A linearization method based on Lie algebra for pose estimation in a time horizon

Nicolas Torres Alberto (1, 2) , Lucas Joseph (3, 4) , Vincent Padois (1) , David Daney (1)

1 AUCTUS - Augmenting human comfort in the factory using cobots
2 Stellantis - PSA Centre Technique de Vélizy
3 Solvay (France)
4 CNRS - Centre National de la Recherche Scientifique

In this paper, a strategy for linear pose estimation over a time horizon is presented. This linearization is crucial for the computationally efficient formulation of predictive and optimization-based control problems in robotics. The proposed approach is based on a truncation of the Magnus expansion for the approximation of the exponential map derivative and employs Lie algebra to represent position and orientation, allowing for a unified vectorial representation in vector form that can be integrated linearly over time, offering a convenient formulation for optimization solvers. The method shows promising results for precision and computation times.

Domaines: Automatique / Robotique; Robotique [cs.RO]; Optimisation et contrôle [math.OC]

Nicolas Torres Alberto, Lucas Joseph, Vincent Padois, David Daney. A linearization method based on Lie algebra for pose estimation in a time horizon. ARK 2022 - 18th International Symposium on Advances in Robot Kinematics, Jun 2022, Bilbao, Spain. ⟨10.1007/978-3-031-08140-8_6⟩. ⟨hal-03621688v3⟩