Quadruped Jump Results about consim HOT 3 CLOSED

Looking at the integration error of the exponential integrator over time:

It seems to be highly correlated to the norm of the robot velocity:

This is reasonable I think, and indeed it happens also when the robot is in the air.
However, this correlation is much less evident for the Euler integrator error (except when the robot is in the air):

My guess is that when the robot is in contact, most of the Euler integration error comes from the contact forces variations during the time step, which are rather independent of the robot velocity norm. Instead, for the Exponential integrator, most of the integration error comes from the variations during the time steps of other terms of the dynamics (e.g., Mass matrix, gravity vector), which are well correlated with the robot velocity norm. This is coherent with the observation that using the exponential integrator the integration error is roughly the same when the robot is in contact or not, which in my opinion is a great result.

from consim.

I forgot to mention that the robot is in the air in the time interval [1, 1.7] s.

from consim.

New results for the same test. Here I'm showing the local integration error as a function of the computation time (per time step, which is 10 ms in this test):

Here Euler is more competitive than in the trot test, but it still never beats the best Exponential integrator, even though sometimes it beats the default Exponential. The best number of matrix multiplications for expm is either 1 or 0.

from consim.