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Kuo 2007

The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective

Tags: #inverted_pendulum #six_determinants #locomotion #gait #dynamic_walking #biomechanics

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Key Definitions

Six Determinants of Gait: proposes a set of kinematic features that help to reduce the displacement of body COM while walking (level COM is main goal of efficient walking)

Inverted Pendulum Theory: proposes that it is energetically less costly for the stance leg to act like a pendulum and prescribe such an arc (pendular leg swing is main goal of efficient walking)

Single Support Phase: phase of walking where only one leg is on the ground

Double Support Phase: phase of walking where both legs are on the ground

Stance Leg: the leg that is supporting the body during single support - is on the ground

Swing Leg: the leg that is swinging to step forward during single support - is not on the ground

Dynamic Walking: systems in which the passive dynamics of the limbs dominate the motion, with minimal actuation applied to sustain periodic behavior

Positive work: work done in the same direction as displacement, i.e. pushing or pulling

Negative Work: work done in the opposite direction as displacement, i.e. resisting or pushing against

Limit Cycle: from dynamic walking, a periodic gait where the initial conditions are reproduced through the natural dynamics. Multiple limit cycles can exist in the same system representing different gaits

Key Takeaways

  1. Both Six Determinants and Inverted Pendulum aim to reduce energetic cost of walking, but take opposing approaches
    • Six Determinants theory tries to keep COM as level as possible
    • Inverted Pendulum requires bobbing COM (arced path)
  2. Walking significantly differs from propulsive locomotion in the relationship of positive to negative work, and the analogy used to explain walking leads to significant (and testable) theoretical differences
    • In propulsive locomotion, the environment performs negative work that must be overcome with positive work
    • In walking, the body performs both positive and negative work
    • Walking is thus better represented as a co-contraction task, where legs perform work against each other during double support
    • Six determinants focus on level COM is a bobbing-like analogy
    • Understanding walking requires at least as much attention to negative work
  3. The Six Determinants and Inverted Pendulum provide opposite estimates of energetic cost of walking
    • Six Determinants predicts a very high cost of walking when accounting for high joint torques and substantial work performed
    • Inverted Pendulum predicts no energy cost during single support phase due to pendular dynamics
      • this only represents a lower bound on energy cost
      • push off force during double support can account for observable energy costs
  4. Dynamic walking investigates what is fundamentally necessary for the creation of gait, aiming to complete the gait cycle with minimal actuation
    • Based on and extends the inverted pendulum model by including the entire gait cycle, not just the single support phase
      • Models step to step transition as a collision causing energy loss throughout the system
      • Step to step collision also changes trajectory of COM and velocities of the legs
  5. The step to step transition as explained by dynamic walking accounts for some of the actual energy cost of walking that the inverted pendulum cannot account for
    • Still underestimates the energy cost of walking, but functions as a theoretical lower bound
      • Since humans are limited with how strong of a push off they can achieve and how quickly they can perform it, they will always expend more energy than the model
      • Model also correctly predicts sharp, fast steps are most energy efficient
    • Force required to move legs (even that not performing actual work) explains some of the energy cost missing from the model
      • Muscles expend energy through cross bridge attachment and calcium transport regardless of work performed
        • This is confirmed by studies performed on isolated swinging of the leg
    • Also has benefit of passive stability, not requiring position control input for stability
      • Humans use passive dynamic stability, especially in the front-rear direction
  6. Above leads to creation of new refined inverted pendulum model
    • [[Six Determinants and Inverted Pendulum - Kuo 2007#Refined Inverted Pendulum Model|See below for details]]

Arguments against Six Determinants

  1. Accepted without experimental testing
  2. At least three determinants do not contribute to keeping COM level
  3. Humans spend more energy keeping COM level than when walking with normal gait
  4. Model predicts about twice the energetic cost of transport than that observed in humans - grossly overestimates energy expenditure of walking
  5. Is descriptive of normal human gait, but not valuable as an explanatory tool

Arguments for Inverted Pendulum

  1. Measurements of kinetic and potential energy of COM fluctuate as inverted pendulum model would predict
  2. Entirely predicts single support phase, as shown by passive dynamic walkers

Refined Inverted Pendulum Model

  1. Single support leg acts as an inverted pendulum to move COM with little muscle work/force
  2. Single Support inverted pendulum required a step to step transition where work is performed to redirect the COM
    • this transition may account for 60-70% of the metabolic energy expended while walking
  3. Forced leg motion can reduce step to step transition costs by using energy for force production
    • The balance between step to step transition costs and energy used for forced leg motion can predict the optimum step length and frequency combination for a given speed
  4. Provides a new analogy for walking: a ball flying through the air and being periodically redirected by a pair of hands
    • Has periods of parabolic forward motion governed by force of gravity (single support phase), with a periodic reset where the ball is redirected back upwards while maintaining its forward movement (double support)
    • Hands are providing a co-contraction style combination of positive and negative work