  The paper presents a new observer for tilt estimation of a 3-D non-rigid
pendulum. The system can be seen as a multibody robot attached to the
environment with a ball joint. There is no sensor for the joint position of the
sensor. The estimation of tilt, i.e. roll and pitch angles, is mandatory for
balance control for a humanoid robot and all tasks requiring verticality. Our
method obtains tilt estimations using encoders on other joints and inertial
measurements given by an IMU equipped with tri-axial accelerometer and
gyrometer mounted in any body of the robot. The estimator takes profit from the
kinematic coupling resulting from the pivot constraint and uses the entire
signal of accelerometer including linear accelerations. Almost Global
Asymptotic convergence of the estimation errors is proven together with local
exponential stability. The performance of the proposed observer is illustrated
by simulations.
