Recursive Least Squares with Log-Determinant Divergence Regularisation for Online Inertia Identification

This study presents a recursive algorithm for solv- ing the regularised least squares problem for online identifica- tion of rigid body dynamic model parameters with emphasis on the physical consistency of estimated inertial parameters. One of the geometric approaches is to use a regulariser that represents how close the pseudo-inertia matrix is to a given reference on the feasible manifold in the regression problem. The proposed extension enables memory-efficient online learning in addition to the benefits of geometry-aware convex regularisation using the log-determinant divergence of the pseudo-inertia matrix. Also, the recursive version endows the estimator with the capa- bility to deal with time-variation of parameters by introducing an optional forgetting mechanism. The characteristics of the recursive regularised least squares algorithm is demonstrated using the MIT Cheetah 3 leg swinging experiment dataset and compared to the existing batch optimisation method.