  This paper presents a contact-aided inertial-kinematic floating base
estimation for humanoid robots considering an evolution of the state and
observations over matrix Lie groups. This is achieved through the application
of a geometrically meaningful estimator which is characterized by concentrated
Gaussian distributions. The configuration of a floating base system like a
humanoid robot usually requires the knowledge of an additional six degrees of
freedom which describes its base position-and-orientation. This quantity
usually cannot be measured and needs to be estimated. A matrix Lie group,
encapsulating the position-and-orientation and linear velocity of the base
link, feet positions-and-orientations and Inertial Measurement Units' biases,
is used to represent the state while relative positions-and-orientations of
contact feet from forward kinematics are used as observations. The proposed
estimator exhibits fast convergence for large initialization errors owing to
choice of uncertainty parametrization. An experimental validation is done on
the iCub humanoid platform.
