[gabrielfrasantos]

Implements roadmap item M27 from roadmap/trajectory/TimeOptimalPathParameterization: TOPP-RA (Pham and Pham, IEEE T-RO 34(3), 2018). This was the last roadmap spec, so roadmap/ now holds no pending specs.

What

robotics/trajectory/TimeOptimalPathParameterization.hpp contains:

• PathGeometry<T, Dof>: an interface for the fixed path q(s), q'(s) and q''(s) on s ∈ [0, 1].
• PathCoefficients, JointBounds and PathConstraints<T, Dof>: the interface for the torque coefficients τ = a·s̈ + b·ṡ² + c and the joint bounds.
• InverseDynamicsPathConstraints<T, Dof>: the production adapter. It builds a, b and c from any dynamics::InverseDynamicsModel (M29) with three passes per point.
• TimeOptimalPathParameterization<T, Dof, Grid>:
  • Parameterize(): a backward pass builds the controllable sets with exact Fourier–Motzkin projections of each stage polygon, with no iterative LP. A greedy forward pass then takes the largest control that stays inside them. It returns false if a set is empty, if 0 ∉ K₀, or if the profile cannot leave rest.
  • Sample(t): binary search over the stage start times, then the constant-s̈ stage kinematics mapped through the path. It returns std::nullopt until Parameterize() succeeds.
  • TotalTime().

There is no heap, no recursion, no exceptions, and every buffer has a compile-time size.

New test doubles in robotics/trajectory/test_doubles (robotics.trajectory_test_doubles): MockPathGeometry and MockPathConstraints. robotics.trajectory now links robotics.dynamics.

Deviations from the spec

• Interface name: the spec's JointLimits interface is called PathConstraints, and its adapter InverseDynamicsPathConstraints. This keeps them distinct from M1's dynamics::JointLimits<T>.
• Two extra tests: the spec's cases miss two failure branches.
  • stationary_joint_overload_empties_controllable_set covers an empty controllable set.
  • zero_velocity_bound_stalls_at_rest covers a profile that cannot leave rest.
• Extra assertion: the adapter test also reads Bounds().
• Stage-start times in the continuity test: the planner keeps them private, so the test finds each interior one by bisecting on the sampled position.
• Tolerance ε: a fixed 64·numeric_limits<T>::epsilon() instead of a per-row relative scale.
• Roadmap: the manipulator table and the roadmap/README.md index now say every item has shipped. The canonical-example sentence points to the shipped doc, and its spec stays in the git history.

Verification

• host-single-Debug and coverage builds: ctest 7/7, 12/12 TOPP tests.
• 100% merged line coverage on the header (126/126).
• The spec's reference values reproduce in float:
  • Bang-bang totals: 2.000064 and 4.000128.
  • Velocity-limited total: 2.063492.
  • Coupled two-joint total: 2.256496, with a 0.0178 torque excursion between gridpoints.
• Clang -Wall -Wextra -Werror -Wshadow with -DROBOTICS_TOOLBOX_COVERAGE_BUILD.
• clang-format --dry-run --Werror and the forbidden-pattern check.
• scripts/validate-docs.py passes, and no doc line exceeds 400 characters.
• Not run locally: MSVC, cppcheck, SonarCloud.

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✅⚠️MegaLinter analysis: Success with warnings

Descriptor	Linter	Files	Fixed	Errors	Max errors	Warnings	Elapsed time
✅ ACTION	actionlint	7		0		0	0.69s
✅ CPP	clang-format	212	0	0		0	2.36s
✅ CPP	cppcheck	212		0		0	4.56s
✅ DOCKERFILE	hadolint	1		0		0	0.64s
✅ JSON	jsonlint	8		0		0	0.08s
✅ JSON	prettier	8	2	0		0	0.39s
✅ MARKDOWN	markdownlint	84	0	0		0	2.33s
✅ MARKDOWN	markdown-table-formatter	84	0	0		0	0.26s
⚠️ SPELL	lychee	132		2		0	2.26s
✅ YAML	prettier	12	0	0		0	0.54s
✅ YAML	yamllint	12		0		0	0.56s

Detailed Issues

⚠️ SPELL / lychee - 2 errors

[ERROR] failed to verify TLS certificate: invalid peer certificate: UnknownIssuer
📝 Summary
---------------------
🔍 Total..........379
🔗 Unique.........129
✅ Successful.....367
⏳ 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.
Hint: You can configure accepted/rejected response codes with `-a` or `--accept`

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Quality Gate passed

Issues
1 New issue
0 Accepted issues

Measures
0 Security Hotspots
99.5% Coverage on New Code
0.0% Duplication on New Code

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