Handlebar inertia value is not physically possible

[oliverlee]

Handlebar inertia (moment of inertia of the handlebars and steering column above the torque sensor about the steer axis) is found to be a value larger than the entire steering column without weight plates:

/* moment of inertia of steering assembly about the steer axis, kg-m^2 */
constexpr float STEER_ASSEMBLY_INERTIA_WITH_WEIGHT = 0.1942f; /* with 1 kg weight plate on each side of cross bar*/
constexpr float STEER_ASSEMBLY_INERTIA_WITHOUT_WEIGHT = 0.0828f; /* without weight plates */
constexpr float STEER_ASSEMBLY_INERTIA = STEER_ASSEMBLY_INERTIA_WITH_WEIGHT; /* default configuration */

/* moment of inertia of the handlebars and steering column above the torque sensor, about the steer axis 
 * determined from scripts/calculate_handlebar_inertia.py */
constexpr float HANDLEBAR_INERTIA = 0.118; /* kg-m^2 */

This is not physically possible as we remove mass but inertia increases. We need to determine why is this is the case.

[oliverlee]

Experimental measurement using springs and oscillation period determined that this value is 0.0413 kg-m^2

[oliverlee]

PR here: https://github.com/oliverlee/phobos/pull/100

[oliverlee]

Whipple model with benchmark parameters, forward velocity is fixed at 7.0 m/s

Behavior at system start, handlebar inertia = 0.0413 kg-m^2

Behavior at system start, handlebar inertia = 0.118 kg-m^2

[oliverlee]

Simulating the bicycle model, here's the output with zero torque input:

and with recorded input:

Note that the plots in the previous comment (running on the microcontroller) contain a Kalman filter. The rider steer torque should be zero as no one was applying torque when this data was recorded.

[oliverlee]

It looks like the measured handlebar inertia results in a subjectively worse simulation. This could be because we have modeling errors somewhere in the system and/or due to neglect of friction. In this case, the moment of inertia estimated by the script calculate_handlebar_inertia.py would account for these errors in the sense that it returns a value that best fits our model.

We should make an explicit note in saconfig.hwhy we use the script estimated inertia instead of the inertia measured from the spring experimental setup even though the number may not be physically possible.

[oliverlee]

This is related to issue https://github.com/oliverlee/phobos/issues/109 and essentially, there is the concept of the virtual inertia and physical inertia which are not necessarily equal.