Attitude Control and Reachability Analysis for Unmanned Helicopters via the Zonotopic Kalman Filtering

This paper presents a new methodology to develop an integrated system that is used to stabilize attitude dynamics and to estimate flight envelopes of an unmanned helicopter. This system consists of two blocks: an observer-based feedback controller and a reachability-based flight envelope estimator. Information about the helicopter's state is only partially available through measurement. Thus, an element of this system playing an important role to provide information about unmeasurable state variables is an observer, which is then referred to as a zonotopic Kalman filter. Such a Kalman filter is constructed to yield sets of state estimates of the helicopter in terms of zonotopes. Each state-zonotope estimate is defined by a center vector and a generator matrix, which respectively represent a nominal state estimate and possible variations around the center vector. The state-zonotope estimates are utilized by the integrated system to produce control input signals and flight envelope estimates of the helicopter via a zonotopic reachability analysis. The latter is useful for enhancing operator's awareness about helicopter dynamics, especially when the helicopter suffers from actuator faults. It is well known that the actuator faults may give rise to control effectiveness degradation and accidents in the worst cases. The benefit of applying the zonotopic Kalman filter is shown via an example where noise perturbations upon the helicopter do not possess Gaussian properties. In this case, the zonotopic Kalman filter outperforms an ordinary stochastic Kalman filter in providing meaningful estimates of the helicopter's state variables.