Groupe d’études et de recherche en analyse des décisions

Observer design on SO(3) - Fast convergence and practical considerations

James Richard Forbes Professeur agrégé, Département de génie mécanique, Université McGill, Canada

Robotic vehicles require accurate knowledge of their position and orientation to execute autonomous maneuvers. However, orientation, also referred to as attitude, cannot be directly measured. Instead, the attitude of a vehicle must be ascertained from a variety of available measurements, many of which may be of poor quality. Complicating matters is the fact that direction cosine matrices (DCMs), which are a global and unique representation of attitude, are elements of the special orthogonal group, SO(3). As such, linear estimation methods are not directly applicable to estimation of position and orientation. This talk will discuss observer design on SO(3) within a deterministic framework. In particular, an alternate attitude error function to what is typically used in the literature is presented and used in Lyapunov analysis. The alternate attitude error function leads to a different innovation term that in turn results in estimator dynamics that have superior convergence properties for large initial estimation error compared to existing schemes in the literature. Estimator design with bias compensation is also considered. Motivated by the fact that there are no "attitude sensors" the use of vector measurements directly within the estimator is considered as well.

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