The objective of the control algorithm of the four-link inverted pendulum was to maintain stability while the model is exposed to six-DOF ship motion as recorded from the sea trial, and those forces should be able to correlated to the forces and motions that were measured for each human subject during the sea trial. Thereby, the control algorithm should be similar to actual human balance control.
The image below shows a visual overview of the design problem. It shows the control moments as they are applied to each link and the mass distribution between the links as a percentage of the total mass. Since the control moments are generated at the joints, they will contribute equal and opposite torques to the two links they are connected to. One can immediately see that care must be taken to balance the moments within each individual link such that the desired orientation is reached, and to coordinate the moments between links such that the very large torso mass does not cause the lower links to buckle.
A standard method for controlling an inverted pendulum model in shipboard environments is to use full-state feedback control to maintain a vertical orientation with respect to inertial coordinates. In such a case, it would be assumed tat the magnitude of the restoring control moment would be directly proportional to the displacement and velocity of the centre of mass relative to the deck attachment point. While this is a logical expectation, it was found from the experimental data that the magnitude of the reaction moments did not consistently correlate to body displacements. It was found, however, that the moments correlated very well to the magnitude of the angles that the total acceleration vector made with respect to the ship. This makes sense from a sensory-control point of view. The experiments took place in an enclosed area within the ship such that participants did not have any indicators of the orientation of themselves with respect o the inertial coordinate system. In such a case, they were forced to do their best to (1) opposite the effects of the total acceleration of the ship, and (2) maintain upright stance within the ship frame in order to carry out their assigned tasks.
The final control system consisted of two components.
1) A component focused on aligning the inverted pendulumís centre of mass with the ship acceleration vector by applying closed-loop control torques to the ankle joint and open-loop torques to the other joints.
2) A closed-loop component focused on minimizing the relative displacement and velocity between body segments.
Here is a video that shows the controller in action:
The results of the simulation for a subject standing at 0 degrees with respect to the ship centerline are shown below. It can be observed that the results are in phase for roll (side-to-side rotation of the person) but not so much for pitch. The moments required to maintain balance for the model are greater than that than the experimental data due to simplifications in the model.
Below are shown the results for a subject standing at 90 degrees with respect to the ship centerline. It can be seen that the results are very close for pitch (front-back rotation of the person) but not for roll.
Based on the results above, it appears that the accuracy of the model depends not on how well the person represents an inverted pendulum in the roll or pitch directions, but on the magnitude of the ship motions.
For each of the graphs above, for each of the test cases (47 in total spread across 8 participants), a correlation coefficient (between -1 and 1) was calculated with represents how well the two data sets matched. The results were then plotted:
This graph shows that roll moments consistently correlated for a person standing at 0 degrees and the pitch moments consistently correlated for a person standing at 90 degrees with respect to the ship centerline.
This final set of graphs compares the direction of best X and Y torque correlations (4BAR) with the direction of greatest X and Y ship motion (Ship). The third value (BVH) is the direction of greatest moment from the experimental data. It can be seen in the graphs that the direction of greatest ship motion and the direction of greatest correlation between the model and experimental data are very close (the angle between the red and blue lines is very small).