SE2 left jacobians #12
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…SE2 group - FAILS for small tangent vecs (theta)
…pass unit test(s)
VascoSch92
reviewed
Feb 6, 2024
| @@ -82,14 +82,14 @@ def left_jacobian(cls, phi): | |||
| if phi.dim() < 1: | |||
| phi = phi.unsqueeze(dim=0) | |||
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| jac = phi.__class__(phi.shape[0], cls.dim, cls.dim) | |||
| jac = phi.__class__(phi.shape[0], cls.dim, cls.dim).to(phi.device) | |||
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| # Near phi==0, use first order Taylor expansion | |||
| small_angle_mask = utils.isclose(phi, 0.) | |||
| small_angle_inds = small_angle_mask.nonzero().squeeze_(dim=1) | |||
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| if len(small_angle_inds) > 0: | |||
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Implemented the SE(2) group jacobian (and inverse) in numpy and torch.
These did not seem to be covered in Barfoot and so the reference for the solution implemented in this PR is a Lie theory described in https://arxiv.org/pdf/1812.01537.pdf.
Specifically, I ported the left jacobian implementation from the C++ code here: https://github.com/artivis/manif/blob/6f2c1cd3e050a2a232cc5f6c4fb0d33b74f08701/include/manif/impl/se2/SE2Tangent_base.h
The paper does not provide a closed form solution for the inverse left jacobian, so I used MATLAB's symbolic toolbox to arrive at one - for both the general and small angle cases.
This has all been unit tested in the same style as SE(3) cases.
Incidentally, when testing this on GPU (torch version), I ran into a few problems with the SO2/base interfaces. This PR thus includes a few fixes along those lines.