Simplified Q1 and Q2 terms for Gal(3) and SEn(3) left Jacobian matrix - #8
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giuliodelama wants to merge 2 commits into
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Simplified Q1 and Q2 terms for Gal(3) and SEn(3) left Jacobian matrix#8giuliodelama wants to merge 2 commits into
giuliodelama wants to merge 2 commits into
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giuliodelama
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Jul 7, 2025
giuliodelama
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- Reduced complexity of the Q1(w, z) and Q2(w, z) calculation by considering that w^w^z^w^ = w^z^w^w^ and w^w^z^w^w^ = -||w|| w^z^w^
- Tested!
…n matrix - Reduced complexity by considering w^w^z^w^=w^z^w^w^ and w^w^z^w^w^=-||w||w^z^w^ - Tested!
- U1(w) = SO3.Gamma1(w) - SO3.Gamma2(w)
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Pull request overview
This PR simplifies the closed-form expressions used in the Gal(3) and SEn(3) left Jacobian computations by reducing redundant high-order matrix products and reusing SO(3) helper matrices (e.g., Gamma2) to streamline intermediate terms.
Changes:
- Simplified the Q1 term (and corresponding coefficient) used in SE(3)/SEn(3) and Gal(3) left Jacobians by removing an algebraically redundant matrix-product term.
- Simplified the Gal(3) Q2 term by reducing the number of basis matrix products and collapsing coefficients accordingly.
- Removed
Gal3leftJacobianU1and replaced its usage with the equivalentSO3JL - SO3Gamma2formulation.
Reviewed changes
Copilot reviewed 2 out of 2 changed files in this pull request and generated 1 comment.
| File | Description |
|---|---|
| include/groups/SEn3.hpp | Simplifies the SE(3) Q-term computation used inside SEn(3) Jacobian-related logic. |
| include/groups/Gal3.hpp | Refactors Gal(3) left/inverse-left Jacobian construction and simplifies Q1/Q2 computations (including removing U1). |
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| FPType ang_p6 = ang_p5 * ang; | ||
| FPType ang_p7 = ang_p6 * ang; | ||
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| FPType c0 = 1 / 6; |
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