System identification

Estimate dynamics from measurements#

MIT's system-identification chapter distinguishes estimating parameters in a known mechanical model from learning a model whose structure is not already known. For a robot with a known joint arrangement, the equations may be established while masses, inertias, friction, or joint offsets need estimation.

For example, measured joint positions, velocities, and commanded inputs can help fit a model of an arm's response. This model can support simulation and controller design.

Identification differs from state estimation#

State estimation asks what the robot's state is now, such as its current pose or velocity. Identification asks which model explains how that state changes. A practical identification procedure can use a state estimator as one stage.

The MIT notes also explain why inverse dynamics offers useful structure: rigid-body inverse-dynamics equations are affine in inertial parameters, whereas solving forward dynamics generally loses that property.

A small fitting error can hide a poor model#

Fitting one-step predictions and fitting an entire simulated trajectory are different objectives. The notes show that a model with small one-step error can still accumulate large simulation error.

Model complexity matters as well. A model must capture the behavior relevant to the intended task while remaining usable by the chosen planning and control methods.