System_Identification

Physically-Consistent Parameter Identification of Robots in Contact.

This repository provides an offline system identification pipeline to estimate physically-consistent inertial parameters of legged robots from joint torque measurements. The main focus is to deal with contact-rich dynamics of legged robots and guarantee physical feasibility of the identified parameters (e.g., positive-definite rotational inertia, valid mass and COM relationships), which is essential for stable simulation, control, and downstream estimation.

The codebase includes two complementary solvers:

• (1) Convex LMI-based identification (SDP)
  A semidefinite-programming formulation with physical-consistency constraints expressed as LMIs. Solved via CVXPY with the MOSEK backend.

• (2) Nonlinear least-squares (NLS) with log-Cholesky parameterization
  A nonlinear formulation that enforces physical consistency through a log-Cholesky parameterization of inertia-related matrices, enabling unconstrained optimization while maintaining valid inertial quantities by construction.

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Key features

• Offline identification from joint torques (and corresponding trajectories)
• Enforces physically-consistent inertial parameters (no “non-physical” inertia tensors)
• Two solver backends: LMI/SDP and NLS (log-Cholesky)
• Robot model loading via URDF / Pinocchio
• Demos and example robot description files included

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Repository structure (high-level)

• src/ : main identification code (dynamics, solvers)
• utils/ : utilities (plotting, etc.)
• demo/ : runnable example scripts
• data/ : example datasets / logs
• files/spot_description/ : example robot model assets (URDF/meshes/etc.)
• environment.yml : conda environment specification

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Installation

(1) Clone

git clone https://github.com/ShahramKhorshidi/system_identification.git
cd system_identification

(2) Create the conda environment

Using the provided environment file:

conda env create -f environment.yml
conda activate sys_idn

(3) Installing MOSEK (required for the LMI/SDP solver)

The LMI solver relies on MOSEK as the SDP backend (via CVXPY). MOSEK requires (i) installing the Python package and (ii) installing a license.

(i) Install the MOSEK Python package

Recommended (Conda):

conda install -c mosek mosek

(ii) Get a license (academic or trial)

Personal Academic license is free for faculty/students/staff at degree-granting institutions (request must use an academic email).

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Run the identification

(1) Run a demo

Check the demo/ folder for example scripts/notebooks. Typical workflow:

• Load a robot model (URDF + meshes) via Pinocchio
• Load trajectories / torque measurements
• Run either:
  • LMI/SDP solver (physically-consistent via convex constraints)
  • NLS log-Cholesky solver (physically-consistent via parameterization)
• Export identified parameters and evaluate reconstruction error / residuals

python demo/run_identification.py --robot spot --solver lmi
python demo/run_identification.py --robot spot --solver nls

The data from Spot quadruped includes 10,500 samples of the robot (collected at 100 Hz) performing various trajectories, such as base wobbling, squatting with all feet in contact, forward-backward walking, and side-to-side walking.

(2) Adding a new robot

The framework is robot-agnostic and can be extended to new platforms by providing a robot model and a corresponding configuration file.

(i) Robot description (URDF)

To add a new robot:

• Include the robot URDF file and associated assets (meshes, materials).
• Place them under:

files/<robot_name>_description/

• The URDF must define:
  • Correct joint ordering
  • Link inertial parameters (used as nominal values)
  • Consistent link and frame naming

(ii) Robot configuration file

For each robot, a YAML configuration file must be provided.
Use spot_config.yaml as a reference template.

The configuration file specifies:

• name: robot name
• mass: robot mass
• link_names: list of links included in the identification
• end_effector_frame_names: frames used for contact modeling

The entries in link_names and end_effector_frame_names must exactly match the corresponding link and frame names defined in the URDF. Any mismatch will lead to incorrect regressor construction or runtime errors.

(iii) Mesh files (required for LMI solver)

When using the LMI solver, geometric information is required to construct bounding ellipsoids for each link, which enforce physical consistency of the inertial parameters.

Therefore:

• Each identified link must have an associated mesh file (or a rough geometric approximation).
• Mesh files must:
  • Be placed in the robot description folder
  • Have the same name as the corresponding link
  • Represent a reasonable approximation of the link geometry

These meshes are used only for physical consistency constraints and do not need to be visually accurate.

(iv) Updating the demo script

After adding the robot description and configuration:

• Register the robot in demo/run_identification.py
• Include robot trajectories for identification in the data folder
• Run:

python demo/run_identification.py --robot <robot_name> --solver <solver_name>

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Citation

If you use this repository in an academic work, please cite the following paper:

@inproceedings{khorshidi25icra,
  title={Physically-Consistent Parameter Identification of Robots in Contact}, 
  author={Khorshidi, Shahram and Dawood, Murad and Nederkorn, Benno and Bennewitz, Maren and Khadiv, Majid},
  booktitle={Proc. of the IEEE International Conference on Robotics and Automation (ICRA)}, 
  year={2025}
}