On perfectly plastic impact dynamics of planar multi-link robotic systems contact with the environment

Impact dynamic equations for planar multi-link robotic collisions are modified, which can model both cases of full-ranked and rank-deficient Jacobian matrices. Rank-deficient Jacobian matrices cause the impact equations to be indeterminate. It is shown that (i) the post impact angular velocities are determined and can be solved explicitly without extra equations, and (ii) a set of linear equations with unknown impulses can be obtained where the impulses can only be solved if extra equations of impulses are provided. Two robot collision problems with rank-deficient Jacobian matrices are presented to exemplify the method

[1]  K. Kreutz-Delgado,et al.  Optimal biped walking with a complete dynamical model , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[2]  Rongqiang Liu,et al.  Optimal Biped Walking Locomotion Solved by Trajectory Planning Method , 2002 .

[3]  Yuan F. Zheng,et al.  Mathematical modeling of a robot collision with its environment , 1985, J. Field Robotics.

[4]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..

[5]  Martin Buehler,et al.  Quadruped trotting with passive knees: design, control, and experiments , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[6]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[7]  Nariman Sepehri,et al.  On dynamic stability of manipulators mounted on mobile platforms , 2001, Robotica.

[8]  Qiong Wu,et al.  A complete dynamic model of five-link bipedal walking , 2003, Proceedings of the 2003 American Control Conference, 2003..

[9]  Spyros G. Tzafestas,et al.  Robust sliding-mode control applied to a 5-link biped robot , 1996, J. Intell. Robotic Syst..

[10]  A Kelvin theorem and partial work of impulsive forces , 1997 .

[11]  Yuan F. Zheng,et al.  Impact effects of biped contact with the environment , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Yildirim Hurmuzlu,et al.  Dynamics of Bipedal Gait: Part I—Objective Functions and the Contact Event of a Planar Five-Link Biped , 1993 .

[13]  A. Ivanov.  On multiple impact , 1995 .

[14]  Yildirim Hurmuzlu,et al.  Rigid body collisions of a special class of planar kinematic chains , 1992, IEEE Trans. Syst. Man Cybern..

[15]  A. Ruina,et al.  Two Interpretations of Rigidity in Rigid-Body Collisions , 1998 .

[16]  Y. Hurmuzlu,et al.  Three-dimensional rigid-body collisions with multiple contact points , 1995 .