MIME-VER-123 — RobotArmNode Gravity-Compensated Static Hold#

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_ver123_gravity_hold Acceptance: max joint drift \(< 10^{-3}\) rad after 1000 steps at \(\Delta t = 10^{-3}\) s

Goal#

Drive the arm with a gravity-compensation torque \(\tau = g(q)\) re-evaluated at the current configuration each step, integrate for 1000 steps at \(\Delta t = 10^{-3}\) s, and verify that the joint angles do not drift more than \(10^{-3}\) rad from the initial pose. This is a closed-loop check on the integrator: if integration error or any sign mistake leaked through, gravity compensation would no longer cancel gravity and the arm would fall.

Configuration#

Parameter

Value

URDF

tests/control/fixtures/three_link_planar.urdf

Initial \(q\)

\((0.3, -0.4, 0.5)\) rad

Initial \(\dot q\)

\(0\)

External wrenches

\(0\)

Joint friction

\(0\) (overridden in test fixture)

Gravity

\((0, 0, -9.80665)\) m/s²

Timestep

\(10^{-3}\) s

Steps

1000 (1 s of simulated time)

JAX precision

float64 (via @pytest.mark.x64)

Hot loop

jax.jit-compiled step(q, qd) → (q', qd')

Procedure#

  1. Set initial state \((q_0, \dot q_0 = 0)\).

  2. JIT-compile a step closure that recomputes \(\tau_{\mathrm{cmd}} = g(q)\) from the current \(q\) and calls arm.update.

  3. Run 1000 jitted steps.

  4. Compute drift \(\max_i |q_{1000,i} - q_{0,i}|\).

  5. Assert drift \(< 10^{-3}\) rad.

Result#

PASS. The arm holds within the tolerance — semi-implicit Euler is symplectic, so even tiny gravity-comp residuals do not accumulate secularly over the 1000-step horizon.

Scope and Limitations#

  • One initial pose. A more thorough test would sweep multiple poses, but the integrator is linear in the residual so a single pose is representative.

  • Tests integrator drift, not steady-state error under disturbance. Disturbance rejection is implicitly exercised by MIME-VER-124.

Reproducibility#

  • Run: JAX_PLATFORMS=cpu .venv/bin/python -m pytest tests/verification/test_robot_arm.py::test_ver123_gravity_hold -x -q.