Identification Protocol

The protocol specifies the excitation trajectory—a carefully designed motion sequence for the robot that ensures persistent excitation. This means the control inputs must be rich enough to stimulate all dynamic modes of the system (e.g., inertial, Coriolis, friction effects) to make their parameters observable. Common designs include swept-sine waves, random steps, or optimized trajectories that maximize information content while respecting joint limits and velocity constraints.

This component defines the sensors, sampling rates, and synchronization methods for collecting input-output data. Inputs are the commanded actuator torques or currents; outputs are the measured joint positions, velocities, and sometimes accelerations. The protocol mandates ground truth alignment, ensuring all data streams are temporally synchronized and spatially registered to a common coordinate frame, which is critical for minimizing calibration error.

At the core of parameter estimation is the dynamic regressor, a mathematical model derived from the equations of motion (e.g., Newton-Euler or Lagrangian). It linearly relates measurable signals (joint states) to the unknown physics parameters (link masses, inertias, friction coefficients). The protocol selects the appropriate model structure—whether a full rigid-body model or a simplified one—defining which parameters are to be identified.

This step applies a numerical algorithm to solve the inverse problem posed by the dynamic regressor. Using the collected data, it computes the optimal set of parameters. Common methods include:

• Least Squares Estimation: For linear regressions with Gaussian noise.
• Bayesian Calibration: Treats parameters as probability distributions, useful for quantifying model uncertainty.
• Grey-Box Identification: Combines the physics-based regressor with data-driven residual modeling to capture unmodeled dynamics.

The final, critical component is quantitative validation. The protocol requires testing the identified model on a different set of validation trajectories not used during estimation. Performance is measured using fidelity metrics like:

• Normalized Mean Squared Error (NMSE) between predicted and actual torque.
• Trajectory tracking error under a standard controller. This step quantifies the transfer error expected when the model is used in simulation for policy training.

A formal identification protocol is fully documented, ensuring repeatability across different hardware units or labs. It includes:

• A bill of materials for the test setup.
• The exact software scripts for trajectory generation and data processing.
• The defined system ID pipeline from start to finish.
• Acceptance criteria for model fidelity. This standardization is essential for benchmarking different simulators and for reliable digital twin creation.

A fundamental protocol where a sudden, sustained change in actuator command (e.g., torque or voltage) is applied. The system's transient and steady-state response is recorded to identify first-order dynamics, time constants, and steady-state gains. This is often the first test for motors and simple linkages.

• Primary Use: Identifying basic inertial and frictional parameters.
• Key Output: Step response curve, used to compute rise time and settling time.
• Limitation: Provides poor excitation for higher-order dynamic modes.

A protocol where the system is excited by a sinusoidal torque or position command whose frequency increases continuously over time. This provides broadband excitation across a defined spectrum.

• Primary Use: Identifying frequency response, resonant modes, and damping characteristics.
• Key Output: Bode plots (magnitude and phase) showing system behavior vs. frequency.
• Advantage: Efficiently excites a wide range of dynamic modes in a single experiment.

A protocol that computes actuator commands to maximize the Fisher Information Matrix or minimize the condition number of the regressor matrix. The goal is to design motions that provide the best possible data for parameter estimation.

• Primary Use: High-precision identification of all inertial and friction parameters of multi-link robots.
• Method: Often formulated as a trajectory optimization problem, constraining motion to joint limits and torque bounds.
• Result: A trajectory that ensures persistent excitation and minimizes parameter covariance.

A protocol where identification data is collected while the system operates under feedback control (e.g., a PID position loop). Special techniques are required to avoid biasing estimates due to the correlation between noise and the control signal.

• Primary Use: Identifying systems that are unstable or dangerous to operate in open loop.
• Common Methods: Use of dither signals (small injected noise) or two-stage methods that first identify the closed-loop sensitivity.
• Challenge: More complex than open-loop identification but often necessary for real hardware.

A protocol where the robot is commanded to hold a series of static poses while external known loads (weights) are applied at the end-effector. The required joint torques to counteract gravity and the load are recorded.

• Primary Use: Precisely identifying link masses, center of mass locations, and gravitational parameters.
• Process: The robot acts as a precision scale. The linear relationship between measured torque and applied force is used to solve for mass parameters.
• Foundation: Forms the basis for calibrating the gravitational component of a dynamic model.

The core computational protocol. Measured joint positions, velocities, and accelerations are fed into a dynamic regressor matrix, which linearly relates these signals to the unknown inertial and friction parameters. Batch least-squares is then applied to solve for the parameters.

• Primary Use: The standard algorithm for processing data from excitation trajectories.
• Key Step: Accurate computation or filtering of joint accelerations is critical.
• Validation: Parameters are validated by simulating the identified model and comparing its output to a separate, unseen dataset.

System identification is the overarching process of constructing mathematical models of dynamic systems from measured input-output data. An identification protocol is a standardized procedure within this process. The goal is to characterize system behavior and estimate unknown physics parameters like mass, inertia, and friction coefficients. Key steps include:

• Designing excitation trajectories.
• Collecting sensor data (torque, position, acceleration).
• Applying parameter estimation algorithms.
• Validating the model with unseen data.

Parameter estimation is the core computational step of an identification protocol. It involves inferring the unknown constant values within a system's mathematical model from observed data. Methods range from least-squares optimization applied to a dynamic regressor to Bayesian calibration, which provides probabilistic distributions over parameters. Accurate estimation requires persistent excitation in the input signals to uniquely identify all dynamic modes.

An excitation trajectory is a deliberately designed sequence of control inputs or motions specified by an identification protocol. Its purpose is to persistently excite all relevant dynamic modes of the system. A well-designed trajectory:

• Covers the full operational workspace.
• Includes a rich mix of frequencies and accelerations.
• Enables the dynamic regressor to be well-conditioned for parameter estimation.
• Poor excitation leads to unreliable, non-unique parameter estimates and high model uncertainty.

A dynamic regressor is a mathematical formulation, often derived from the equations of motion (forward dynamics/inverse dynamics), that linearly relates measurable signals (joint positions, velocities, accelerations) to the unknown dynamic parameters. It is the foundation for many parameter estimation techniques. The structure is: Y(q, q̇, q̈) * Φ = τ, where Y is the regressor matrix, Φ is the vector of unknown parameters (inertias, masses), and τ is the measured torque.

Model fidelity is the ultimate goal of executing an identification protocol. It quantifies how accurately a simulation model represents the real system. After parameter calibration, quantitative validation is performed using fidelity metrics like mean squared error on force/torque or trajectory prediction. High fidelity minimizes the reality gap and simulation bias, leading to more successful sim-to-real transfer. Residual calibration error indicates unmodeled dynamics.

A system identification pipeline is the complete, automated workflow that encapsulates the identification protocol. It structures the end-to-end process:

1. Experiment Design: Generate excitation trajectories.
2. Data Collection: Execute motions on real hardware, log sensor data.
3. Pre-processing: Filter noise, perform ground truth alignment.
4. Model Selection: Choose a model structure (e.g., rigid-body dynamics).
5. Parameter Estimation: Run least-squares or Bayesian calibration.
6. Validation: Assess model fidelity on a validation dataset.