Replace Jacobian pseudo-inverse with Damped Least Squares (panic-free IK)

[kmolan]

Summary

Swaps JacobianIkSolver's pseudo-inverse step for Damped Least Squares (manipulability-based
dynamic damping) and adds opt-in null-space joint-limit avoidance (Liégeois). DLS solves min ‖JΔθ − e‖² + λ²‖Δθ‖², which replaces the pseudo-inverse's unbounded singular values 1/σ with σ/(σ²+λ²) — finite for all σ, so the step stays bounded and the normal matrix JJᵀ+λ²I is always invertible (SPD) instead of blowing up near singularities. Cleans up the logic to now have a single path for IK instead of the earlier three separate branches. Also added more tests for IK.

Changes

• One damped Cholesky solve (JJᵀ + λ²I, ≤6×6) replaces the three pseudo-inverse branches; the
  .unwrap() panic sites become a graceful InverseMatrixError.
• λ² = 0 when well-conditioned, so DLS reduces exactly to the old pseudo-inverse.
• New set_joint_limit_avoidance_gain (default 0.0 = inert) + damping setters, all with doctests.
• New 7-DOF fixture, integration/unit tests (singularity, avoidance, locked joints, fuzz), and a
  before/after benchmark writeup.

Compatibility

Default gain = 0 ⇒ existing results unchanged; only near-singular behavior changes (panic → bounded).
Ship as 0.33.0.

Results

Ran examples/ik_benchmark.rs before and after my changes. Comparison result:

i7-12650H, --release, 200 seeded solves/regime.

Robustness / accuracy (residuals over successes)

Target set	Success (before → after)	Panics/Non-finite	Rot residual mean (before → after)
Well-conditioned	100% → 100%	0 / 0	2.19e-3 → 2.19e-3 (identical)
Near-singular	9.0% → 13.0%	0 / 0	1.23e-3 → 1.91e-4 (~6× cleaner)
Redundant + limits	99.5% → 99.5%	0 / 0	9.10e-2 → 9.10e-2 (identical)

Timing (criterion mean vs saved before baseline)

Benchmark	Before	After	Change
bench_redundant_constrained (m=5, n=6)	7.11 µs	4.24 µs	−40.3%
bench_wellconditioned (m=n=6)	3.86 µs	4.43 µs	+14.7% (~+0.57 µs)

Well-conditioned & redundant results are unchanged (backward-compat); near-singular stays finite with
much cleaner solutions. Redundant path is 40% faster (Cholesky replaces SVD); the square path costs
~0.57 µs more for the damping (negligible on a sub-5 µs solve).