Duration figure

[moorepants]

@tvdbogert I was curious how the duration of the measured data affects the ability to accurately identify the parameters.

Setup:

• Simulate the closed loop model with no process (reference) noise under 10 cm of lateral platform motion for 600 seconds at 100 hz.
• Do not add any measurement noise to the data: states, platform accel, or joint torques.
• Segment the data into durations from short to long on a logarithmic scale so we.
• Directly identify the gains for each duration length using the states and joint torques.
• Indirectly identify the gains with direct collocation using the states and platform accel measurements and an initial guess including the measured states and known gains, i.e. give the know answer as the initial guess.
• Plot the relative error of the gains with respect to the known gains as a function of measured data duration.

Directly Identified (each plot is a gain):

Indirect:

Current conclusions:

• The longest duration of 60,000 nodes (240,008) unknowns takes IPOPT about 1.5 minutes to solve with the really good guess.
• The duration does not affect the ability to identify the gains in the direct method if there is no measurement noise. Makes sense.
• The duration does have some kind of affect on the ability to identify the gains with the indirect method. But the relative error is still really small, with <1% for most gains, and ~2% for one gain. There is some indication that relative error decreases with duration. There isn't much change from 10 to 100 seconds.

Next steps:

• I realized that these plots are probably more useful when measurement noise is applied. I'll run them again with measurement noise applied to everything.

[moorepants]

Ok, I reran this with:

• reference noise = 0
• measurement noise applied to: states, joint torques, and acceleration

Directly identified gain error:

Indirectly identified gain error:

Conclusions:

• For direct id the error decreases as duration increases. Seems like at least 10 seconds is needed to start getting decent results. But > 100 seconds seems best.
• For indirect with collocation it seems that there is little correlation between duration and error. These graphs also show some oddities. I'll go back and make sure a minimum was found. It could be that some of the optimizations are hitting the max iteration limit. For some reason the 100-300s identifications are wildy erroneous. And the bottom left gain (ankle angle to hip torque) is only good at one id.

I'll think about the direct id plot and make sure I'm doing things correctly.