A Simplified Model of Snake Robot Locomotion on Planar Surfaces

The underlying theme of this book is analytical approaches aimed at increasing our understanding of snake robot locomotion. The mathematical model of the snake robot is the basis for these analytical studies, which means that the analysis relies heavily on the form and complexity of the model. In this chapter, we employ first principles to develop a mathematical model of the kinematics and dynamics of a snake robot with N links moving on a horizontal and flat surface. The links of the robot are influenced by ground friction forces which propel the motion. Due to the many degrees of freedom of the robot and the dynamical couplings between the links, the resulting model will turn out to be quite complex. We will eliminate some of this complexity by partially linearising the model. This is achieved by introducing a change of coordinates which enables us to partition the model into an actuated part (the joint angles of the snake robot) and an unactuated part (the position and orientation of the snake robot). Through an input transformation, we are then able to linearise the actuated part of the model.

[1]  Shugen Ma,et al.  Analysis of Creeping Locomotion of a Snake-like Robot on a Slope , 2001, Auton. Robots.

[2]  Gregory S. Chirikjian,et al.  Kinematics of Hyper-Redundant Manipulators , 1991 .

[3]  J. W. Humberston.  Classical mechanics , 1980, Nature.

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

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

[6]  Gregory S. Chirikjian,et al.  The kinematics of hyper-redundant robot locomotion , 1995, IEEE Trans. Robotics Autom..

[7]  Yangsheng Xu,et al.  A normal form augmentation approach to adaptive control of space robot systems , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

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

[9]  Mark W. Spong,et al.  Partial feedback linearization of underactuated mechanical systems , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

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

[11]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[12]  Howie Choset,et al.  Approximating displacement with the body velocity integral , 2009, Robotics: Science and Systems.

[13]  Gregory S. Chirikjian,et al.  Theory and applications of hyper-redundant robotic manipulators , 1992 .

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

[15]  Kristin Y. Pettersen,et al.  Exponential stabilization of an underactuated surface vessel , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[16]  I. Kenyon,et al.  Classical Mechanics (3rd edn) , 1985 .

[17]  Wolfram Burgard,et al.  Robotics: Science and Systems XV , 2010 .

[18]  Shigeo Hirose,et al.  Study on the 3D shape of active cord mechanism , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[19]  Yoshihiro Takita,et al.  Control of 3D Snake-Like Locomotive Mechanism Based on Continuum Modeling , 2005 .

[20]  James P. Ostrowski,et al.  Motion planning for anguilliform locomotion , 2003, IEEE Trans. Robotics Autom..

[21]  Arjan van der Schaft,et al.  Dynamics and control of a class of underactuated mechanical systems , 1999, IEEE Trans. Autom. Control..