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Identification Walkthrough

The problem

Dynamic models generated from CAD have 20-50% error in mass, inertia, and friction parameters — CAD doesn't know about cables, connectors, paint, or assembly tolerances. Accurate dynamic parameters matter for feedforward torque control, energy-efficient trajectory planning, collision detection, and any digital-twin/simulation use of the model.

Dynamic parameter identification recovers the true parameters from logged motion + torque data.

The model

The robot's equation of motion:

τ = M(q) q̈ + C(q, q̇) q̇ + G(q) + F(q̇)

is linear in the dynamic parameters φ (masses, first mass moments, inertia tensor entries, friction coefficients), so it can be rewritten as:

τ = W(q, q̇, q̈) · φ

W is the regressor matrix — computed purely from motion (q, q̇, q̈), independent of the unknown φ. Given enough logged (q, q̇, q̈, τ) samples from a sufficiently "exciting" trajectory, φ is recovered by linear least squares.

The pipeline

  1. Base parameter analysis — QR decomposition of W finds the minimal set of identifiable linear combinations of φ (many individual parameters aren't observable in isolation; only combinations of them are).
  2. Signal processing — filter noisy position/torque logs (median filter for outliers, Butterworth for noise) and estimate velocity/acceleration if not measured directly.
  3. Regressor construction — build W from the processed motion data.
  4. Parameter estimation — solve the linear least-squares problem for the base parameters (FIGAROH's solver supports OLS, WLS, ridge, and several constrained/robust variants).
  5. Validation — compare predicted vs. measured torques on held-out data.

Running it

from examples.tiago.utils.tiago_tools import TiagoIdentification
from figaroh.tools.robot import load_robot

robot = load_robot("path/to/robot.urdf", load_by_urdf=True)
identifier = TiagoIdentification(robot, "config/tiago_unified_config.yaml")
identifier.initialize()
result = identifier.solve(decimate=True, html_report=True)

verdict = identifier.verify()
print("PASS" if verdict.passed else "FAIL")

decimate=True downsamples the regressor to reduce redundant, highly correlated rows before the solve — cheaper and often better-conditioned than fitting on every raw sample.

From the command line:

cd examples/tiago
python identification.py                          # html-report + verify on by default
python identification.py --no-html-report --no-verify

For a one-line version without a robot-specific subclass, see Integration API.

What you configure

The identification: section of your unified config sets has_friction, has_actuator_inertia, has_external_forces, signal-processing (sampling_frequency, cutoff_frequency), and joint/velocity/torque limits used to sanity-check the logged data.

Expected results

  • Base parameters identified with under ~5% uncertainty
  • Torque prediction accuracy above ~95% (validation_correlation above the default 0.9 threshold) on held-out trajectories
  • A condition number well under the default 1000.0 threshold — see verification thresholds

The quality of all three depends heavily on the trajectory used to collect data — see Optimal Experiment Design.

Next steps