Predictive preview trajectory tracking control for quadruped robots with Zero Moment Point

In this paper, we propose a control algorithm for quadruped walking robots to track the Zero Moment Point (ZMP) trajectory using Preview Control. In critical moment of trot pace, we can assume the robot as a linear inverted pendulum so that the linear inverted pendulum model can be applied to describe the dynamic behavior of our quadruped robot. A preview controller therefore is designed for this non-minimum phase system to get the optimal input of the system. ZMP reference trajectory can be decomposed into two parts. One is on the direction of movement, and the other is on the vertical direction of it. With the preview controller we can track the reference in both two directions and the optimal trajectory tracking can be achieved.

[1]  Yangsheng Xu,et al.  Trajectory fitting with smoothing splines using velocity information , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[2]  Daniel E. Koditschek,et al.  RHex: A Simple and Highly Mobile Hexapod Robot , 2001, Int. J. Robotics Res..

[3]  T. Katayama,et al.  Design of an optimal controller for a discrete-time system subject to previewable demand , 1985 .

[4]  Kazuhito Yokoi,et al.  Biped walking pattern generation by using preview control of zero-moment point , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[5]  Fucheng Liao,et al.  Design of an optimal preview controller for linear discrete-time causal descriptor systems , 2012, Int. J. Control.

[6]  Kevin Blankespoor,et al.  BigDog, the Rough-Terrain Quadruped Robot , 2008 .

[7]  M. Vukobratovic,et al.  On the stability of anthropomorphic systems , 1972 .

[8]  Zheng-Wei Shen,et al.  Optimal preview control for linear time-variant discrete systems , 2009, 2009 International Conference on Machine Learning and Cybernetics.

[9]  C.H. Lee A phase space spline smoother for fitting trajectories , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[10]  K. Lau,et al.  Undershoot and settling time tradeoffs for nonminimum phase systems , 2003, IEEE Trans. Autom. Control..

[11]  Kemalettin Erbatur,et al.  Zero Moment Point based pace reference generation for quadruped robots via preview control , 2012, 2012 12th IEEE International Workshop on Advanced Motion Control (AMC).

[12]  Kazuhito Yokoi,et al.  The 3D linear inverted pendulum mode: a simple modeling for a biped walking pattern generation , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).