This paper reviews the Euler–Rodrigues formula in the axis–angle representation of
rotations, studies its variations and derivations in different mathematical forms as vectors …

The Kalman filter—or, more precisely, the extended Kalman filter (EKF)—is a fundamental
engineering tool that is pervasively used in control and robotics and for various estimation …

Molecular conformer generation is a fundamental task in computational chemistry. Several
machine learning approaches have been developed, but none have outperformed state-of …

We present Theseus, an efficient application-agnostic open source library for differentiable
nonlinear least squares (DNLS) optimization built on PyTorch, providing a common …

A Lie group is an old mathematical abstract object dating back to the XIX century, when
mathematician Sophus Lie laid the foundations of the theory of continuous transformation …

Direct methods for visual odometry (VO) have gained popularity for their capability to exploit
information from all intensity gradients in the image. However, low computational speed as …

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state
estimation via nonlinear optimization. However, real-time optimization quickly becomes …

Legged robots require knowledge of pose and velocity in order to maintain stability and
execute walking paths. Current solutions either rely on vision data, which is susceptible to …

Recent results in monocular visual-inertial navigation (VIN) have shown that optimization-
based approaches outperform filtering methods in terms of accuracy due to their capability to …

This article is an exhaustive revision of concepts and formulas related to quaternions and
rotations in 3D space, and their proper use in estimation engines such as the error-state …