MIME-VER-121 — RobotArmNode Mass-Matrix Symmetry & PD#

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_ver121_mass_matrix_symmetric_pd Acceptance: $|M - M^{!\top}|F < 10^{-12}$ and $\lambda{\min}(M) > 0$

Goal#

Confirm that the joint-space mass matrix $M(q)$ produced by the CRBA-based mime.control.kinematics.crba.mass_matrix is symmetric and positive-definite at five random configurations on the 3-link planar fixture. These are necessary conditions for the forward- dynamics solve $M\ddot q = \mathrm{rhs}$ to be well-posed.

Configuration#

Parameter

Value

URDF

tests/control/fixtures/three_link_planar.urdf

Configurations

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

JAX precision

x64 enabled at module load

Procedure#

For each random $q$:

  1. Compute $M = \texttt{mass_matrix}(\mathrm{tree}, q)$ as a NumPy array.

  2. Verify $|M - M^{!\top}|_F < 10^{-12}$.

  3. Verify $\lambda_{\min}(M) > 0$ via numpy.linalg.eigvalsh.

Result#

PASS. Symmetric to within machine precision and PD across all 5 sampled configurations.

Scope and Limitations#

  • Five random configs is a smoke-grade sample. Adding configs is cheap but tests are already comprehensive across the kinematics-package suite.

  • Does not verify scale (numerical magnitude vs. analytical reference); scale is exercised indirectly by MIME-VER-122 / 123 / 124 where a wrong $M$ would produce wrong dynamics.

Reproducibility#

  • Seed: NumPy default_rng(20260430).

  • Run: JAX_PLATFORMS=cpu .venv/bin/python -m pytest tests/verification/test_robot_arm.py::test_ver121_mass_matrix_symmetric_pd -x -q.