Using Deep Learning Models to Predict Prosthetic Ankle Torque

Abstract

Inverse dynamics from motion capture is the most common technique for acquiring biomechanical kinetic data. However, this method is time-intensive, limited to a gait laboratory setting, and requires a large array of reflective markers to be attached to the body. A practical alternative must be developed to provide biomechanical information to high-bandwidth prosthesis control systems to enable predictive controllers. In this study, we applied deep learning to build dynamical system models capable of accurately estimating and predicting prosthetic ankle torque from inverse dynamics using only six input signals. We performed a hyperparameter optimization protocol that automatically selected the model architectures and learning parameters that resulted in the most accurate predictions. We show that the trained deep neural networks predict ankle torques one sample into the future with an average RMSE of 0.04 ± 0.02 Nm/kg, corresponding to 2.9 ± 1.6% of the ankle torque's dynamic range. Comparatively, a manually derived analytical regression model predicted ankle torques with a RMSE of 0.35 ± 0.53 Nm/kg, corresponding to 26.6 ± 40.9% of the ankle torque's dynamic range. In addition, the deep neural networks predicted ankle torque values half a gait cycle into the future with an average decrease in performance of 1.7% of the ankle torque's dynamic range when compared to the one-sample-ahead prediction. This application of deep learning provides an avenue towards the development of predictive control systems for powered limbs aimed at optimizing prosthetic ankle torque.

Keywords: biomechanics; deep neural networks; machine learning; robotic ankle prosthesis.

Figure A1

The prototype PAFP represented as two linkages connecting the drivetrain to the ankle joint. Pin joint A is where the ball screw connects to the shank link, pin joint B is where the ball screw nut housing connects to the ankle link, and pin joint O is where the ankle joint is connected to the drivetrain. Lowercase letters represent lengths and Greek letters represent angles. The variable $\omega$ represents the direction of positive angular velocity about the ankle joint.

Figure 1

Block diagram of the architecture of a generic model-based prosthesis control system. A trajectory generator outputs a desired ankle torque $y_d$, which is then fed into an optimizer. The optimizer samples different possible control commands $u_k$ and conducts forward simulations based on system model predictions. The optimizer uses the results to determine which control command would achieve the closest one-sample ahead ankle torque response $y_{k+1}$ to the desired behavior. This control command is then sent to the human–robot system and the measurements of the system $x_k$ (e.g., loading and motion information from wearable sensors) are fed back to the optimizer for the next control sample.

Figure 2

Illustrative rendering of the prototype PAFP with major components labeled (note that some components are transparent for ease in visualization).

Figure 3

Visual illustration of the deep neural network architectures. The time history of input features are concatenated and fed into each network. Each DNN is trained to output a predicted PAFP ankle torque one timestep ahead or twenty timesteps ahead of the current timestep. Note that only one FFN and GRU are displayed in this diagram, but multiple layers were tested during hyperparameter optimization.

Figure 4

One-sample ahead model predictions of total PAFP torques across gait cycles. The periodic time series are time-normalized across the gait cycle for better visualization. The black time series data labeled as “MoCap” represents the PAFP ankle torque calculated using inverse dynamics. This data serve as the ground truth for model validation. The thin solid lines represent the mean and the corresponding shaded areas represent ±1 standard deviation.

Figure 5

RMSE (top row) and RMSE percent error (bottom row) for each model class for both one-sample ahead (left column) and twenty-sample ahead (right column) predictions. RMSE percent error was calculated by dividing the RMSE value by the range of ankle torque values within the walking trial. Errors are shown for stance and swing phases individually as well as the full gait cycle. The error bars represent the standard error.