## 3 Human Derived Self-Balancing Control
### Balancing Experiment  
In order to experimentally simulate a user-exoskeleton interaction scenario, we used the robot Lucy to represent the exoskeleton and challenged its disturbance compensation by sinusoidal support surface tilts of peak-to-peak \(4^{\circ}\) and \(8^{\circ}\) in the body's sagittal plane. Such disturbance is relatively small compared to the capability of the system--for this reason, the robot is not expected to fall. The robot (Figure 2C) has 14 DoF. The control in the sagittal plane is implemented using 4 control modules \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Symbol** & **Quantity** & **Value** \\ \hline
**ANKLE** & & & \\ \(K_{p}\) & proportional gain & 119.57 & Nm/rad \\ \(K_{d}\) & derivative gain & 11.95 & Nms/rad \\ \(G_{ext}\) & external torque gain & 0.5 & \\ \(\omega_{ext}\) & External torque filter cutoff frequency & 5 & rad/s \\
**KNEE** & & & \\ \(K_{p}\) & proportional gain & 55.72 & Nm/rad \\ \(K_{d}\) & derivative gain & 0.458 & Nms/rad \\ \(G_{ext}\) & external torque gain & 0.5 & \\ \(\omega_{ext}\) & External torque filter cutoff frequency & 5 & rad/s \\
**HIP** & & & \\ \(K_{p}\) & proportional gain & 22.71 & Nm/rad \\ \(K_{d}\) & derivative gain & 5.67 & Nms/rad \\ \(G_{ext}\) & external torque gain & 0.5 & \\ \(\omega_{ext}\) & External torque filter cutoff frequency & 5 & rad/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Control parameters. (Figure 3B). The hypothetical exoskeleton, shown in Figure 1, has 3 DoF in the sagittal plane. In the scenario presented, the additional DoF in the back do not produce a relevant effect on the behavior. Figure 4A shows the body sway of all the body segments, computed on the basis of the internal sensors. All the segments are swaying together, i.e., the difference between the body segments' orientation in space is very small and not exceeds considerably \(1^{\circ}\). This suggests that it is legitimate to describe the kinematics of the body in this scenario with the sway of the body CoM (Figure 5). Figure 4: (**A**) body sway in space of the body segments in the sagittal plane computed using the internal sensors in the presence of a peak-to-peak \(8^{\circ}\) tilt and with the addition of an eccentric weight to the pelvis (compare Figure 2A). TS—trunk-in-space; PS—pelvis-in-space; LS—leg-in-space; SS—shank-in-space; FS—foot in space. All body segments move together in this scenario, and all sways are within a range smaller than \(1^{\circ}\); (**B**) stick figure showing the position of the segments at different times (every 10 s). As already shown in the classical work of [PERSON] and [PERSON] [24], the here implemented 'ankle strategy' turns the body into an inverted pendulum. Its COM is maintained close to the upright using primarily ankle torque. For example, during an evoked forward sway, muscles on the backside of the body are activated in a bottom-up way (separated by a few milliseconds) in the wake of maintaining the body segments aligned and upright. A backward sway evokes the same response pattern on the front side of the body. A different balance strategy, also described by [PERSON] and [PERSON] [24] is the 'hip strategy', which is seen for example when humans are standing on a narrow beam. As mentioned above (Section 2), balance is then maintained by rapid hip flexion/extension, creating horizontal shear forces on the body support--a method that is restricted in its usefulness and under normal standing conditions would be more exhausting and less efficient. A modified version of the ankle strategy is seen with large perturbations where the ankle joint torques tend to exceed its limit. Human subjects then tend to bend transiently the knees to get into a squat position [23]. Conceivably, use of the ankle strategy is restricted to lower body exoskeletons with actuated ankle joints, as for example in the exoskeleton Robot [14].