# Stochastic Models and Control of Anchoring Mechanisms for Grasping in Microgravity
## 1 Introduction  
In recent years, researchers have become increasingly interested in small solar system objects [1; 2]. Satellites equipped with advanced equipment, such as thermal imaging, are used to observe the physical properties of objects at close range [3; 4; 5; 6]. These scientific missions focus on observing physical information, such as heat distribution, composition, and revolution of the asteroid surface. At present, the Hayabusa, Hayabusa2, and OSIRIS-REx probes have successfully collected asteroid samples [7; 8; 9; 10]. Due to the microgravity environment of small celestial bodies, few researchers explore the mobile robots moving on their surfaces. The traditional wheeled rover cannot travel easily in the microgravity environment [11]. The Minerva detector mounted on Hayabusa2 abandons the traditional mode of motion [12]. As a jump system, a flywheel is installed in the Minerva detector. The inertial reaction generated by driving the flywheel makes the detector jump [13]. The design of the jump system has proven to be successful. However, it poses great challenges in predicting the position and time after hopping. Legged robots are widely considered to have excellent movement ability and can cross irregular terrain, such as slopes and gravel piles. Compared with a wheeled rover, a legged robot can cross obstacles longer than the fuselage by adjusting its gait. However, the small collision force between its limbs and the asteroid surface is enough to push the asteroid robot into space [14]. In the face of complex situations, the anchoring mechanism is necessary to assist the asteroid robot to firmly grasp the asteroid surface to resist the interference of unstable factors to the asteroid robot. In order to realize the movement of legged robots on the surface of asteroids, researchers have proposed several kinds of anchoring mechanisms. [PERSON] presented an anchoring foot mechanism for moving on an asteroid [15; 16; 17; 18; 19]. This mechanism had two degrees of freedom. One was used to control the lifting and lowering of the carriage. Theother was used to tighten cables to pull microspines in the carriage to grasp the rough surface. [PERSON] presented a six-legged asteroid surface robot for exploring asteroids [20]. A steel nail was installed at the end of each leg [21]. Any five of the six legs formed a gripper when they were in contact with the ground. Another asteroid-exploration robot proposed by [PERSON] was equipped with three grippers that recognized millimeter features [20]. The gripper was covered with small steel nails, and they could grasp the brick and rock surface. Throughout their research, these researchers focused on designing a mechanism to assist the asteroid robot to maintain its grip on the asteroid surface. However, there is little research on the modeling and grasping process of the anchoring mechanism or gripper. For the anchoring mechanism, its function is to firmly grasp the surface of the asteroid. Therefore, it is necessary to further study the grasping mechanism of the anchoring mechanism. Many asteroids have a regolith layer on their surface, which is the result of collisions on the asteroid surface over tens of thousands of years [22; 23; 24; 25]. Pores of different sizes are distributed on its surface, which can be used as the anchor point of the robot. Obviously, a microspine is suitable for grasping these tiny pores. Microspines are widely used in various grippers [26; 27; 28; 29]. [PERSON] put forward a small robot crawling on the wall of the building, which established the grasping model of the microspine [30]. Based on the adhesion model of the microspine, the motion of the robot was planned. As mentioned above, the robot presented by [PERSON] could grasp rough surfaces through hundreds of microspines. The microspine technology is also applied to mountainering tools to assist people to stand [31]. The microspine array contains multiple microspines. The movement of each microspine does not affect the others.