Identification of human control during walking

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

Sandra K. Hnat

Antonie van den Bogert

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

Cleveland State University, Cleveland, Ohio, USA

June 10, 2014

Our big questions (maybe some of yours too?)

What are the fundamental control mechanisms used during human gait?

Zero moment point control: Asimo, etc
Optimal control: maximize stability, minimize energy, etc?
Something else?

What control mechanisms can powered prosthetics utilize to recreate able bodied human gait?

Maybe the previous are good choices, maybe not.
Is it possible to develop a data driven controller for a particular prosthetic that behaves like a human, defects and all?
What can common gait lab data from able-bodied humans tell us about the control mechanisms during gait? Can we measure what we really want to?
What kind of experiments can generate rich data needed to identify controllers?

How can we identify these controllers from large sets of gait data?

Maybe standard system identification methods?

Direct Approach
Indirect Approach

Our goal

Desired Improvements

Natural gait patterns
Balance

Additional Benefits

Quantification of control can possibly be used to assess subjects with new set of numbers

Clips collected from [1], [2], [3], and [4].

Our current approach

Collect common gait data from many (500-1000) gait cycles
During cycles, apply pseudo-random external perturbations to the human
Assume a simple time varying linear MIMO control structure
Find the best fit of the control model to the data with a direct approach
Test the resulting controller(s) in simulation and in actual devices (in progress)

Idealized Gait Feedback Control

Estimated

\(\varphi\): Phase of gait cycle
\(\mathbf{s}(t)\): Joint angles and rates
\(\mathbf{m}(t)\): 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

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

Gain Matrix

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 \(m\) cycles there are \(mnq\) equations and which can be used to solve for the \(nq(p+1)\) 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.

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

\(n=20,m\sim=400,q=6,p=12\)
\(\mathbf{A}\) (48000 x 1560): joint angles and rates
\(\mathbf{b}\) (48000 x 1): joint torques
\(\mathbf{x}\) (1560 x 1): \(\mathbf{K}(\varphi)\) and \(\mathbf{m}^*(\varphi)\)

Random Belt Speed Variations

Gains: v=0.8 m/s

Gain variation with speed

How good is the model?

Can we put this controller into an exoskeleton?

Maybe

Alternative Controller Structures

Additional sensors: acceleration, foot pressure, etc
Add in neural time delays \( \mathbf{m}(t) = \mathbf{m}^*(\varphi) - \mathbf{K}(\varphi)\mathbf{s}(t) - \mathbf{K}(\varphi)s(t-\tau)\)
Remove clock from controller (state dependent): \(\mathbf{m}(t) = \mathbf{m}^*(\mathbf{s}(t)) - \mathbf{K}(\mathbf{s}(t))\mathbf{s}(t) - \mathbf{K}(\mathbf{s}(t))s(t-\tau)\)
Non-linear control models: e.g. neural network

Alternative Identification Methods

Indirect Identification

Cost Function: \[ J = \sum_{i=0}^n || y_i - y_i^m || + \ldots\]
Equations of motion used for simulating (shooting) or optimization constraints (direct collocation)
Shooting: high computation costs, few optimization parameters
DC: lower computation cost, many optimization parameters
Both depend on fidelity of the plant model

Back to the questions

Can data driven approaches find controllers that mimic the human better than other approaches?
Is it possible to identify only the parts of the human control system needed to control powered prosthetics from a more complex system?
Which control structures are most useful as parameterized models? Completely black box, or physically influenced models.
How can you verify that directly identified controllers are valid?
What kind of experiments will give the rich data that is needed to expose all of the control mechanisms?