Geometric maneuverability with applications to low reynolds number swimming

A mobile system's maneuverability describes the scale and span of the velocities with which it can move. In this paper, we present a new geometric framework for describing the maneuverability of kinematic locomoting systems, inspired by the manipulability analysis of robotic arms. This framework describes both the local maneuverability in the neighborhood of each shape the system can assume and the cyclic maneuverability achieved by executing gaits from a library. Additionally, the gait-level analysis includes tools that direct the search for gaits whose inclusion into the library will usefully improve the maneuverability. Throughout, we provide examples based on a swimming system operating at low Reynolds number.

[1]  Howie Choset,et al.  Geometric motion planning: The local connection, Stokes’ theorem, and the importance of coordinate choice , 2011, Int. J. Robotics Res..

[2]  Richard M. Murray,et al.  Geometric phases and robotic locomotion , 1995, J. Field Robotics.

[3]  Howie Choset,et al.  Geometric Motion Planning Analysis for Two Classes of Underactuated Mechanical Systems , 2007, Int. J. Robotics Res..

[4]  F. Wilczek,et al.  Efficiencies of self-propulsion at low Reynolds number , 1989, Journal of Fluid Mechanics.

[5]  C. Gosselin.  The optimum design of robotic manipulators using dexterity indices , 1992, Robotics Auton. Syst..

[6]  Chen Li,et al.  Undulatory Swimming in Sand: Subsurface Locomotion of the Sandfish Lizard , 2009, Science.

[7]  Howie Choset,et al.  Optimizing coordinate choice for locomoting systems , 2010, 2010 IEEE International Conference on Robotics and Automation.

[8]  R.L. Hatton,et al.  Connection vector fields for underactuated systems , 2008, 2008 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics.

[9]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[10]  Howie Choset,et al.  Parameterized and Scripted Gaits for Modular Snake Robots , 2009, Adv. Robotics.

[11]  S. Shankar Sastry,et al.  On reorienting linked rigid bodies using internal motions , 1995, IEEE Trans. Robotics Autom..

[12]  H. Choset,et al.  Connection Vector Fields and Optimized Coordinates for Swimming Systems at Low and High Reynolds Numbers , 2010 .

[13]  E. Kanso.  Swimming due to transverse shape deformations , 2009, Journal of Fluid Mechanics.

[14]  Joel W. Burdick,et al.  The Geometric Mechanics of Undulatory Robotic Locomotion , 1998, Int. J. Robotics Res..

[15]  O. Raz,et al.  A geometric theory of swimming: Purcell's swimmer and its symmetrized cousin , 2007, 0712.2047.

[16]  J. A. Carretero,et al.  Formulating Jacobian matrices for the dexterity analysis of parallel manipulators , 2006 .

[17]  L. E. Becker,et al.  On self-propulsion of micro-machines at low Reynolds number: Purcell's three-link swimmer , 2003, Journal of Fluid Mechanics.

[18]  Clarence W. Rowley,et al.  Motion Planning for an Articulated Body in a Perfect Planar Fluid , 2006, SIAM J. Appl. Dyn. Syst..

[19]  Tsuneo Yoshikawa,et al.  Manipulability of Robotic Mechanisms , 1985 .

[20]  E. Purcell.  Life at Low Reynolds Number , 2008 .

[21]  A. Bloch,et al.  Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[22]  Daniel Tam,et al.  Optimal stroke patterns for Purcell's three-link swimmer. , 2006, Physical review letters.

[23]  F. Wilczek,et al.  Geometry of self-propulsion at low Reynolds number , 1989, Journal of Fluid Mechanics.