Observability in Inertial Parameter Identification

We present an algorithm to characterize the space of identifiable inertial parameters in system identification of an articulated robot. This problem has been considered in the literature for decades; however, existing methods suffer from common drawbacks. Methods either rely on symbolic techniques that do not scale, or rely on numerical techniques that are sensitive to the choice of an input motion. The contribution of this work is to propose a recursive algorithm for this problem that requires only the structural parameters of a mechanism as its input. This Recursive Parameter Nullspace Algorithm (RPNA) can be applied to general open-chain kinematic trees, and does not rely on symbolic techniques. Drawing on the exponential parameterization of rigid-body kinematics, classical linear controllability and observability results can be directly applied to inertial parameter identifiability. The high-level operation of the RPNA is based on a key observation – undetectable changes in inertial parameters can be interpreted as sequences of inertial transfers across the joints. This observation can be applied recursively, and lends an overall complexity of O(N) to determine the minimal parameters for a system of N bodies. MATLAB source code for the new algorithm is provided.