MIME-VER-100 — MotorNode Step Response (Torque Mode, No Load)#

Date: 2026-04-30 Node under test: mime.nodes.actuation.motor.MotorNode Algorithm ID: MIME-NODE-100 Benchmark type: Analytical (Mode 2 independent) Test file: tests/verification/test_motor.py::test_ver100_torque_step_response Acceptance: relative RMS error of \(\omega(t)\) over a 1 s trajectory < 5 %

Goal#

Verify that MotorNode in torque-mode with no electrical model and no external load reproduces the analytical first-order velocity step response of a damped rotor:

\[ J \dot{\omega} = \tau - b \omega \quad \Longrightarrow \quad \omega(t) = \frac{\tau}{b} \left( 1 - e^{-bt/J} \right). \]

This is the simplest possible regression on the mechanical integration path. It exercises the semi-implicit-Euler step, the boundary-input plumbing for commanded_torque, and the rotor-pose composition into rotor_pose_world (the latter cross-checked by a separate test, not this one).

Configuration#

Parameter

Value

inertia_kg_m2 (\(J\))

\(1 \times 10^{-4}\) kg·m²

damping_n_m_s (\(b\))

\(5 \times 10^{-4}\) N·m·s

kt_n_m_per_a (\(k_t\))

not exercised in torque-mode

r_ohm, l_henry

not exercised in torque-mode

commanded_torque (\(\tau\))

\(0.01\) N·m (constant step)

commanded_voltage

\(0.0\)

commanded_velocity

\(0.0\)

parent_pose_world

identity

axis_in_parent_frame

\((0,0,1)\)

Timestep \(\Delta t\)

\(1 \times 10^{-4}\) s

Duration

\(1.0\) s (\(10^4\) steps)

JAX precision

float64 (via @pytest.mark.x64)

Analytical reference (numpy, double precision)#

\[ \omega_{\text{ref}}(t_n) = \frac{\tau}{b}\left( 1 - e^{-b t_n / J} \right), \qquad t_n = n \cdot \Delta t. \]

Steady-state value: \(\omega_\infty = \tau/b = 20 \text{ rad/s}\). Time constant: \(J/b = 0.2\) s.

Procedure#

  1. Construct the node and obtain its initial state.

  2. For \(n \in [0, 10^4)\): call node.update(state, {"commanded_torque": 0.01}, dt), append state["angular_velocity"] to a trajectory array.

  3. Compute omega_ref on the same time grid using the closed form above.

  4. Compute relative RMS error \(\sqrt{\overline{(\omega - \omega_{\text{ref}})^2}} \,/\, \omega_\infty\).

Result#

Status: PASS.

Relative RMS error is well under the 5 % acceptance, dominated by \(O(\Delta t)\) truncation of the semi-implicit-Euler integrator (theoretical bound at this step size: ~0.05 %). Exact value is recorded by the test; see latest CI run.

Scope and Limitations#

This benchmark validates only:

  • The torque-mode integration path of MotorNode.

  • The first-order analytical agreement of a rotor-with-damping ODE.

It does not validate:

  • The voltage-mode RL armature integration (covered by a separate test in the same file, not a verification benchmark).

  • The velocity-mode PI loop (separate test).

  • Cogging torque or rotor imbalance (out of scope for v1 — both MotorMeta.has_cogging and MotorMeta.has_imbalance_vibration default to False).

  • The interaction with RobotArmNode end-effector reaction (one-way coupling in v1; tracked as a known anomaly).

Reproducibility#

  • Hardware: any platform with JAX ≥ 0.4 (CPU is sufficient).

  • Software: MIME 0.1.0; MADDENING pinned in pyproject.toml.

  • RNG seed: not used (deterministic input).

  • Run with JAX_PLATFORMS=cpu .venv/bin/python -m pytest tests/verification/test_motor.py::test_ver100_torque_step_response -x -q if local GPU is contended.