The Mechanics and Control of Undulatory Robotic Locomotion

In this dissertation, we examine a formulation of problems of undulatory robotic locomotion within the context of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using a connection on a trivial principal fiber bundle. We begin by reviewing the processes of Lagrangian reduction and reconstruction for unconstrained mechanical systems with Lie group symmetries, and present new formulations of this process which are easily adapted to accommodate external constraints. Additionally, important physical quantities such as the mechanical connection and reduced mass-inertia matrix can be trivially determined using this formulation. The presence of symmetries then allows us to reduce the necessary calculations to simple matrix manipulations. The addition of constraints significantly complicates the reduction process; however, we show that for invariant constraints, a meaningful connection can be synthesized by defining a generalized momentum representing the momentum of the system in directions allowed by the constraints. We then prove that the generalized momentum and its governing equation possess certain invariances which allows for a reduction process similar to that found in the unconstrained case. The form of the reduced equations highlights the synthesized connection and the matrix quantities used to calculate these equations. The use of connections naturally leads to methods for testing controllability and aids in developing intuition regarding the generation of various locomotive gaits. We present accessibility and controllability tests based on taking derivatives of the connection, and relate these tests to taking Lie brackets of the input vector fields. The theory is illustrated using several examples, in particular the examples of the snakeboard and Hirose snake robot. We interpret each of these examples in light of the theory developed in this thesis, and examine the generation of locomotive gaits using sinusoidal inputs and their relationship to the controllability tests based on Lie brackets

Zur Mechanik vibrationsgetriebener Roboter für terrestrische und aquatische Lokomotion

This thesis discusses the mechanics of mobile robots for terrestrial and aquatic locomotion. Vibration-driven locomotion systems are characterised by an internal periodic excitation, which is transformed to a directed motion due to asymmetric properties of the system. To perform a two-dimensional and controllable locomotion, mechanical properties of robots are investigated dependent on the frequency of the internal excitation. The mechanical description of the robots is done using analytical and numerical methods and supported by experimental studies. The applicability of the results in mobile robots is proved by prototypes.On the basis of mechanical fundamentals, terrestrial and aquatic locomotion principles are discussed and classified. Actuators are reviewed. The purpose is to evaluate the performance as vibration sources for terrestrial and aquatic systems. Piezoelectric bending elements are particular suitable for it. An extensive overview on the state of the art shows the great potential of vibration-driven locomotion systems for miniaturised applications in technics.Systems with bristles can perform unidirectional terrestrial locomotion. Different working principles of bristles are studied based on a rigid body model and experimental investigations. A prototype for the locomotion in tubes is presented. To perform a controllable two-dimensional locomotion with only one actuator, it is needed to overcome the limits of rigid body systems. The applied approach uses the frequency-dependent vibration behaviour of elastic systems, like beams and plates. Models of continuum mechanics and finite element methods are used and supported by experiments. Based on the investigations, a programmable and remote controlled prototype is developed. The locomotion of it can be controlled on different surfaces by a change of the excitation frequency. The velocity of the prototype is up to 100 mm/s and it can support five times its own weight.Concluding, an innovative prototype with a single piezoelectric actuator for a controllable locomotion on flat ground and floating in fluids is developed. The terrestrial and aquatic locomotion behaviour of the robot is investigated. The carrying capacity of it is calculated using a hydrostatic model.Die Mechanik von mobilen Robotern für terrestrische und aquatische Lokomotion ist der Gegenstand der Arbeit. In den untersuchten Systemen wird die periodische Erregung eines inneren Antriebs durch nicht symmetrische Systemeigenschaften in eine gerichtete Fortbewegung gewandelt. Durch die Nutzung des frequenzabhängigen Schwingungsverhaltens von elastischen Systemen, wie Balken oder Platten, werden Systeme realisiert, die durch nur einen Antrieb eine steuerbare zweidimensionale Lokomotion auf festem Untergrund und an der Oberfläche von Flüssigkeiten durchführen können. Der Schwerpunkt der Arbeit liegt auf der mathematisch-mechanischen Beschreibung der Roboter mittels analytischer und numerischer Methoden sowie ihrer experimentellen Untersuchung. Prototypen mobiler Roboter dienen dem funktionellen Nachweis.Auch im Buchhandel erhältlich: Zur Mechanik vibrationsgetriebener Roboter für terrestrische und aquatische Lokomotion / Felix Becker Ilmenau : Univ.-Verl. Ilmenau, 2015. - XIX, 149 S. ISBN 978-3-86360-124-9 URN urn:nbn:de:gbv:ilm1-2015000338 Preis (Druckausgabe): 21,30