An intrinsic robust PID controller on Lie groups

This paper presents a PID controller for fully actuated, left-invariant, mechanical systems on a general Lie group. The class of problems solved includes tracking of a smoothly time-varying desired orientation for a rigid body with fully actuated attitude dynamics in two or three dimensions. If the reference velocity and unmodeled disturbance forces converge to constant values, then the closed-loop system will be almost-globally exponentially stable. The controller is robust to errors or variations in the inertial parameters and the actuator parameters. We explicitly construct the controller on the group of rigid body rotations and demonstrate its performance in quadrotor attitude tracking.