Optimizing the stroke of Purcell's rotator, a low Reynolds number swimmer

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 24).Purcell's rotator is a theoretical low Reynolds number swimmer that can act as a model of more complex natural microorganisms, such as E.coli. Because of the low Reynolds number environment, the swimmer has approximately no inertia and it's motion is dominated by viscous forces. The version of Purcell's rotator examined in this paper is two dimensional and has three rigid links which rotate about the center of the body. It is able to propel itself by moving these links in a repetitive, nonreciprocal stroke motion. Using a mathematical model of the swimmer, two strokes were found, one which optimizes its rotation of the swimmer and one which optimizes its translation.by Victoria N. Hammett.S.B

Towards Geometric Motion Planning for High-Dimensional Systems: Gait-Based Coordinate Optimization and Local Metrics

Geometric motion planning offers effective and interpretable gait analysis and optimization tools for locomoting systems. However, due to the curse of dimensionality in coordinate optimization, a key component of geometric motion planning, it is almost infeasible to apply current geometric motion planning to high-dimensional systems. In this paper, we propose a gait-based coordinate optimization method that overcomes the curse of dimensionality. We also identify a unified geometric representation of locomotion by generalizing various nonholonomic constraints into local metrics. By combining these two approaches, we take a step towards geometric motion planning for high-dimensional systems. We test our method in two classes of high-dimensional systems - low Reynolds number swimmers and free-falling Cassie - with up to 11-dimensional shape variables. The resulting optimal gait in the high-dimensional system shows better efficiency compared to that of the reduced-order model. Furthermore, we provide a geometric optimality interpretation of the optimal gait.Comment: 7 pages, 6 figures, submitted to the 2024 IEEE International Conference on Robotics and Automation (ICRA 2024

Geometric Swimming at Low and High Reynolds Numbers

Several efforts have recently been made to relate the displacement of swimming three-link systems over strokes to geometric quantities of the strokes. In doing so, they provide powerful, intuitive representations of the bounds on a system’s locomotion capabilities and the forms of its optimal strokes or gaits. While this approach has been successful for finding net rotations, noncommutativity concerns have prevented it from working for net translations. Our recent results on other locomoting systems have shown that the degree of this noncommutativity is dependent on the coordinates used to describe the problem, and that it can be greatly mitigated by an optimal choice of coordinates. Here, we extend the benefits of this optimal-coordinate approach to the analysis of swimming at the extremes of low and high Reynolds numbers.This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by IEEE-Institute of Electrical and Electronics Engineers and can be found at: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8860. ©2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Keywords: Swimming, Coordinate choice, Geometric mechanics, Lie brackets, LocomotionKeywords: Swimming, Coordinate choice, Geometric mechanics, Lie brackets, Locomotio

Morphological properties of mass-spring networks for optimal locomotion learning

Robots have proven very useful in automating industrial processes. Their rigid components and powerful actuators, however, render them unsafe or unfit to work in normal human environments such as schools or hospitals. Robots made of compliant, softer materials may offer a valid alternative. Yet, the dynamics of these compliant robots are much more complicated compared to normal rigid robots of which all components can be accurately controlled. It is often claimed that, by using the concept of morphological computation, the dynamical complexity can become a strength. On the one hand, the use of flexible materials can lead to higher power efficiency and more fluent and robust motions. On the other hand, using embodiment in a closed-loop controller, part of the control task itself can be outsourced to the body dynamics. This can significantly simplify the additional resources required for locomotion control. To this goal, a first step consists in an exploration of the trade-offs between morphology, efficiency of locomotion, and the ability of a mechanical body to serve as a computational resource. In this work, we use a detailed dynamical model of a Mass–Spring–Damper (MSD) network to study these trade-offs. We first investigate the influence of the network size and compliance on locomotion quality and energy efficiency by optimizing an external open-loop controller using evolutionary algorithms. We find that larger networks can lead to more stable gaits and that the system’s optimal compliance to maximize the traveled distance is directly linked to the desired frequency of locomotion. In the last set of experiments, the suitability of MSD bodies for being used in a closed loop is also investigated. Since maximally efficient actuator signals are clearly related to the natural body dynamics, in a sense, the body is tailored for the task of contributing to its own control. Using the same simulation platform, we therefore study how the network states can be successfully used to create a feedback signal and how its accuracy is linked to the body size

Geometry of Locomotion

Many animals and robots move through the world by coupling cyclical changes in shape called gaits to an interaction with the environment. Because mobility is an important aspect of such robots, a key metric when evaluating design and performance of mobile robots is the efficiency of their optimal gaits. The major contribution of this thesis is a set of geometric principles for understanding the geometry of optimal gaits for drag-dominated kinematic systems. We demonstrate these principles on a variety of system geometries (including Purcell's swimmer) and for optimization criteria that include maximizing displacement and efficiency of motion for both translation and turning motions. We also demonstrate how these principles can be used to simultaneously optimize a system's gait kinematics and physical design. We present an analysis of how the shape of these optimal gaits are altered by the presence of passive elements like springs. We use frequency domain analysis to relate the motion of the passive joint to the motion of the actuated joint. We couple this analysis with elements of the geometric framework introduced in our first contribution, to identify speed-maximizing and efficiency-maximizing gaits for drag-dominated swimmers with a passive elastic joint