Second-Order-Optimal Filter on Lie Groups for Planar Rigid Bodies

IEEE Transactions on Automatic Control, vol. 67, pp. 4971–4977

Abstract

Attitude estimation is a core problem in many mobile robotic systems, such as unmanned aerial and ground vehicles. The configuration space of these systems is properly modeled by exploiting the theory of Lie groups. In this article, we propose a second-order-optimal minimum-energy filter on the matrix Lie group TSE(2), the tangent bundle of the special Euclidean group SE(2), where the optimality is with respect to a cost function in the unknown input and output error measurements. In this article, the measurement equation consists of a global positioning system-like device with two antennas attached to the planar rigid body and an inertial measurement unit-like device. Even though the mathematics is quite complicated, the accuracy of the filter justifies this approach. Simulations show the effectiveness of the proposed filter.

Authors 4

1. Damiano Rigo

   University of Verona

   Affiliation as printed

   Department of Computer Science, University of Verona, Verona, Italy

2. Chiara Segala Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics, RWTH Aachen University, Aachen, Germany

3. Nicola Sansonetto

   University of Verona

   Affiliation as printed

   Department of Computer Science, University of Verona, Verona, Italy

4. Riccardo Muradore

   University of Verona

   Affiliation as printed

   Department of Computer Science, University of Verona, Verona, Italy