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Different inertia parametrizations and Physical consistency
Pseudo Inertia and Log Cholesky Parametrization
This PR introduces the capability to use pseudo inertia and Log Cholesky parametrization within Pinocchio. These additions are based on recent advancements in ensuring the physical consistency of inertial parameters and provide a novel approach to parameterize the pseudo inertia matrix. The new functionalities include conversions to/from pseudo inertia, Log Cholesky parametrization, and related handy functions such as the Jacobian of Log Cholesky to dynamic parameters. Here you may find some short related notes on these parametrizations.
Key Contributions
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Pseudo Inertia Parametrization:
- Implementation of the pseudo inertia matrix as described in the paper Linear Matrix Inequalities for Physically-Consistent Inertial Parameter Identification: A Statistical Perspective on the Mass Distribution.
- Conversion functions to/from pseudo inertia.
- Ensuring physical consistency constraints via positive definiteness.
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Log Cholesky Parametrization:
- Incorporation of the Log Cholesky decomposition method as detailed in Smooth Parameterization of Rigid-Body Inertia.
- Functions for the Log Cholesky decomposition and reparameterization of the pseudo inertia matrix.
- Jacobian computation for Log Cholesky to dynamic parameters conversion, which may be useful for adaptive control.
This PR also partially close the problem of checking physical consistency mentioned in #2204