Identification of human control during walking

Jason K. Moore j.k.moore19@csuohio.edu

Sandra K. Hnat

Antonie J. van den Bogert

Human Motion and Control Laboratory [hmc.csuohio.edu]

Cleveland State University

March 4, 2014

Lower Extremity Exoskeletons

Clips collected from one, two, three, and four.

Idealized Gait Feedback Control

Idealized Gait Feedback Control

Estimated

  • \(\varphi\): Phase of gait cycle
  • \(\mathbf{s}(\varphi)\): Joint angles and rates
  • \(\mathbf{m}(\varphi)\): Joint torques
  • \(w(t)\): Random belt speed

Unknown

  • \(\mathbf{K}(\varphi)\): Matrix of feedback gains
  • \(\mathbf{s}_0(\varphi)\): Open loop joint angles and rates
  • \(\mathbf{m}_0(\varphi)\): Open loop joint torques

Controller Equations

\[ \mathbf{m}(t) = \mathbf{m}_0(\varphi) + \mathbf{K}(\varphi) [\mathbf{s}_0(\varphi) - \mathbf{s}(t)] \\ \] \[ \mathbf{m}(t) = \mathbf{m}_0(\varphi) + \mathbf{K}(\varphi) \mathbf{s}_0(\varphi) - \mathbf{K}(\varphi) \mathbf{s}(t) \\ \]

Linear Form

\[ \mathbf{m}(t) = \mathbf{m}^*(\varphi) - \mathbf{K}(\varphi) \mathbf{s}(t) \]

Map Human Control to Exoskeleton

Sensors

Assume that a lower limb exoskeleton can sense relative orientation and rate of the right and left planar ankle, knee, and hip angles.

\(\mathbf{s}(t) = \begin{bmatrix} s_1 & \dot{s}_1 & \ldots & s_q & \dot{s}_q \end{bmatrix} \) where \(q=6\)

Controls (plant inputs)

Assume that the exoskeleton can generate planar ankle, knee, and hip joint torques.

\(\mathbf{m}(t) = \begin{bmatrix}m_1 & \ldots & m_q \end{bmatrix} \) where \(q=6\)

Gain Matrix [Proportional-Derivative Control]

\( \mathbf{K}(\varphi) = \begin{bmatrix} k(\varphi)_{s_1} & k(\varphi)_{\dot{s_1}} & 0 & 0 & 0 & \ldots & 0\\ 0 & 0 & k(\varphi)_{s_2} & k(\varphi)_{\dot{s_2}} & 0 & \ldots & \vdots\\ 0 & 0 & 0 & 0 & \ddots & 0 & 0\\ 0 & 0 & 0 & \ldots & 0 & k(\varphi)_{s_q} & k(\varphi)_{\dot{s}_q} \\ \end{bmatrix} \)

Linear Least Squares

With \(n\) time samples in each gait cycle and \(m\) steps there are \(mnq\) equations and which can be used to solve for the \(nq(2q+1)\) unknowns: \(\mathbf{m}^*(\varphi)\) and \(\mathbf{K}(\varphi)\). This is a classic overdetermined system of linear equations that can be solved with linear least squares.

\[\mathbf{A}\mathbf{x}=\mathbf{b}\]

\[\mathbf{x}=(\mathbf{A}^T\mathbf{A})^{-1}\mathbf{A}^T\mathbf{b}\]

Experimental Protocol

Random Belt Speed Variations

Random Belt Speed Variations

Measurement Variations

Measurement Variations

Gains: v=0.8 m/s

Gains: v=1.2 m/s

Gain variation with speed

How good is the model?

Summary

Future

Tutorial

Simulation and Control of Biomechanical Systems with Python

Tonight at 6pm

Chemistry Computer Lab in the Whitby building on the 2nd floor. Next to ASEC (previous location).

https://github.com/pydy/pydy-tutorial-pycon-2014

Information

Contact

Slides

Source code for this analysis

Data

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