Tilt estimator for 3D non-rigid pendulum based on a tri-axial accelerometer and gyrometer

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.