A method for determination of optimal gaits with application to a snake-like serial-link structure

In this paper, we present a method of determining optimal gaits for shape actuated locomotion systems. This method is the synthesis of techniques for computing reduced equations for robotic locomotion systems and a numerical optimal control strategy. Symmetry reduction processes induce a form of locomotion system dynamics that reveals a cyclic-like coupling between group, shape, and momenta coordinates. This form allows one to focus on designing gaits, abandoning concern over shape dynamics. Using this vantage point we indicate how a numerical optimal control method based on Gaussian quadrature may be acclimatized to periodicity, thus providing optimal gaits. The method is demonstrated by means of its application to a snake-like serial-link structure or snake robot. This application provides scientific merit to hypotheses concerning observed locomotion phenomena amongst animals employing undulatory propulsive mechanisms.

[1]  Symmetry in Mechanics: A Gentle, Modern Introduction , 2001 .

[2]  James P. Ostrowski,et al.  Motion planning for dynamic eel-like robots , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[3]  C. Gans,et al.  Kinematics, muscular activity and propulsion in gopher snakes , 1998, The Journal of experimental biology.

[4]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

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

[6]  Vijay Kumar,et al.  Optimal Gait Selection for Nonholonomic Locomotion Systems , 2000, Int. J. Robotics Res..

[7]  James P. Ostrowski,et al.  A Framework for Steering Dynamic Robotic Locomotion Systems , 2003, Int. J. Robotics Res..

[8]  Gen Endo,et al.  Study on self-contained and terrain adaptive active cord mechanism , 1999, Proceedings 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human and Environment Friendly Robots with High Intelligence and Emotional Quotients (Cat. No.99CH36289).

[9]  J. Ostrowski.  The mechanics and control of undulatory robotic locomotion , 1995 .

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

[11]  Enrico Gobbetti,et al.  Encyclopedia of Electrical and Electronics Engineering , 1999 .

[12]  James P. Ostrowski,et al.  A geometric approach to gait generation for eel-like locomotion , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[13]  Frank L. Lewis,et al.  Optimal Control , 1986 .

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

[15]  C. Gans.  Biomechanics: An Approach to Vertebrate Biology , 1974 .

[16]  Sonia Martínez,et al.  Optimal Gaits for Dynamic Robotic Locomotion , 2001, Int. J. Robotics Res..

[17]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[18]  R. Worst,et al.  Construction and operation of a snake-like robot , 1996, Proceedings IEEE International Joint Symposia on Intelligence and Systems.

[19]  Jerrold E. Marsden,et al.  Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems , 1999 .

[20]  Tetsuya Iwasaki,et al.  Serpentine locomotion with robotic snakes , 2002 .

[21]  G. Hicks.  Modeling and Control of a Snake-like Serial-link Structure , 2003 .

[22]  F. Clarac,et al.  Propulsive action of a snake pushing against a single site: Its combined analysis , 1989, Journal of morphology.

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

[24]  J. Lambert.  Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , 1991 .

[25]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[26]  J. Gray.  The mechanism of locomotion in snakes. , 1946, The Journal of experimental biology.

[27]  H. Kobayashi,et al.  An inspection robot for feeder cables-snake like motion control , 1992, Proceedings of the 1992 International Conference on Industrial Electronics, Control, Instrumentation, and Automation.

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

[29]  R. Linnemann,et al.  Motion control of a snakelike robot , 1999, 1999 Third European Workshop on Advanced Mobile Robots (Eurobot'99). Proceedings (Cat. No.99EX355).

[30]  Kazufumi Ito,et al.  Optimal Control Formulation for Determining Optical Flow , 2002, SIAM J. Sci. Comput..

[31]  Shigeo Hirose,et al.  Biologically Inspired Robots: Snake-Like Locomotors and Manipulators , 1993 .

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

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