Section: New Results

Attitude dynamics, control and observation

Participants : Frederic Mazenc [Disco] , Maruthi Akella [Univ of Texas] , Divya Thakur [Univ of Texas] , Sunpil Yang [Univ of Texas] .

We addressed several problems pertaining to the control of fully actuated rigid-body attitude dynamics. The fundamental tool we used is the adaptation of the so called strictification approach to the features of the attitude dynamics (see [3] for an introduction to the 'strictifiation' paradigm). In particular

1) The contribution [31] output feedback stabilization of fully actuated rigid-body attitude dynamics in the presence of unknown point-wise time-delay in the input torque. Specifically, rate-gyros are unavailable here and only the attitude state represented by the unit quaternion is assumed to be measured. It is worth mentioning that the presence of unknown time-delay in the measured variables, imposes formidable technical challenges for the output-feedback attitude stabilization problem on hand. One of the central difficulties stems from the availability of only a weak Lyapunov-like function for the passivity based dynamic output feedback controller in the absence of delay. This obstacle is circumvented in this contribution by a novel process of partially strictifying the underlying weak Lyapunov-like function.

2) In [57] , we considered stabilization of fully actuated rigid-body attitude dynamics in the absence of angular velocity measurements and presents new robustness results to bounded unknown external disturbance torques. In particular, it is assumed that only body orientation is measured in the form of a unit-quaternion signal. It is well known that the passivity properties of the dynamics allows design of velocity-free controllers using a first-order stable filter driven by measured states. When external disturbance torques are taken into account, however, the robustness properties of these passivity-based output feedback controllers cannot be readily analyzed because the Lyapunov-like function from which the controller is derived has a time-derivative that is only negative semidefinite, and therefore non-strict. This obstacle is circumvented through a new partial-strictification approach which ultimately allows the characterization of robustness properties for this closed-loop system.

3) In [18] , we proposed a smooth angular velocity observer for the attitude tracking control of a rigid body in the absence of angular velocity measurements. The observer design ensures asymptotic convergence of angular velocity state estimation errors irrespective of the control torque or the initial attitude state of the spacecraft. Unlike existing rate observer formulations that attain estimation error convergence by imposing certain switching conditions or hybrid-logic, the proposed observer has a smooth structure that ensures continuity of all estimated states.Lyaounov strictification is again the key technical result making us to establish the results.