Graduate Students, Program in Applied Mathematics
When
1 – 2 p.m., Today
Where
Speaker: Vianella Spaeth, Applied Math
Title: Geometric PID Control for Pose Regulation and Trajectory Tracking on SE(3)
Title: Geometric PID Control for Pose Regulation and Trajectory Tracking on SE(3)
Abstract: The increasing demand for high-agility proximity operations and precision pointing in modern space missions requires control frameworks capable of handling large-scale orbital maneuvers and complex attitude maneuvers. This work addresses the problem of pose (position and attitude) regulation and trajectory tracking for a fully actuated rigid body, such as a spacecraft or unmanned aerial vehicle. We present a geometric PID control framework defined directly on the Special Euclidean group SE(3) for full 6-DOF control. By formulating the control law on the manifold, the proposed approach avoids the singularities inherent in local parameterizations. The controller combines a proportional term based on the pose tracking error, a derivative term based on the velocity error, and an integral action to improve robustness to persistent disturbances and unmodeled dynamics. Unlike traditional schemes that decouple translational and rotational motion, this framework respects the underlying Lie group structure to account for nonlinear coupling. Lyapunov-based analysis guarantees almost global asymptotic stability, and the performance is validated through numerical simulations.