Gait controllability for legged robots

We present a general method for determining controllability of a class of kinematic legged robots. The method is general in that it is independent of the robot's morphology; in particular, it does not depend upon the number of legs. Our method is based on an extension of a nonlinear controllability test for smooth systems to the legged case, where the relevant mechanics are not smooth. Our extension is based on the realization that legged robot configuration spaces are stratified. The result is illustrated with a simple example.

[1]  R. Abraham,et al.  Manifolds, Tensor Analysis, and Applications , 1983 .

[2]  Marc H. Raibert,et al.  Legged Robots That Balance , 1986, IEEE Expert.

[3]  H. Sussmann.  A general theorem on local controllability , 1987 .

[4]  R. Abraham,et al.  Manifolds, tensor analysis, and applications: 2nd edition , 1988 .

[5]  Kenneth J. Waldron,et al.  Machines That Walk: The Adaptive Suspension Vehicle , 1988 .

[6]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[7]  Shuuji Kajita,et al.  Study of dynamic biped locomotion on rugged terrain-derivation and application of the linear inverted pendulum mode , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  Shin-Min Song,et al.  Path planning and gait of walking machine in an obstacle-strewn environment , 1991, J. Field Robotics.

[9]  S. Kajita,et al.  Study of dynamic biped locomotion on rugged terrain-theory and basic experiment , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[10]  Joel W. Burdick,et al.  The mechanics of undulatory locomotion: the mixed kinematic and dynamic case , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

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

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

[13]  V. Jurdjevic.  Geometric control theory , 1996 .

[14]  Joel W. Burdick,et al.  Trajectory generation for kinematic legged robots , 1997, Proceedings of International Conference on Robotics and Automation.

[15]  J. Goodwine.  Control of stratified systems with robotic applications , 1998 .