[gabrielfrasantos]

This PR is wave 4 of the roadmap: the small consumers that build on the wave-3 foundation (frame chain, geometric Jacobian, chain dynamics model). The wave's mobile items (W4–W8) still wait on SE(2) (NT66) in numerical-toolbox-cpp.

As in earlier waves, each item is one self-contained commit following roadmap/DEPLOYMENT.md:

• header and coverage .cpp;
• the spec's test cases;
• CMake wiring;
• doc page and doc-table rows;
• removal of the item's roadmap/ spec and its rows in ROADMAP.md and roadmap/README.md.

Items

Commit	Item	Summary
b89828a	M32 RNEA with an external tool wrench	Adds ToolWrench plus an InverseDynamics overload that subtracts the environment's wrench in the backward pass. Satisfies τ(w) − τ(0) = −Jᵀw, which the tests check against GeometricJacobian.
22f7d63	M12 ComputedTorqueControl	Computes a_q = q̈_d + Kd·ė + Kp·e, then makes one InverseDynamicsModel call. With an exact model, the plant's tracking error matches the ideal error dynamics ë + Kd·ė + Kp·e = 0 step by step in closed loop.
cb58fd9	M11 ManipulabilityIndex	Yoshikawa index from J·Jᵀ or Jᵀ·J (whichever is not rank-deficient by shape) via LU. Velocity-ellipsoid axes and condition number via SVD; a near-singular guard. Works on any JacobianProvider.
0d855a2	M14 RedundancyResolution	q̇ = J⁺_λ·ẋ + (I − J⁺J)·q̇₀ on upstream solvers::DampedPseudoInverse (NT62). The projector is undamped and rank-thresholded, so secondary motion never reaches the task for any damping λ.
cf7a452	M10 CartesianSlerpInterpolation	Straight-line position plus shortest-arc quaternion SLERP on one time law. The time law is a template parameter, so there is no virtual call. Also returns the twist feed-forward (v; ω) = ṡ·(Δp; φ·k).
b47f46e	P2 PotentialField	Quadratic-then-conic attraction plus Khatib repulsion, clamped to a maximum speed. Each command reports Moving, Reached or Stalled, so local minima are detected rather than hidden.

Changes from the specs

• New test doubles:
  • dynamics::MockInverseDynamicsModel in robotics.dynamics_test_doubles, for M12.
  • kinematics::MockJacobianProvider in a new robotics.kinematics_test_doubles target, for M11.
• M14: the undamped_primary_task_is_exact test also asserts J·J⁺ = I. This covers the DampedPseudoInverse(q) accessor, which no spec case exercised.
• P2: the FieldStatus values are PascalCase (Moving, Reached, Stalled) to match the repo's other enums. The spec had them lowercase.
• Roadmap README: its canonical worked example pointed at the ComputedTorqueControl spec, which this PR deletes. It now points to ImpedanceControl.
• Build: robotics.trajectory now links numerical.motion_profiles, and the dynamics test target links robotics.kinematics for the M32 Jacobian cross-check.

Verification

• The host-single-Debug build and the coverage build (EMIL_ENABLE_COVERAGE=On) both pass 5/5 test executables.
• Merged gcov line coverage is 100% on every new or changed header.
• Reference values from the specs are met, including M14's 1e-5 exactness checks on a 7R arm (iiwa-like DH table) and M11's condition numbers within 0.1%.
• clang-format and scripts/validate-docs.py pass. No doc line exceeds markdownlint's 400-character limit, and doc tables are aligned.

Not run locally: the Qt simulator build, cppcheck, and SonarCloud. CI covers these.

---

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✅⚠️MegaLinter analysis: Success with warnings

Descriptor	Linter	Files	Fixed	Errors	Max errors	Warnings	Elapsed time
✅ ACTION	actionlint	7		0		0	0.48s
✅ CPP	clang-format	89	0	0		0	0.96s
✅ CPP	cppcheck	89		0		0	1.37s
✅ DOCKERFILE	hadolint	1		0		0	0.36s
✅ JSON	jsonlint	8		0		0	0.09s
✅ JSON	prettier	8	2	0		0	0.32s
✅ MARKDOWN	markdownlint	152	0	0		0	1.85s
✅ MARKDOWN	markdown-table-formatter	152	0	0		0	0.19s
⚠️ SPELL	lychee	195		2		0	16.09s
✅ YAML	prettier	12	0	0		0	0.43s
✅ YAML	yamllint	12		0		0	0.47s

Detailed Issues

⚠️ SPELL / lychee - 2 errors

[ERROR] failed to verify TLS certificate: invalid peer certificate: UnknownIssuer
📝 Summary
---------------------
🔍 Total..........217
🔗 Unique..........93
✅ Successful.....205
⏳ Timeouts.........0
🔀 Redirected.......5
👻 Excluded.........9
❓ Unknown..........0
🚫 Errors...........2
⛔ Unsupported......2

Errors in .github/workflows/static-analysis.yml
[403] https://binaries.sonarsource.com/Distribution/sonar-scanner-cli/sonar-scanner-cli-$ (at 37:21) | Rejected status code: 403 Forbidden

Errors in doc/kinematics/InverseKinematics.md
[ERROR] https://mathweb.ucsd.edu/~sbuss/ResearchWeb/ikmethods/iksurvey.pdf (at 125:169) | SSL certificate not trusted. Use --insecure if site is trusted

Hint: Followed 5 redirects. You might want to consider replacing redirecting URLs with the resolved URLs. Use verbose mode (`-v`/`-vv`) to see redirection details.
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Quality Gate passed

Issues
1 New issue
0 Accepted issues

Measures
0 Security Hotspots
98.9% Coverage on New Code
0.0% Duplication on New Code

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