No abstract

This paper addresses the problem of estimating the attitude and angular velocity of a rigid object by exploiting its second order kinematic model. The approach is particularly useful in cases where angular velocity measurements are not available and the attitude and angular velocity of an object need to be estimated from accelerometers and magnetometers. We propose a novel sensor modality that uses multiple accelerometers to measure the angular acceleration of an object as well as using magnetometers to measure partial attitude. We extend the approach of equivariant observer design to second order attitude kinematics by demonstrating that the special Euclidean group acts as a symmetry group on the system considered. The observer design is based on the lifted kinematics and we prove almost global asymptotic stability and local uniform exponential stability of the estimation error. The performance of the observer is demonstrated in simulation.

The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that any system posed in a homogeneous space can be extended to a larger system that is equivariant under a symmetry action. The equivariant structure of the system is exploited to propose a novel new filter, the Equivariant Filter (EqF), based on linearisation of global error dynamics derived from the symmetry action. The EqF is applied to an example of estimating the positions of stationary landmarks relative to a moving monocular camera that is intractable for previously proposed symmetry based filter design methodologies.