Optimized hip–knee–ankle exoskeleton assistance at a range of walking speeds

Background Autonomous exoskeletons will need to be useful at a variety of walking speeds, but it is unclear how optimal hip–knee–ankle exoskeleton assistance should change with speed. Biological joint moments tend to increase with speed, and in some cases, optimized ankle exoskeleton torques follow a similar trend. Ideal hip–knee–ankle exoskeleton torque may also increase with speed. The purpose of this study was to characterize the relationship between walking speed, optimal hip–knee–ankle exoskeleton assistance, and the benefits to metabolic energy cost. Methods We optimized hip–knee–ankle exoskeleton assistance to reduce metabolic cost for three able-bodied participants walking at 1.0 m/s, 1.25 m/s and 1.5 m/s. We measured metabolic cost, muscle activity, exoskeleton assistance and kinematics. We performed Friedman’s tests to analyze trends across walking speeds and paired t-tests to determine if changes from the unassisted conditions to the assisted conditions were significant. Results Exoskeleton assistance reduced the metabolic cost of walking compared to wearing the exoskeleton with no torque applied by 26%, 47% and 50% at 1.0, 1.25 and 1.5 m/s, respectively. For all three participants, optimized exoskeleton ankle torque was the smallest for slow walking, while hip and knee torque changed slightly with speed in ways that varied across participants. Total applied positive power increased with speed for all three participants, largely due to increased joint velocities, which consistently increased with speed. Conclusions Exoskeleton assistance is effective at a range of speeds and is most effective at medium and fast walking speeds. Exoskeleton assistance was less effective for slow walking, which may explain the limited success in reducing metabolic cost for patient populations through exoskeleton assistance. Exoskeleton designers may have more success when targeting activities and groups with faster walking speeds. Speed-related changes in optimized exoskeleton assistance varied by participant, indicating either the benefit of participant-specific tuning or that a wide variety of torque profiles are similarly effective. Supplementary Information The online version contains supplementary material available at 10.1186/s12984-021-00943-y.


Torque parameterization
The hip profile was defined by 8 parameters (Fig. 2 Hips). These parameters defined the rise time, peak time and peak magnitude of hip extension and the peak time, peak magnitude and fall time of hip flexion. A period of no torque was prescribed between extension and flexion periods and was defined by the mid-point timing and duration.
The knee profile was defined by 10 parameters (Fig. 2 Knees). It consisted of a virtual spring during stance, time based flexion torque near toe off, and a virtual damper during swing. The virtual spring was defined by the stiffness, onset time and offset time. The spring torque was the stiffness multiplied by the knee joint angle, which was set to zero when the knee was straight. Knee flexion torque near toe off was defined by the peak time, peak magnitude, rise time and fall time. The virtual damper during swing was parameterized with a damping coefficient, onset time and offset time, similar to the parameterization of the virtual spring.
The ankle profile was defined by 4 parameters similar to knee flexion near toe-off ( Fig. 2 Ankles). These defined the peak time, peak magnitude, rise time, and fall time. Ankle torque was set to zero at 65% of stride at the latest to avoid torque application during swing. This constraint could shorten the fall time, for example a peak time of 55% of stride would result in a maximum fall time of 10% of stride.

Parameter ranges and optimized values
The optimization algorithm varied the red nodes and state-based periods. This parameterization was successful in a previous optimization experiment with our device (Franks 2021). We experimentally found the parameter constraints while piloting the assistance. We swept through parameter values to determine the range of comfortable assistance.
The timing parameters are defined as a percent of stride where 1 is 100%. The magnitude parameters are in Nm/kg so we can compare across participants. The medium-speed initial parameters for P2 were based on the optimized assistance at the hip, knee and ankle individually. The initial values for P1 at that speed were based on the optimized values for P2, and the initial values for P3 were the average of the optimized assistance across all participants in Franks 2021.
For slow and fast walking, the initial parameters were based on each participant's optimized parameters from the medium speed. The timing parameters were the same as the medium-speed optimized parameters and the magnitude parameters were set to 75% of the optimized values to allow the assistance and the participant to adapt to the new conditions.

Hip parameter ranges and optimized values
The hip profile was defined by 8 parameters. It applied hip extension torque through heel strike, so the stride timer began at 84% of stride to avoid discontinuities in the desired profile at heel strike. To convert the hip timing parameters to be based off of heel strike, subtract 16% from the current value. The knee profile was defined by 10 parameters. The stride time is 0% at heel strike and 100% at the following heel strike of that leg. The knee profile has two state based periods, a virtual spring during stance and a virtual damper during late swing. These two periods were defined by the onset and offset timing of the periods and by the stiffness or damping constant. During the period of virtual spring torque, if the knee joint angle went to 0 before the end of the period, the exoskeleton stopped applying torque for participant comfort.

Ankle parameter ranges and optimized values
The ankle profile was defined by 4 parameters. The stride time is 0% at heel strike and 100% at the following heel strike of that leg. *Torque was limited to be applied no later than 65% of stride, so, for example, if peak time was at its latest allowed value (55% of stride), fall time was limited to be 10% of stride. Torque tracking can somewhat influence human-in-the-loop optimization if there is an impact to user performance. For example, if torque tracking is too variable, the assistance can be destabilizing which can affect the metabolic result. Consistent torque tracking can lead to better user responses. Torque tracking also dictates the possible applied profiles. There are some torque profiles that are beyond the capabilities of the device such as an impulse. While an impulse may not be useful, there may be effective torque profiles beyond the capabilities of the exoskeleton. Human-in-the-loop optimization can find effective torque profiles within the capabilities of the device with poor torque tracking so long as the torque error is consistent. The optimizer varies parameters in response to the measured user performance but does not see how well the device follows those desired parameters. If the torque tracking error is consistent, the optimizer can vary parameters in such a way that it determines useful assistance even if the applied profiles do not perfectly match the desired profiles. Figure 7. Metabolic impact of the cloth mask under the metabolic mask. Participant 1 measured their metabolic cost of quiet standing and walking on the treadmill for 6 minutes each. All measurements were collected in the same session. They measured their metabolic cost with no cloth mask (blue) and with a cloth mask under the metabolics mask (red). The average of the last 3 minutes of walking is shown with the solid line, and the dashed lines show the range for one standard deviation. The participant was the only person in the lab space, so they did not put others at risk by not wearing a mask. The cloth mask lowered the metabolic cost by 0.33 W/kg for the standing condition and by 0.68 W/kg for the walking condition.