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Linear approximations for swing leg motion during gait.

W H Lee, J M Mansour

    Journal of Biomechanical Engineering
    |May 1, 1984
    PubMed
    Summary
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    Linear systems analysis accurately models 2D swing leg motion, particularly with time-varying systems. Time-invariant systems show limited accuracy for longer swing phases.

    Area of Science:

    • Biomechanics
    • Robotics
    • Control Systems Engineering

    Background:

    • Investigating simplified models for complex biological movements like leg swing is crucial for advancements in prosthetics and robotics.
    • Nonlinear dynamics govern human and robotic leg motion, posing challenges for precise analytical modeling.

    Purpose of the Study:

    • To assess the effectiveness of linear systems analysis in modeling two-dimensional (2D) swing leg motion.
    • To compare the accuracy of linear time-varying and linear time-invariant models against nonlinear simulations and actual subject data.

    Main Methods:

    • Developed two linear systems: a linear time-varying (LTV) system and multiple linear time-invariant (LTI) systems.
    • Linearized nonlinear swing leg equations around nominal trajectories (LTV) and fixed limb positions (LTI).

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  • Compared simulation results from both linear models against nonlinear simulations and experimental subject motion data.

    • Main Results:

    • The LTV system provided accurate representations of thigh and shank motion but showed reduced accuracy for foot motion.
    • LTI systems demonstrated significant inaccuracies for thigh, shank, and foot motion when simulating beyond a quarter of the swing phase.
    • Linear system analysis offered insights into state variable and control interdependencies during swing leg motion.

    Conclusions:

    • Linear time-varying models offer a viable and accurate approach for simulating 2D swing leg motion, especially for biological and robotic applications.
    • Linear time-invariant models are less suitable for comprehensive swing phase analysis due to accuracy limitations over extended durations.