Drop a held tail instead of appending a duplicate end knot

[Yuan-Xinyi]

Stack

• Base: feat/differentiable-toppra (Replace external TOPPRA with differentiable CPU/CUDA retiming #724)
• Depends on: Replace external TOPPRA with differentiable CPU/CUDA retiming #724
• Proposed as a follow-up to Replace external TOPPRA with differentiable CPU/CUDA retiming #724; it can also be folded into it.

Description

#724 keeps the previous waypoint cleanup exactly, including its final step: when the last sample was merged as a duplicate, it is appended again. A path that ends in repeated samples therefore keeps a zero-length last segment. The not-a-knot spline bends back through it, and because the knot count changes, every knot's uniform spacing changes too — the whole curve moves, not just the tail.

That tail is exactly what a batched NMG rollout produces: an environment that converges early holds its pose while the others finish. With the current cleanup, an environment's retimed trajectory depends on which other environments share its batch.

This PR moves the last kept knot onto the final sample instead of appending it, in both the NumPy reference (_toppra.py) and the Warp preparation kernel (_warp/toppra.py), so the two stay identical. Two edge cases are kept deliberately:

• a lone first point still gains the final sample when they differ at all, so a move below the tolerance keeps a positive duration, as Replace external TOPPRA with differentiable CPU/CUDA retiming #724 intends;
• an all-identical row stays stationary.

Dependencies: none.

Type of change

• Bug fix (non-breaking change which fixes an issue)

Measured evidence

A real NMG rollout (7 samples, Franka FR3 limits), retimed alone and with four held samples appended, on #724 as-is and with this change:

	knots kept	duration, alone	duration, held tail
#724	7 → 8	0.9933 s	1.0553 s (+6.2%)
this PR	7 → 7	0.9933 s	0.9933 s

NumPy and Warp agree to 1e-15 in both cases.

The one-joint case [0.3, 0.3, 0.5, 0.5] shows the mechanism directly. #724 keeps three knots; the not-a-knot fit through them is a parabola that overshoots the goal to 0.525 before returning. With this change it keeps two and moves monotonically to 0.5.

Measured before #724 with the external toppra package, which had the same cleanup: dashed is the same problem inside a batch, solid is the problem alone. After about 0.75 s the batched trajectory departs, gains an extra reversal before the goal, and ends 60 ms later. #724 reproduces the same knot list, so it reproduces this.

Validation

• pytest tests/compute/test_toppra.py tests/sim/motion/planners/test_toppra_batched.py --run-gpu — 97 passed.
• pytest tests/compute/ tests/sim/motion/ — 1151 passed, 111 skipped.
• New tests: a held tail leaves the duration, sampled positions and fitted path unchanged, at the reference, Warp (CPU and CUDA) and planner levels; and the [0.3, 0.3, 0.5, 0.5] case no longer reverses. Four of them fail on Replace external TOPPRA with differentiable CPU/CUDA retiming #724 as-is.
• test_legacy_waypoint_cleanup_preserves_spline_geometry fixed the old knot list; its held-tail case now expects [0, 3] instead of [0, 2, 3], it gains a move-then-hold case, and it is renamed for what it now checks. The other cases are unchanged.
• black . — clean. check_api_docs.py — aligned, no public API change. context.py check — ok; planner-details.md no longer says the final knot is preserved and states the held-tail rule instead.

Checklist

• I have run the black . command to format the code base.
• I reviewed affected documentation and agent context, updated it where needed, or explained why no update was needed.
• Public API changes are reflected in the API docs (python docs/scripts/check_api_docs.py), if applicable
• I have added tests that prove my fix is effective or that my feature works
• Dependencies have been updated, if applicable. No dependency changes were required.

🤖 Generated with Claude Code

[greptile-apps]

Confidence Score: 5/5

[Medium risk] Changes trajectory path deduplication logic in motion planning.

The PR appears safe to merge; no actionable regression was identified.

Summary

The PR changes NumPy and Warp waypoint cleanup to replace the last retained knot with a held final sample instead of adding a duplicate end segment.

• Adds reference, Warp, and planner-level coverage for held tails.
• Updates motion-planning context to describe the new behavior.

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