T-111: SO-100 manipulator dynamics via Featherstone ABA (3rd real robot)

[machinavitalis]

Makes "compile a calibrated robot" true for the zoo's first manipulator. Zoo status: 3 of 4 robots now end-to-end (cartpole, crazyflie, so100).

Why it's different

A manipulator's forward dynamics need M(q)⁻¹, which the lowering coverage table has no solve for. The lowerable route is Featherstone's Articulated Body Algorithm — O(n) forward dynamics using only spatial matmuls and scalar reciprocals 1/D_i, never forming a matrix inverse.

What

• jaxility/zoo/so100/_dynamics.py — the ABA (spatial [angular;linear] algebra); the spatial tree (transforms, axes, per-link mass/com/inertia) is read from the calibrated Robot so calibration propagates.
• so100 __init__ — _dynamics_factory returns (f, (12,), (6,)); the entry is now a real dynamics factory.
• Lowering (jax_to_casadi.py) — three general completeness fixes that unblock rigid-body dynamics (and any matrix-heavy JAX fn), each with capability tests:
  • broadcast_in_dim: rank-1→rank-2 row/col promotion + scalar→vector materialization (a scalar feeding a matmul must be a real column, not a scalar-multiply).
  • dot_general: lift numpy constants; dispatch on contracting dims so a 1D·1D inner product lowers to aᵀ @ b (scalar), not a 6×6.
  • add/sub/mul/div: broadcast non-scalar shapes (outer products u[:,None] * u[None,:]).

Verified

ABA matches MJX functional_dynamics to ~1e-5 (manipulator grade), lowers to CasADi (== JAX to 9e-13), calibration propagates. Full unit suite green (520 passed).

Honest fidelity note

so100 is validated to manipulator grade, not ULP. An independent ABA and MuJoCo's internal cinert CRB diverge ~1e-6 on this featherweight arm (distal inertias ~1e-5) — a deterministic representational floor, not a bug or round-off (established by an exhaustive debugging pass: FK exact 1e-16, com-Jacobian gravity exact 5e-17, longdouble-invariant). Tested at a 1e-4 bound.

so100's WBC OCP template is a T-024 follow-on, so jaxility build so100 fails structurally (like crazyflie) until it lands. Doc-drift: CLAIMS / KNOWN_GAPS / README + zoo tests updated.

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