# Dynamic Modeling and Simulation of a Robotic Lander Based on Variable Radius Drums
## 1 Introduction  
In space exploration, landing on a planet, an asteroid or any other celestial body is an extremely important task and can determine the success or the failure of the entire mission. In the past decades, many missions failed due to the crash of the lander to the ground during this delicate operation. Despite these failed missions, many other missions succeeded and over the years many systems were tested and employed to achieve a soft landing. The most remarkable mission, known as Apollo 11, from the NASA Agency, had the objective to land a probe transporting humans for the first time on the Moon's surface. Successful landing was obtained first by executing a powered descent maneuver. Then, successful touchdown was achieved by means of a suspension system having a honeycomb shock absorber on each lander-leg strut [1]. During the Vikings mission started in 1975, two twin probes named Viking 1 and Viking 2 were sent to Mars. The landers of the two probes were legged, and a combination of parachute and rocket propulsion was used to achieve soft-landing on the planet surface [2]. The same operations were implemented for the lander used in 1997 for the Cassini-Huygens NASA-ESA-ASI mission, which landed successfully on Titan, one of the moons of Saturn. After the Viking mission, NASA sent further probes to investigate Mars planet. First, it was the turn for NASA's Pathfinder mission, which started in 1996 [3]. Then, in 2004, the NASA's Mars Exploration Rovers Spirit and Opportunity were sent to the red planet. In these three missions, a system based on gas-filled airbags was adopted to achieve soft-landing [4]. Another remarkable mission was theMars Science Laboratory, which deployed successfully the lander Curiosity on the Mars surface in 2011. Successful landing was achieved by adopting a combination of parachute, rockets, and the Sky Crane system. More recently, the Rosetta mission from ESA used a powered descend to land on the comet and a system of anchors to remain attached to it once controlled impact occurred [5]. In parallel to NASA, during the Space Race, the Soviet Space Program, starting with impactors [6], implemented several innovations which led to the first-ever soft-landing on another planet with the lander Luna 9 in February 1966 [7]. In 1970, the Soviet Lunokhod 1 was the first successful rover to land on another planetary body [8]. In the 1990s, the Chinese space agency (China National Space Administration) started a program which enabled the soft-landing of the Chang'e 3 lunar lander and rover Yutu in December 2013 [9]. The lander Chang'e 4 followed in January 2019 [10]. In past years, many authors have studied the problem of soft-landing of landers in different fields. For example, [PERSON] et al. in 2019 studied the use of magnetorheological fluid dampers with semi-active control on damping force in order to adjust to landing conditions [11]. Furthermore, the shock absorber design [12] and the lander stability [13] have been investigated numerically by mean of optimization algorithms. Moreover, legged landers with capabilities of walking on planet surface after the landing have been studied in [14; 15]. Two main problems can be addressed to the study of soft landing operations: the modeling of the system dynamics, and the modeling of the interactions between the lander and the soil. Several authors tried to study the soft landing problem by means of simulation software, and chose as a case study a four-legged lander. For example, [PERSON] et al. in 2011 simulated the soft-landing of a lunar lander first using MSC-ADAMS considering the lunar soil as a rigid body, and then MSC-DYTRAN considering the lunar soil as a flexible body [16]. [PERSON] et al. in 2010, chose MSC-DYTRAN to simulate soft-landing of a lunar lander with the finite elements method and a nonlinear transient dynamics approach [17]. [PERSON] et al. in 2018, simulated the impact of a legged lander using explicit finite element analysis using LS-DYNA and ABAQUS softwares [18]. [PERSON] et al.