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

• 成果类型: Article
• 署名作者: Rigo, Damiano; Segala, Chiara; Sansonetto, Nicola; Muradore, Riccardo
• 署名单位: University of Verona; RWTH Aachen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3179988
• 发表日期: 2022
• 页码: 4971-4977
• 关键词: Filtering theory; Algebra; Transmission line matrix methods; mathematical models; Antenna measurements; Kalman filters; Position measurement; Geometric modeling; nonlinear filters; nonlinear dynamical systems; optimization

摘要

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.