D. Estimating the Instantaneous Knee Moment Profile

In addition to models predicting knee moment extrema and dynamic stiffness, we developed two additional models to predict the knee extensor moment profile during the weight acceptance phase of the gait cycle (profile estimation models 1 and 2). Accurate assessment of the knee moment profile during weight acceptance is critical for specification of a powered knee orthosis because of the precise timing necessary to sharply increase knee extensor torque during weight transfer followed by a sharp decease to maintain forward momentum [20]. In the case of crouch gait from CP, accurately predicating this profile for each individual is even more critical since these individuals typically show the largest deviations from non-impaired populations at the knee [2].

For wearable robotic applications, onboard sensors (e.g. joint angle encoders) can be used to measure joint position. Therefore, we defined the flexion and extension phases of weight-acceptance based on the knee joint angle and time derivatives. The instant of peak knee flexion angular velocity following foot contact was defined as the starting point for the flexion phase. We found this to be a strong indicator of when the knee joint moment switches from flexion to extension following heel strike.

In profile estimation model 1 (equation 1), the knee extensor moment during flexion and extension was calculated using the instantaneous change in knee angle and the predicted dynamic knee stiffness for weight acceptance flexion and extension, respectively. Profile estimation model 1 estimated the knee extensor moment as follows:

where k_F represents the predicted dynamic stiffness during flexion, k_E represents the predicted dynamic stiffness during extension, θ represents the knee joint angle, KEM(nFlex) is the knee extensor moment calculated at the end of the flexion phase, and t represents the t^th time step. The transition from the flexion phase to the extension phase (nFlex) occurred when the angular velocity changed signs (negative during flexion to positive during extension).

In model 1, the predicted moment during the extension phase relies on the accurate prediction of the knee extensor moment at the end of flexion (i.e. KEM(nFlex)). Thus, errors in the estimated moment during flexion may propagate during extension. For example, if the knee moment is under predicted during the flexion phase, it will remain under predicted during extension.

To address this issue, we developed profile estimation model 2 (equation 2), which incorporated a correction factor at the flexion-extension transition. During flexion, the knee extensor moment was calculated using the instantaneous change in knee angle and the predicted flexion dynamic knee stiffness as in model 1. At the flexion-extension transition, we used the predicted first peak of the knee extensor moment (KEM_WA) to estimate the peak moment at the end of flexion. As such, KEM(nFlex) was set to KEM_WA at this transition, and the knee extensor moment during extension was calculated using the instantaneous change in knee angle and the predicted extension dynamic knee stiffness, again as in model 1. Profile estimation model 2 estimated the knee extensor moment as follows:

where k_F represents the predicted dynamic stiffness during flexion, k_E represents the predicted dynamic stiffness during extension, θ represents the knee joint angle, KEM_WA represents the predicted first peak of the knee extensor moment, and t represents the t^th time step.

For both profile estimation models, we specified the end of the extension phase (nExt) when either the angular position of the knee during the extension phase reached the angle of the knee at heel strike or the angular velocity became positive. The predicted moments were constrained to non-negative (i.e. extensor) values.

The RMSE between the estimated and computed instantaneous knee extensor moment profiles during weight-acceptance was used to evaluate the predictive performance of each model.