Loss of control (LOC) is the primary cause of failure of Unmanned Aerial Vehicles (UAV). The safety of these systems can be largely improved by facilitating techniques to prevent LOC to occur, such as Flight Envelope Protection, enabling controllers to keep the system within the Safe Flight Envelope (SFE).
The aim of this work is to examine the behaviour of the global SFE of a quadcopter subjected to varying system dynamics, including the effects of longitudinal center of gravity displacements and actuator dynamics.
The analysis has been split into the forward reachable set (FRS) and the backward reachable set (BRS). The FRS is estimated through an optimized Monte-Carlo (MC) simulation approach. Verification shows that the system specific optimized MC simulation approximates the true reachable sets with high accuracy, while exceeding performance on both accuracy as well as computation time compared to the Level-Set method.
The BRS is derived from the FRS directly using a minimum-time optimal control (MTOC) routine including actuator dynamics. This approach guarantees that the BRS is contained within the FRS and bypasses the need to simulate the dynamics backwards in time. Both methods exploit the control affine system structure from which it can be derived that the MTOC for both the FRS and BRS is bang-bang control, which drastically reduces the sampling space and optimal control complexity.
The results show that both the location of the centroid of the FRS and the return time distribution of the BRS are a function of the offset position. A large decrease in the FRS area is seen for larger center of gravity offset positions. Furthermore, the actuator dynamics reduce the FRS by 85%, irrespective of center of gravity location, while the BRS without actuator modelling shows impractical return times as a result of unfeasible instantaneous rotor speed changes.
A novel experimental validation procedure on the quadcopter FRS has been performed. The results show a general overestimation with respect to the flight data, which is expected when comparing an open-loop simulation with closed-loop performed flight maneuvers.