A Geometric Characterization of Observability in Inertial Parameter Identification

TL;DR

This paper introduces a geometric algorithm to determine inertial parameter identifiability in articulated robots, applicable to various systems, using a finite set of conditions without approximation, and based on linear systems theory.

Contribution

It provides the first provably correct, general solution for inertial parameter identifiability in open-chain kinematic trees, with an efficient recursive analysis method.

Findings

Algorithm tests identifiability across infinite configurations.

Applicable to industrial manipulators and legged robots.

Complexity of the method is linear in the number of bodies.

Abstract

This paper presents an algorithm to geometrically characterize inertial parameter identifiability for an articulated robot. The geometric approach tests identifiability across the infinite space of configurations using only a finite set of conditions and without approximation. It can be applied to general open-chain kinematic trees ranging from industrial manipulators to legged robots, and it is the first solution for this broad set of systems that is provably correct. The high-level operation of the algorithm is based on a key observation: Undetectable changes in inertial parameters can be represented as sequences of inertial transfers across the joints. Drawing on the exponential parameterization of rigid-body kinematics, undetectable inertial transfers are analyzed in terms of observability from linear systems theory. This analysis can be applied recursively, and lends an overall complexity of $O(N)$ to characterize parameter identifiability for a system of $N$ bodies. Matlab source code for the new algorithm is provided.