## 1 Introduction  
Helicopters are vertical take-off and landing aircraft able to hover, fly sideward, fly backward, and fly forward. They can perform other desirable maneuvers in civilian fields such as sea and mountain rescue, police surveillance, and firefighting, or in military missions such as battlefield surveillance, troop transport, assaults, and antirank operations [1]. In normal landing conditions, the pilot controls the rate of descent to ensure a smooth touchdown while the engine still operates, in a maneuver known as power-on landing [2]. However, common phenomena such as ground effect [1], ground resonance [3], and slope landings [4] can cause operational challenges and also significantly reduce landing gear performance. Moreover, during power-off landing maneuvers, there are more risks inherent in performing autorotation [1, 2, 4]. Typically, landing gears with skids or passive dampers are set up to improve safety and pilot comfort. However, they are also designed based on only one critical touchdown condition. Accordingly, there are limitations in landing performance in different landing cases. Thus, the development of a helicopter landing gear system is necessary to reduce vibration as well as to improve safety and pilot comfort during touchdown in different landing scenarios. Thus far, many helicopter landing gear systems have been developed through experiments and theoretical studies. For example, [PERSON] et al. [5] applied a sky-hook control algorithm to improve the landing performance of a single helicopter landing gear with a magnetroheological (MR) damper. [PERSON] et al. [6] designed a helicopter skid landing gear system with an MR damper. The simple semi-active controller based on optimum Bingham numbers was applied to generate the desired yield force. [PERSON] et al. [7; 8] designed and analyzed an adaptive landing gear system using an MR damper for a lightweight helicopter. In all the previous studies, helicopter landing gear systems equipped with MR dampers were among the most promising choices for enhancing performance and adaptability. However, the control algorithms were designed based on only one critical touchdown condition. Control problems with multiple landing gears being subjected to differing landing scenarios have not yet been fully investigated. Skyhook control, which is the most popular control algorithm used in vehicle suspension systems, is a candidate to solve this problem. Skyhook control is simple and easy to understand because it needs little information on the system's state for implementation [9]. Skyhook control has proved its ability to reduce vehicle vibration, both with single suspension [10] or multiple suspensions [11]. The control objective of a suspension system of a vehicle is usually to attenuate vibration to improve driver comfort. However, the control target of a landing gear system of a helicopter is not only to improve the pilot's comfort but also to mitigate the impact of heavy shock on touchdown. Moreover, a helicopter's landing gear system must be tested with hard landing conditions [12], which can occur when the sink speed is larger than intended due to external factors, as mentioned earlier. Thus, the skyhook control in a helicopter's landing gear system needs to be properly modified, in contrast to the vehicle's suspension system. The main contribution of this study is to develop an easy-to-implement control algorithm for a helicopter with multiple landing gears equipped with MR dampers, which reduces the acceleration at the helicopter's center of gravity under off-normal attitude conditions. As the first step, a 9-degree of freedom (DOF) helicopter model with multiple landing gears equipped with MR dampers was built using RECURDYN, which is a commercial multibody simulation software. In the second step, a control algorithm was designed based on the traditional skyhook control, called the skyhook extended control, to mitigate the magnitude of acceleration at the center of gravity with different initial pitch and roll angles.