Passivity-Based Attitude Control on the Special Orthogonal Group of Rigid-Body Rotations

Set-point regulation and tracking control of a rigid body is considered. The rigid body, which could be a spacecraft, underwater vehicle, or unmanned aerial vehicle, is equipped with various sensors, including those that provide unit-length vector measurements. At no point is the rotation matrix associated with the rigid-body's orientation parameterized. The control algorithms developed in this paper are posed directly on the special orthogonal group of rigid-body rotations SO(3). The set-point controller presented is composed of a proportional control term and an angular velocity control term. The proportional control term is a function of the vector measurements and a set of desired vector measurements that are used to compute the orientation error of the rigid body. Passive systems theory is used to motivate the use of a strictly positive real angular velocity controller. The set-point regulator is robust to modeling errors associated with the mass distribution of the body. Tracking control is also considered. To ensure robust tracking control, an adaptive scheme is developed in which the controller is composed of feedback and feedforward terms. The feedback term is composed of a proportional term and a strictly-positive-real-based angular velocity term, similar to the set-point regulator. The feedforward term is a function of an estimate of the spacecraft mass distribution. The synthesis of strictly positive real controllers to be used within the set-point and tracking controllers is discussed. Numerical simulation results that demonstrate successful set-point regulation and tracking control are presented.