# Helicopter Safe Landing Trajectory after Main Rotor Actuator Failures
## 1 Introduction  
Helicopter control, whether for manned or unmanned helicopters, is primarily done by the control system of the main rotor, consisting of the swashplate, servos, pitch links and pitch horns. Blade controls of the main rotor, namely the collective pitch, lateral pitch and longitudinal pitch, are provided by the motion of the swashplate. Therefore, main rotor actuator failures lead to a severe loss of controllability of the helicopter. Actuator faults of helicopters are different between actuator types. For large scale helicopters, the swashplate is mainly driven by the hydraulic system. Two common types of hydraulic actuator failure are described in [1], which respectively result in partial loss of effectiveness of actuators, and stuck-in-place of actuators. For small scale helicopters, electric servos are widely used. Three types of actuator failure are explained in [2], consisting of the partial loss of effectiveness, control bias, and actuator stuck. Although plenty of work has been done on fixed-wing actuator faults or failures [3; 4; 5; 6], most studies on helicopters have been focusing on the partial loss of effectiveness of actuators and actuator control bias [7; 8; 9; 10; 11; 12]. However, limited work has focused on helicopter actuator stuck problems. Within the scope of actuator stuck problems, [PERSON] and [PERSON] [13] propose a reconfiguration method of the control mixer, and demonstrate that the attitude is still controllable while the vertical control is sacrificed. The control of vertical velocity is then mainly achieved by changing the forward speed, and the variation of rotor speed, and two different flight-control systems are verified by simulation approaches. [PERSON]'s study [14] develops a fault-tolerant control system, which is integrated with Fault Detection and Identification (FDI) and Reconfigurable Flight Control (RFC). After one of the actuators gets stuck, the helicopter is controlled by the other two remaining actuators of the swashplate and variation of rotor speed for vertical control. [PERSON] [15] proposes a control system based on a linear-quadratic regulator, and focuses on finding new references by a reference redesign method after one actuator is stuck. In their studies, the control inputs consist of rotor speed as well. Instead ofcontrolling the vertical velocity by rotor speed, [PERSON] [16] uses the horizontal tail as a redundant control to compensate for the original flight control system after one actuator is stuck. As shown above, in present studies, vertical control is mainly achieved by introducing new control inputs, such as the control of rotor speed or horizontal tail. However, using the horizontal tail to control vertical speed is limited to helicopters equipped with all-moving horizontal tails, and such method is not practical for low speed-flights, because empennages only work effectively under situations of medium-speed or high-speed flights. Controlling the vertical channel by rotor speed is widely used for small-scale electric helicopters, but is, for now, unrealistic for engine-driven helicopters, of which rotor speed is kept constant during flight. However, the collective pitch required has the characteristic \"bucket profile\" [17] as a function of forward speed. Thus, if the longitudinal speed is changed while retaining the collective pitch, there will be a corresponding response in vertical speed. Although it is mentioned in [13] that the vertical speed can be obtained by flying to a specific forward speed that supports the decent rate, such a phenomenon is only utilized within a small speed range around the speed where the failure takes place. This is due to the non-monotonic relationship of the collective pitch required by different forward speeds. In order to fully explore the ability of the remaining manipulations, we employ an optimal control method to obtain feasible trajectories to achieve a safe landing by the remaining actuators after one actuator gets stuck in place.