Comments (2)
In the test shown above the matrix exponential was used for the prediction, but not really for the integration (actually it was used also for the integration, but with such a small time step 0.1ms that it hardly played a role). In the next test, I should instead use the exponential for integrating with a large time step, to see whether the overall state integration is accurate. If it's not (as I expect, given my previous tests reported in the issue #9 ) then it means that some of the other terms in the dynamics are changing too fast for the time step used. Once I've identified which terms are causing this problem, I could consider having intermediate steps in which I only update these terms, without recomputing the matrix exponential.
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Here another few examples of nontrivial force predictions using the matrix exponential. All force predictions are over an horizon of 5 ms, whereas the ground truth is computed with a time step of 0.1 ms. In these examples we can appreciate how the matrix exponential is able to predict complex force trajectories that have varying trends (e.g., first increase and then decrease).
This one is very nice and corresponds to the beginning of the simulation, where we start with zero contact force and the matrix exponential predicts correctly the sudden rise of the contact forces. I think this is encouraging for the use of exponential integrators in case of impacts:
In this example the force first decreases rapidly, then it increases slowly, and then in decreases again, but slowly, so we have 3 trends in only 5 ms. The force prediction matches quite well the first two trends, but then fails to predict the last decrease.
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Related Issues (20)
- First benchmark Exponential vs Euler HOT 9
- Bug in exponential integrator without double integral HOT 5
- Results with seldom updates of matrix exponential HOT 2
- gcc internal error segmentation fault
- Reset of contact state HOT 4
- New method for friction cone constraints HOT 1
- Sanity check: Sliding point mass HOT 3
- Integration accuracy without contacts HOT 7
- Accuracy of the Euler integration HOT 4
- Potential influcence of the cone projection HOT 2
- ExponentialSimulator accuracy with nonzero impact velocity HOT 5
- EulerSimulator discontinuity in friction force during sliding HOT 2
- bug in c++ exponential simulator HOT 3
- Quadruped Trot Results HOT 7
- Quadruped Jump Results HOT 3
- Romeo walking Results HOT 4
- Quadruped Squat Results
- missing reference trajectory HOT 1
- few issues with HalfPlane HOT 2
- Exponential VS Rigid-contacts HOT 9
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