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<p>The sit-to-stand (STS) transition is among the most dangerous daily activities for the elderly, yet its dynamics remain poorly understood. STS starts with momentum generation from sitting and ends with stabilization at standing, consisting of 3–4 distinct phases, with smooth transitions between. To better understand STS dynamics, we introduce a modeling methodology based on Koopman operator theory, which subsumes segmented local dynamics into a globally linear model. A special class of nonlinear basis functions, termed state-membership product (SMP) observables, is introduced to combine and subsume local dynamics. An SMP-based model tuned to published experimental STS data successfully reproduces multi-phase STS dynamics with a single linear model. Additionally, a closed-loop model is developed, which combines an SMP-based open-loop mechanistic model with a linear quadratic regulator to model multi-phase STS without explicit controller switching between phases. The results reveal critical global and local properties of STS transitions.</p>

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Multi-phase sit-to-stand dynamics represented using Koopman operators incorporating segmented local dynamics into globally linear models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月7日

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  • John Bell,
  • H. Harry Asada

摘要

The sit-to-stand (STS) transition is among the most dangerous daily activities for the elderly, yet its dynamics remain poorly understood. STS starts with momentum generation from sitting and ends with stabilization at standing, consisting of 3–4 distinct phases, with smooth transitions between. To better understand STS dynamics, we introduce a modeling methodology based on Koopman operator theory, which subsumes segmented local dynamics into a globally linear model. A special class of nonlinear basis functions, termed state-membership product (SMP) observables, is introduced to combine and subsume local dynamics. An SMP-based model tuned to published experimental STS data successfully reproduces multi-phase STS dynamics with a single linear model. Additionally, a closed-loop model is developed, which combines an SMP-based open-loop mechanistic model with a linear quadratic regulator to model multi-phase STS without explicit controller switching between phases. The results reveal critical global and local properties of STS transitions.