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Hof Et Al 2005

The Condition For Dynamic Stability

Tags: #locomotion #gait #biomechanics #control #COM #inverted_pendulum #extrapolatedCOM #dynamic_balance

Related: [[N-Step Capturability - Koolen Et Al. 2012]] [[Extrapolated COM - Hof 2007]]

Key Definitions

Base of Support: area of possible locations of the center of pressure, or the possible locations of the ground reaction force

Center of Pressure: the origin of the ground reaction force

Extrapolated COM: Projected COM (onto groundplane) plus the COM velocity divided by a constant related to stature (x + v_x/w_o).

Margin of Stability: the shortest perpendicular distance between the XcoM and the boundary of the base of support

Temporal Margin of Stability: time needed to reach the boundary of the base of support

Key Takeaways

  1. Key questions are (1) what condition has to be fulfilled for balance to be maintained, and (2) how can we tell how good balance is in a given situation? The normal response to (1) is whether the projected COM is within the base of support. But this fails in dynamic situations because it does not take into account velocity of the COM.
  2. The extrapolated center of mass XcoM can remedy this by dealing with balance in situations where the COM has velocity. It is the COM trajectory extrapolated in the direction of its velocity.
    1. The condition for dynamic stability is that the XcoM should be within the base of support.
  3. This also gives rise to a measure of dynamic stability: the margin of stability. This is the shortest perpendicular distance between the XcoM and the boundary of the base of support.
    1. The margin of stability is proportional to the impulse needed to unbalance a subject.
    2. The margin of stability benefits are:
      1. It accounts for COM velocity
      2. Can be easily visualized
      3. Has biomechanical meaning by relating to the impulse needed to unbalance a subject
      4. Can be applied not just to standing but to almost any erect position
  4. Can also create another measure of dynamic stability: a time to boundary temporal margin of stability. This is the time it takes to reach the boundary of the base of support. Gives another measure of stability but seems to conflict with existing temporal measures of stability in the literature.

Limitations

  1. Movements in which the distance from foot to CoM shows major changes will probably not follow the rules
  2. Temporal boundary of stability seems to conflict with existing temporal measures of stability in the literature.
  3. Next to the movement of the whole-body CoM, which is the only variable in inverted pendulum models, the segments can also move with respect to this CoM, and the acceleration of these movements can give an appreciable contribution to the moment equation
    1. By using these mechanisms, e.g. by bending the hips or by moving the arms, a disbalance with the XcoM outside the BoS, thus with negative b, can still be restored