On the Observability and Observer Design on the Special Orthogonal Group Based on Partial Inertial Sensing

The aim of this article is to discuss the observability properties and observer design for the attitude of a rigid body, under conditions of partial inertial sensing. In particular, we introduce an observability analysis tool for the attitude dynamics when only accelerometer and gyroscope measurements are available, as in several robotics applications. In various scenarios, in fact, the measurement of the magnetic field via a magnetometer is unreliable, due to magnetic interferences. Herein, we first focus on a formal observability analysis, which reveals that the target dynamics is
weakly locally observable
, but not first-order observable. The lack of first-order observability prevents standard observers from achieving global convergence. Therefore, we discuss a more suitable approach for observer design to deal with this problem. The proposed approach is validated by providing numerical and experimental results. The former show that the proposed approach is able to achieve convergence (final error 0.004
$\%$
). Experiments validate our inference about observability and show the improvements brought by the proposed approach concerning the error convergence (final error 0.15
$\%$
).