Geometric interpretation of the Zero-Moment Point

In this article we show that the concept of screws and wrenches gives us tools to geometrically establish the relation between the ground reaction wrench and the Zero-Moment Point. In order to arrive at this, we show how a wrench can be decomposed into separate components. The proposed method gives a general, completely coordinate-free way to find the ZMP and contributes in improving the geometrical insight.

[1]  Tsuneo Yoshikawa,et al.  FSW (feasible solution of wrench) for multi-legged robots , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[2]  Shuuji Kajita,et al.  ZMP analysis for arm/leg coordination , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[3]  Jonghoon Park,et al.  Control of Ground Interaction at the Zero-Moment Point for Dynamic Control of Humanoid Robots , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[4]  C. Barus.  A treatise on the theory of screws , 1998 .

[5]  Ambarish Goswami,et al.  Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point , 1999, Int. J. Robotics Res..

[6]  Roy Featherstone,et al.  Rigid Body Dynamics Algorithms , 2007 .

[7]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[8]  Jerry Pratt,et al.  Velocity-Based Stability Margins for Fast Bipedal Walking , 2006 .

[9]  Miomir Vukobratovic,et al.  Zero-Moment Point - Thirty Five Years of its Life , 2004, Int. J. Humanoid Robotics.

[10]  Guy Bessonnet,et al.  Forces acting on a biped robot. Center of pressure-zero moment point , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[11]  J. D. Everett.  A Treatise on the Theory of Screws , 1901, Nature.

[12]  R. Ball.  A treatise on the theory of screws, by Sir Robert Stawell Ball. , .

[13]  M Vukobratović,et al.  Contribution to the synthesis of biped gait. , 1969, IEEE transactions on bio-medical engineering.

[14]  Yoshihiko Nakamura,et al.  Making feasible walking motion of humanoid robots from human motion capture data , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).