Control of humanoids

Macroscopic dynamics and control -- COM-ZMP model

As explained in Humanoid motion section, the macroscopic dynamics is represented by the relationship between COM and the total external force. More concretely stating, the translational COM acceleration is proportional to the total external force. Hence, COM can be controlled through the manipulation of the total external force (Witt 1968, Yamashita et al. 1972, Fujimoto & Kawamura 1995).

One should notice that the external force satisfies the following constraints.

    1. Unilaterality: abstract forces cannot be exerted at any contact points, and
    2. Friction: any tangential forces cannot exceed the maximum static friction force.

The former is more severe, which is substitutable with a condition where the center of pressure of the external force must lie within the supporting region (the convex hull of contact points) (Vukobratovic et al. 1969). The center of pressure is also defined as the zero-moment point or ZMP in short, since the horizontal component of the moment of force (torque) acting about that point is zero (Vukobratovic et al. 1972).

The relationship between COM and the total external force is also represented by that between COM and ZMP under the following approximations: (1) the total mass is concentrated at COM, and (2) the height of COM is constant. In such situations, the manipulation of ZMP is almost equivalent with the manipulation of the external force (Mitobe et al. 1996). It originates in a fact that the dynamics of COM-ZMP is similar to that of an inverted pendulum (Nagasaka et al. 1999). The question is in what way ZMP should be manipulated.

Dynamics morphing

Humanoid control involves a variety of objectives such as keeping stance configuration, stepping out to avoid falling down, alternating the pivot foot and walking. Controller should be designed to achieve each objective based on the common equation of motion of the COM-ZMP model and dynamical contraints. However, it is not desirable to switch many different controllers which are individually designed for each objective according to the situations due to the following two reasons. First, the borderlines between "the situations" are not so clear that they are easily classified; if the controllers are designed based on the assumption that situations are well-defined, they don't properly work against the changes of realistic situations. Second, it is hard to design the behavior in the upper layer upon a patchwork of individual controllers.

A benefit of COM-ZMP model is that the system behavior is easily visualized including the constraint where ZMP lies within the supporting region. In this study, a seamlessly morphing controller which starts from the standing to self-excited oscillation, the pivot foot alternation and the stepping-out was designed based on the behavior of COM visualized on a phase portrait. The voluntary morphing of the system by the controller is synchronized to the passive morphing of the system by the deformation of the supporting region. We named this framework the dynamics morphing.

[References]

  • H. Atsuta and T. Sugihara, Lateral Walk Control of a Biped Robot Based on Dynamics Morphing, in Proceedings of 19th Robotics Symposia, Arima Grand Hotel, 1B4, pp.49-54, 2014. 3.15.
  • T. Sugihara, Reflexive Step-out Control Superposed on Standing Stabilization of Biped Robots, 2012 IEEE-RAS International Conference on Humanoid Robots, pp.741-746, Osaka, Dec. 1st, 2012.
  • T. Sugihara, Biped Control To Follow Arbitrary Referential Longitudinal Velocity based on Dynamics Morphing, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.1892-1897, Vilamoura, Oct. 9th, 2012.
  • T. Sugihara, Consistent Biped Step Control with COM-ZMP Oscillation Based on Successive Phase Estimation in Dynamics Morphing, 2010 IEEE International Conference on Robotics and Automation, pp.4224-4229, Anchorage, May, 6th, 2010.
  • T. Sugihara, Dynamics Morphing from Regulator to Oscillator on Bipedal Control, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.2940-2945, St.Louis, Oct, 13th, 2009.
  • T. Sugihara, Standing Stabilizability and Stepping Maneuver in Planar Bipedalism based on the Best COM-ZMP Regulator, 2009 IEEE International Conference on Robotics and Automation, pp.1966-1971, Kobe, May, 15th, 2009.

* This work was supported by Grant-in-Aid for Young Scientists (B) #20760170 and Grant-in-Aid for Young Scientists (A) #22680018, Japan Society for the Promotion of Science.

Reaching feedback control with rapid & slow adaptation

* This is a co-work with Dr. Seto in Future Robotics Laboratory of Chiba institute of technology (at that point).

Although the reaching motion is one of the most fundamental human motions, the control mechanism of this easiest task has not been unclarified, yet.

It is known that the velocity profile of the reaching trajectory forms a symmetric bell-shaped curve and the acceleration profile does a sinusoidal curve (Abend et al. 1982). The controller design with such a property is not easy, so that most of the conventional studies have rather focused on the trajectory design as a function of time (Flash&Hogan 1985, Uno et al. 1989, Tsuji et al. 2002, etc.). Even a few works have some problems that they are sensitive to disturbances (Hoff&Arbib 1992) or they do not take disturbances into consideration (Sekimoto et al. 2006).

In this study, an artificial nonlinear potential field is generated from the goal point. The field is deformed slowly with respect to the degree of achievement to the goal, and rapidly with respect to the degree of deviation due to disturbances from the goal. It realized a human-like smooth reaching motion in which the arm complies to perturbations and goes back to the smooth motion when the perturbation is gotten rid of.

[References]

  • F. Seto and T. Sugihara, Motion Control with Slow and Rapid Adaptation for Smooth Reaching Movement Under External Force Disturbance, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.1650-1655, Taipei, Oct, 19th, 2010.
  • F. Seto and T. Sugihara, Online Nonlinear Reference Shaping with End-point Position Feedback for Human-Like Smooth Reaching Motion, 2009 IEEE-RAS International Conference on Humanoid Robots, pp.297-302, Paris, Dec, 8th, 2009.
  • F. Seto and T. Sugihara, Online Reference Shaping with End-point Position Feedback for Large Acceleration Avoidance on Manipulator Control, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.5743-5748, St.Louis, Oct, 14th, 2009.

Index

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