Accuracy of the Euler integration about consim HOT 4 CLOSED

Interesting, I didn't know this semi-implicit scheme was second order. If you have a reference at hand that explains why I'd love to take a look. Otherwise I'm gonna look for one by myself.

from consim.

I was incorrect when saying second-order, but this method is much more stable in the sense that it preserves the mechanical energy of the system. See https://en.wikipedia.org/wiki/Semi-implicit_Euler_method for more details.
Euler explicit has very bad behavior with this aspect.

from consim.

Hello @jcarpent
I've implemented semi-implicit Euler and tested it on the quadruped jumping motion. Surprisingly it doesn't do better than explicit Euler. Here the mean infinity norm of the local integration error:

Semi-implicit Euler performs a bit better than explicit Euler for dt=10 ms, but in all other cases it does a bit worse than explicit Euler, and for one case the error goes out of the chart.
For small time steps (<=0.3 ms), the error seems to be basically the same as for explicit Euler.

from consim.

Given these results, it doesn't seem worth it to use semi-implicit Euler, so I am going to close this issue for now.

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