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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:29:39 +0000Geometric Phases and Robotic Locomotion
https://resolver.caltech.edu/CaltechCDSTR:1994.CIT-CDS-94-014
Authors: {'items': [{'id': 'Kelly-S-D', 'name': {'family': 'Kelly', 'given': 'Scott D.'}}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 1994
Robotic locomotion is based in a variety of instances upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. This is true for legged robots, snakelike robots, and wheeled mobile robots undertaking maneuvers such as parallel parking. In this paper we explore the use of tools from differential geometry to model and analyze this class of locomotion mechanisms in a unified way. In particular, we describe locomotion in terms of the geometric phase associated with a connection on a principal bundle, and address issues such as controllability and choice of gait. We also provide an introduction to the basic mathematical concepts which we require and apply the theory to numerous example systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ssytx-z6q73Modelling and experimental investigation of carangiform locomotion for control
https://resolver.caltech.edu/CaltechAUTHORS:KELacc98
Authors: {'items': [{'id': 'Kelly-S-D', 'name': {'family': 'Kelly', 'given': 'Scott D.'}}, {'id': 'Mason-R-J', 'name': {'family': 'Mason', 'given': 'Richard J.'}}, {'id': 'Anhalt-C-T', 'name': {'family': 'Anhalt', 'given': 'Carl T.'}}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}, {'id': 'Burdick-J-W', 'name': {'family': 'Burdick', 'given': 'Joel W.'}}]}
Year: 1998
DOI: 10.1109/ACC.1998.703619
We propose a model for planar carangiform swimming based on conservative equations for the interaction of a rigid body and an incompressible fluid. We account for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observed behavior to that predicted by unsteady hydrodynamics. Our analysis of thrust generation by an oscillating hydrofoil allows us to characterize and evaluate certain families of gaits. Our final swimming model takes the form of a control-affine nonlinear system.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d9y01-f4g15The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices
https://resolver.caltech.edu/CaltechAUTHORS:SHApof02
Authors: {'items': [{'id': 'Shashikanth-B-N', 'name': {'family': 'Shashikanth', 'given': 'Banavara N.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Burdick-J-W', 'name': {'family': 'Burdick', 'given': 'Joel W.'}}, {'id': 'Kelly-S-D', 'name': {'family': 'Kelly', 'given': 'Scott D.'}}]}
Year: 2002
DOI: 10.1063/1.1445183
This paper studies the dynamical fluid plus rigid-body system consisting of a two-dimensional rigid cylinder of general cross-sectional shape interacting with N point vortices. We derive the equations of motion for this system and show that, in particular, if the vortex strengths sum to zero and the rigid-body has a circular shape, the equations are Hamiltonian with respect to a Poisson bracket structure that is the sum of the rigid body Lie–Poisson bracket on Se(2)*, the dual of the Lie algebra of the Euclidean group on the plane, and the canonical Poisson bracket for the dynamics of N point vortices in an unbounded plane. We then use this Hamiltonian structure to study the linear and nonlinear stability of the moving Föppl equilibrium solutions using the energy-Casimir method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nr58s-atj40Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape
https://resolver.caltech.edu/CaltechAUTHORS:20101005-085628821
Authors: {'items': [{'id': 'Shashikanth-B-N', 'name': {'family': 'Shashikanth', 'given': 'Banavara N.'}}, {'id': 'Sheshmani-A', 'name': {'family': 'Sheshmani', 'given': 'Artan'}}, {'id': 'Kelly-S-D', 'name': {'family': 'Kelly', 'given': 'Scott David'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2008
DOI: 10.1007/s00162-007-0065-y
We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tgxfy-9t725Geometric control of particle manipulation in a two-dimensional fluid
https://resolver.caltech.edu/CaltechAUTHORS:20190322-111541230
Authors: {'items': [{'id': 'Or-Y', 'name': {'family': 'Or', 'given': 'Yizhar'}, 'orcid': '0000-0002-9091-9357'}, {'id': 'Vankerschaver-J', 'name': {'family': 'Vankerschaver', 'given': 'Joris'}}, {'id': 'Kelly-S-D', 'name': {'family': 'Kelly', 'given': 'Scott D.'}}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2009
DOI: 10.1109/CDC.2009.5399499
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0pcte-k2z58