Control and estimation on lie groups : application on autonomous underwater vehicles

Abstract

This work focuses on the estimation and control of dynamical systems evolving on Lie groups, with applications in robotics. Indeed, most dynamical systems evolve naturally on SO(3) and SE(3). However, designing controllers and observers which can provide precise estimation and drive the system to the desired position on Lie groups is quite challenging. This work elaborates on the solution of both of these problems, by designing common controllers such as Proportional Derivative, Sliding Mode, LQR on Lie groups and by constructing Observers which can estimate states that exist on Lie groups such as the Lie Group version of the Extended Kalman Filter. Finally, My contribution is the implementation of An LG-EKF observer-based PD-controller on an autonomous underwater vehicle evolving on SE(2).