . . . . . . . . . . . . . . . . . 32 2.6 Discrete Adaptation of the Reset Disambiguation Algorithm . . . . . . . . 33 2.7 Generalizing SRA and RDA: Penalty-Based Algorithms and DTA . . . . . 34 2.7.1 Illustration of the Algorithms . . . . . . . . . . . . . . . . . . . . . 36 2.8 Computational Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.8.1 Environment A (The COBRA Data) Experiments . . . . . . . . . 40 2.8.2 Environment B Experiments . . . . . . . . . . . . . . . . . . . . . 41 2.8.3 Environment C Experiments . . . . . . . . . . . . . . . . . . . . . 43 2.9 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 A Impact of Cost Change in Parallel Graphs 47 Bibliograph

Research on the accuracy of algorithms for autonomous aircraft navigation

Disertacijoje nagrinėjamos nedidelių autonominių orlaivių navigacijos algoritmų įtakos skrydžio tikslumui bei orlaivio deviacijos nuo užduotos skrydžio trajektorijos vertinimo problemos. Pagrindinis tyrimų objektas yra autonominės navigacijos algoritmai. Autonominio skrydžio tikslumas yra tiesiogiai susijęs su skrydžio sauga. Dėl šios priežasties pagrindinis disertacijos tikslas yra ištirti naudojamus ar siūlomus naudoti navigacijos algoritmus bei pateikti autonominio skrydžio saugos gerinimo metodus per navigacijos prizmę. Darbe sprendžiami trys pagrindiniai uždaviniai: autonominio orlaivio navigacijos matematinio modelio parinkimas bei matematinis aprašymas, navigacijos algoritmų įtakos skrydžio tikslumui vertinimas, mažesnę įtaką skrydžio nuokrypiams turinčio algoritmo sukūrimas, kurio paskirtis – saugiai apskristi ir išvengti antžeminių kliūčių. Pirmasis uždavinys skirtas įvertinti didelės imties navigacijos duomenų statistinę aibę. Antrasis bei trečiasis skirti pačių algoritmų analizei. Disertaciją sudaro įvadas, trys skyriai, bendrosios išvados, literatūros ir autoriaus publikacijų disertacijos tema sąrašai ir šeši priedai. Įvadiniame skyriuje aptariama tiriamoji problema, darbo aktualumas, aprašomas tyrimų objektas, formuluojamas darbo tikslas bei uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, darbo rezultatų praktinė reikšmė, ginamieji teiginiai. Įvade pateiktos disertacijos tema autoriaus paskelbtos publikacijos ir pranešimai konferencijose bei disertacijos struktūra. Pirmasis skyrius skirtas literatūros analizei. Jame pateikta autonominių orlaivių klasifikacija. Pateikta autonominių orlaivių navigacijos, kontrolės bei valdymo algoritmų analizė. Skyriaus pabaigoje formuluojamos išvados ir tikslinami disertacijos uždaviniai. Antrajame skyriuje pateiktas tyrimuose taikomas matematinis autonominio orlaivio navigacijos modelis. Pateikta šiuo modeliu gautų navigacijos duomenų analizė bei vertinimas. Trečiajame skyriuje teoriniai rezultatai lyginami su gautais praktinių skrydžių metu bei naudojant SITL (angl. Software In The Loop) skrydžio imitaciją. Pasiūlyta metodika bei autonominių orlaivių navigacijos algoritmas automatizuotam antžeminių kliūčių apskridimui. Disertacijos tema paskelbti 6 straipsniai: du – straipsniai žurnaluose, įtrauktuose į Thomson ISI duomenų bazę, du – recenzuojamuose žurnaluose kitose duomenų bazėse, bei du – kitų tarptautinių bei respublikinių konferencijų medžiagoje. Disertacijos tema perskaityti 6 pranešimai Lietuvos bei kitų šalių konferencijose