Multibody system dynamics for bio-inspired locomotion: from geometric structures to computational aspects

This article presents a set of generic tools for multibody system dynamics devoted to the study of bio-inspired locomotion in robotics. First, archetypal examples from the field of bio-inspired robot locomotion are presented to prepare the ground for further discussion. The general problem of locomotion is then stated. In considering this problem, we progressively draw a unified geometric picture of locomotion dynamics. For that purpose, we start from the model of discrete mobile multibody systems (MMSs) that we progressively extend to the case of continuous and finally soft systems. Beyond these theoretical aspects, we address the practical problem of the efficient computation of these models by proposing a Newton-Euler-based approach to efficient locomotion dynamics with a few illustrations of creeping, swimming, and flying.

[1]  V. Arnold Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits , 1966 .

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

[3]  Frédéric Boyer,et al.  Locomotion Dynamics for Bio-inspired Robots with Soft Appendages: Application to Flapping Flight and Passive Swimming , 2017, J. Nonlinear Sci..

[4]  Charles Richter,et al.  Untethered Hovering Flapping Flight of a 3D-Printed Mechanical Insect , 2011, Artificial Life.

[5]  M. Spivak A comprehensive introduction to differential geometry , 1979 .

[6]  P. Dario,et al.  Design concept and validation of a robotic arm inspired by the octopus , 2011 .

[7]  B. Remes,et al.  Design, Aerodynamics, and Vision-Based Control of the DelFly , 2009 .

[8]  Frédéric Boyer,et al.  Three-dimensional extension of Lighthill's large-amplitude elongated-body theory of fish locomotion , 2011, Journal of Fluid Mechanics.

[9]  Yannick Aoustin,et al.  Optimal reference trajectories for walking and running of a biped robot , 2001, Robotica.

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

[11]  J. C. Simo,et al.  On stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization , 1989 .

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

[13]  M. Dickinson,et al.  Wing rotation and the aerodynamic basis of insect flight. , 1999, Science.

[14]  Frédéric Boyer,et al.  Macro-continuous computed torque algorithm for a three-dimensional eel-like robot , 2006, IEEE Transactions on Robotics.

[15]  R. Murray,et al.  The geometry and control of dissipative systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[16]  Auke Jan Ijspeert,et al.  AmphiBot II: An Amphibious Snake Robot that Crawls and Swims using a Central Pattern Generator , 2006 .

[17]  Frédéric Boyer,et al.  Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons , 2014, Int. J. Robotics Res..

[18]  R J Full,et al.  How animals move: an integrative view. , 2000, Science.

[19]  Frédéric Boyer,et al.  A hybrid dynamic model for bio-inspired robots with soft appendages - Application to a bio-inspired flexible flapping-wing micro air vehicle. , 2013 .

[20]  広瀬 茂男,et al.  Biologically inspired robots : snake-like locomotors and manipulators , 1993 .

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

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

[23]  Mathieu Porez,et al.  Note on the swimming of an elongated body in a non-uniform flow , 2013, Journal of Fluid Mechanics.

[24]  Jason Rife,et al.  Modeling locomotion of a soft-bodied arthropod using inverse dynamics , 2011, Bioinspiration & biomimetics.

[25]  V. V Rumyantsev On the poincaré and chetayev equations , 1998 .

[26]  Frédéric Boyer,et al.  A hybrid dynamic model of an insect-like MAV with soft wings , 2012, 2012 IEEE International Conference on Robotics and Biomimetics (ROBIO).

[27]  Jerrold E. Marsden,et al.  Locomotion of Articulated Bodies in a Perfect Fluid , 2005, J. Nonlinear Sci..

[28]  Pål Liljebäck,et al.  Experimental Investigation of Obstacle-Aided Locomotion With a Snake Robot , 2011, IEEE Transactions on Robotics.

[29]  J. Videler,et al.  How the body contributes to the wake in undulatory fish swimming: flow fields of a swimming eel (Anguilla anguilla). , 2001, The Journal of experimental biology.

[30]  James P. Ostrowski Computing reduced equations for robotic systems with constraints and symmetries , 1999, IEEE Trans. Robotics Autom..

[31]  Hao Liu,et al.  Integrated modeling of insect flight: From morphology, kinematics to aerodynamics , 2009, J. Comput. Phys..

[32]  Howie Choset,et al.  Generating gaits for snake robots by annealed chain fitting and Keyframe wave extraction , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[33]  Howie Choset,et al.  Geometric maneuverability with applications to low reynolds number swimming , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[34]  E. Reissner,et al.  On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory , 1973 .

[35]  Frédéric Boyer,et al.  Macrocontinuous Dynamics for Hyperredundant Robots: Application to Kinematic Locomotion Bioinspired by Elongated Body Animals , 2012, IEEE Transactions on Robotics.

[36]  Frédéric Boyer,et al.  Dynamic Modeling and Simulation of a 3-D Serial Eel-Like Robot , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[37]  Frédéric Boyer,et al.  Recursive Inverse Dynamics of Mobile Multibody Systems With Joints and Wheels , 2011, IEEE Transactions on Robotics.

[38]  Robert J. Wood,et al.  Design, fabrication, and analysis of a 3DOF, 3cm flapping-wing MAV , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[39]  J. Gray,et al.  The Kinetics of Locomotion of the Grass-Snake , 1950 .

[40]  Adrian L. R. Thomas,et al.  Wake Development behind Paired Wings with Tip and Root Trailing Vortices: Consequences for Animal Flight Force Estimates , 2014, PloS one.

[41]  Christine Chevallereau,et al.  3D Bipedal Robotic Walking: Models, Feedback Control, and Open Problems , 2010 .

[42]  P. Likins,et al.  Floating reference frames for flexible spacecraft , 1977 .

[43]  Howie Choset,et al.  Natural Gait Generation Techniques for Principally Kinematic Mechanical Systems , 2005, Robotics: Science and Systems.

[44]  Jérôme Casas,et al.  Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces , 2013, Journal of Experimental Biology.

[45]  Frédéric Boyer,et al.  Erratum to "Reduced Locomotion Dynamics With Passive Internal DoFs: Application to Nonholonomic and Soft Robotics" , 2015, IEEE Trans. Robotics.

[46]  J. Videler,et al.  Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso). , 1997, The Journal of experimental biology.

[47]  Jasmine A. Nirody,et al.  The mechanics of slithering locomotion , 2009, Proceedings of the National Academy of Sciences.

[48]  Christine Chevallereau,et al.  Underwater Reflex Navigation in Confined Environment Based on Electric Sense , 2013, IEEE Transactions on Robotics.

[49]  L. Castano,et al.  Smart fabric sensors and e-textile technologies: a review , 2014 .

[50]  M. Triantafyllou,et al.  An Efficient Swimming Machine , 1995 .

[51]  M. Triantafyllou,et al.  Hydrodynamics of Fishlike Swimming , 2000 .

[52]  Jing Zhao,et al.  Review of graphene-based strain sensors , 2013 .

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

[54]  J. C. Simo,et al.  On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach , 1988 .

[55]  Ian D. Walker,et al.  Analysis and experiments with an elephant's trunk robot , 2001, Adv. Robotics.

[56]  D. Primault,et al.  The Poincaré-Chetayev equations and flexible multibody systems , 2005 .

[57]  G. Lauder,et al.  Passive propulsion in vortex wakes , 2006, Journal of Fluid Mechanics.

[58]  P. Coiffet,et al.  Generalization of Newton‐Euler model for flexible manipulators , 1996 .

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

[60]  Frédéric Boyer,et al.  Poincaré–Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics , 2010, J. Nonlinear Sci..

[61]  C. Poole,et al.  Classical Mechanics, 3rd ed. , 2002 .