  State of the art legged robots are either capable of measuring torque at the
output of their drive systems, or have transparent drive systems which enable
the computation of joint torques from motor currents. In either case, this
sensor modality is seldom used in state estimation. In this paper, we propose
to use joint torque measurements to estimate the centroidal states of legged
robots. To do so, we project the whole-body dynamics of a legged robot into the
nullspace of the contact constraints, allowing expression of the dynamics
independent of the contact forces. Using the constrained dynamics and the
centroidal momentum matrix, we are able to directly relate joint torques and
centroidal states dynamics. Using the resulting model as the process model of
an Extended Kalman Filter (EKF), we fuse the torque measurement in the
centroidal state estimation problem. Through real-world experiments on a
quadruped robot with different gaits, we demonstrate that the estimated
centroidal states from our torque-based EKF drastically improve the recovery of
these quantities compared to direct computation.
