Identifiability and identification of inertial parameters using the underactuated base-link dynamics for legged multibody systems

Abstract

In this paper we study the dynamics of multibody systems with the base not permanently fixed to the inertial frame, or more specifically legged systems such as humanoid robots and humans. The issue is to be approached in terms of the identification theory developed in the field of robotics. The under-actuated base-link which characterizes the dynamics of legged systems is the focus of this work. The useful mechanical feature to analyze the dynamics of legged system is proven: the set of inertial parameters appearing in the equation of motion of the under-actuated base is equivalent to the set in the equations of the whole body. In particular, when no external force acts on the system, all of the parameters in the set except the total mass are generally identifiable only from the observation of the free-flying motion. We also propose a method to identify the inertial parameters based on the dynamics of the under-actuated base. The method does not require the measurement of the joint torques. Neither the joint frictions nor the actuator dynamics need to be considered. Even when the system has no external reaction force, the method is still applicable. The method has been tested on both a humanoid robot and a human, and the experimental results are shown.