A Geometric Characterization of Observability in Inertial Parameter Identification
This solves a fundamental problem in robotics for system identification, enabling accurate modeling of robots like manipulators and legged systems, though it is incremental as it builds on existing linear systems theory.
The paper tackles the problem of determining which inertial parameters of an articulated robot are identifiable from motion data, presenting a geometric algorithm that tests identifiability across all configurations with finite conditions and no approximation, achieving provable correctness and O(N) complexity for N bodies.
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.