Tracking of Rigid Body Motion via Nonlinear H-infinity Control

In the present paper the problem of tracking of rigid body motion in SE(3) in the presence of torque disturbances is addressed. A penalty variable whose Euclidean norm is a measure of the tracking error is deened. Then nonlinear H 1 control theory is applied to design a control law such that the closed loop system has L 2-gain from the torque disturbances to this penalty variable for a xed positive constant. When there exists a linear parameterization of the rigid body dynamics with respect to the unknown parameters, also an adaptive counterpart of this control law is designed.