MIME-VER-122 — RobotArmNode Free-Fall Round-Trip#

Date: 2026-04-30 Node under test: mime.nodes.actuation.robot_arm.RobotArmNode Algorithm ID: MIME-NODE-102 Benchmark type: Analytical (Mode 2 independent) Test file: tests/verification/test_robot_arm.py::test_ver122_free_fall_round_trip Acceptance: $|\ddot q|\infty < 10^{-10}$ when $\tau = g(q)$, $\dot q = 0$, $F{\mathrm{ext}} = 0$

Goal#

Verify the consistency between the RNEA-derived gravity vector and the forward-dynamics solve. With zero velocity and zero external wrench, applying a torque equal to the gravity vector $g(q)$ must produce zero joint acceleration:

$$ M(q),\ddot q = \tau - c(q,\dot q) - g(q) = g(q) - 0 - g(q) = 0 \quad \Longrightarrow \quad \ddot q = 0. $$

Any deviation reveals a numerical inconsistency between mime.control.kinematics.rnea.gravity_vector, mime.control.kinematics.rnea.nonlinear_bias, and mime.control.kinematics.crba.mass_matrix (e.g., a sign error, inertia-tensor misorientation, or RNEA / CRBA spatial-algebra mismatch).

Configuration#

Parameter

Value

URDF

tests/control/fixtures/three_link_planar.urdf

Configurations

5 samples from $\mathcal{U}[-\pi, \pi]^3$ (seed 20260430)

Velocity

$\dot q = 0$ (so bias = $g(q)$ exactly)

Gravity

$(0, 0, -9.80665)$ m/s²

JAX precision

x64 enabled at module load

Procedure#

For each random $q$:

  1. Compute $g(q)$ via gravity_vector(tree, q, g_world).

  2. Compute $c(q, 0) + g(q)$ via nonlinear_bias(tree, q, 0, g_world) and assert it equals $g(q)$ to machine precision.

  3. Compute $M(q)$ via mass_matrix(tree, q).

  4. Solve $\ddot q = M^{-1}(g(q) - \mathrm{bias})$.

  5. Assert $|\ddot q|_\infty < 10^{-10}$.

Result#

PASS. All 5 configurations satisfy the round-trip identity to better than $10^{-10}$ rad/s².

Scope and Limitations#

  • Validates internal consistency between RNEA and CRBA, not agreement with an external reference. External agreement is exercised by the kinematics-package tests (tests/control/test_kinematics.py) which include an RNEA self-consistency benchmark on the same fixture.

  • Coriolis terms are not exercised here (because $\dot q = 0$). The PD-tracking benchmark (MIME-VER-124) implicitly stresses Coriolis via the inverse-dynamics feed-forward.

Reproducibility#

  • Seed: NumPy default_rng(20260430).

  • Run: JAX_PLATFORMS=cpu .venv/bin/python -m pytest tests/verification/test_robot_arm.py::test_ver122_free_fall_round_trip -x -q.