# Stochastic Models and Control of Anchoring Mechanisms for Grasping in Microgravity
## 4 Control of the Asteroid Robot  
The engagement of a single microspine with surface roughness is point contact. Thus, the grasping of the anchoring mechanism can be regarded as a collection of multiple point contacts. Ideally, the planes of the microspines' steel needles are parallel to the asteroid's surface. This ensures that all microspines have the same opportunity to engage with roughness. For the safety of the asteroid-exploration robot, the anchoring mechanism should provide stable adhesion. The escape velocity of small bodies can be lower than 10 cm/s, and therefore the asteroid robot usually locomotes at a relatively slow speed. At the same time, it is also necessary to reduce the external force on the robot to prevent it from jettisoning itself into space. Compared with dynamic gait, the static gait obviously meets the above conditions. The asteroid robot maintains at least three anchoring mechanisms to grasp the surface of the asteroid all the time. Three anchoring mechanisms form stable fulcrums to prevent the reaction from affecting the balance of the robot. Although the angle of the anchor mechanism cannot be controlled, the spherical hinge and the spring damping system connecting the anchor mechanism and the leg give the anchoring mechanism the ability to reposition. Because the anchoring mechanism is symmetrical, the existence of passive joints reduces two rotational degrees of freedom, which mitigates the load of knee joint servo motor. Without compliance control, the anchoring mechanism with accurately controlled angle is likely to collide with the surface of asteroids without accurate angle information. Compliance control also reduces the risk of the robot flying into space. Nevertheless, passive joints did not reduce this potential risk. After the robot's leg stepped forward one step, the included angle between the anchoring mechanism and the surface changed. In order to show this process more intuitively, the simulation of the asteroid robot is shown in  
Figure 9: Relationship between stiffness and displacement of different recovery springs. The stiffness of 1 to 5 in the figure is 1.5, 2, 3, 4 and 5 (N/mm) respectively. Figure 10. The red line in the figure indicates the position of the ball joint in the \(Z\) direction. When the leg was in the beginning of swing phase, the included angle between the leg and the anchor mechanism did not change under the influence of the spring damping system. In the late swing phase, the anchoring mechanism collided with the ground. With the movement of the spherical hinge, the anchoring mechanism gradually approached the ground until the spherical hinge reaches the target position. Obviously, taking the spherical joint as the end of the asteroid robot's leg to plan the path will lead to a violent collision between the anchoring mechanism and the asteroid surface. Due to the existence of passive joints, this collision is inevitable. Therefore, the planning of spherical joints should meet the following two requirements:  
1. The collision between the anchoring mechanism and the ground should be as small as possible to reduce the impact force from the asteroid surface when the leg is in the swing phase;
2. The anchoring mechanism should quickly approach the asteroid surface and grasp it, so as to improve the stability of the robot. In order to discuss the collision between the anchoring mechanism and the ground, the anchoring mechanism was selected as a research object. The coordinates of the spherical joint relative to the fuselage can be recorded as: \(PS=\left[ \begin{array}{ccc}x_{s}&y_{s}&z_{s}\end{array} \right]^{T}\). The coordinates of each microspine array relative to the fuselage are obtained through the geometric relationship with the spherical joint, which can be recorded as:  
\[PM_{i}=\left[ \begin{array}{ccc}x_{s}+r\cos\theta_{i}&y_{s}+r\sin\theta_{i} &z_{s}+h\end{array}