On the stability of indirect ZMP controller for biped robot systems

This paper proposes the indirect zero momentum position (ZMP) controller for biped robot systems and proves its disturbance input-to-state stability (ISS). The ZMP control has been used as a standard method for stable walking control of biped robot systems. Since the ZMP information consists of position and acceleration of the center of gravity (COG) for a biped robot system, the ZMP can be indirectly controlled by the motion of COG. In this paper, the reference COG planner is developed by solving the reference ZMP differential equation. The indirect ZMP controller is proposed to derive the desired motion of COG from the reference ZMP trajectory and the COG error (the difference between the reference and real COG). The ISS of the proposed indirect ZMP controller is proved for the simplified biped robot model. The robustness of the proposed indirect ZMP controller is shown in simulation.

[1]  J.W. Grizzle,et al.  Event-based PI control of an underactuated biped walker , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[2]  Kazuhito Yokoi,et al.  Running pattern generation and its evaluation using a realistic humanoid model , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[3]  Jong Hyeon Park,et al.  Impedance control for biped robot locomotion , 2001, IEEE Trans. Robotics Autom..

[4]  Wan Kyun Chung,et al.  PID Trajectory Tracking Control for Mechanical Systems , 2004 .

[5]  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).

[6]  Kazuhito Yokoi,et al.  A realtime pattern generator for biped walking , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[7]  Kazuhito Yokoi,et al.  Running pattern generation for a humanoid robot , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[8]  Daniel E. Koditschek,et al.  Hybrid zero dynamics of planar biped walkers , 2003, IEEE Trans. Autom. Control..

[9]  Atsuo Takanishi,et al.  Realization of dynamic biped walking stabilized by trunk motion on a sagittally uneven surface , 1990, EEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications.

[10]  Jun-Ho Oh,et al.  Development of a Humanoid Biped Walking Robot Platform KHR-1 Initial Design and Its Performance Evaluation , 2002 .

[11]  Hirochika Inoue,et al.  Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[12]  Kazuhito Yokoi,et al.  Resolved momentum control: humanoid motion planning based on the linear and angular momentum , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[13]  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).