# Coordinated Control after Grasping the Space Targets Using Controllable Damping Mechanism
## 1 Introduction  
The capturing of non-cooperative targets in orbit is still a difficult task for on-orbit missions because of its theoretical challenge as well as practical significance; the compliant contact between the spacecraft-manipulator system and space targets belongs to the vital problems of capture task [1]. A spacecraft-manipulator system is composed of a three-dimensional base (a spacecraft) and an onboard manipulator, and the contact occurs during the end effectors' interaction with the capture target where big contact force can be exerted. To solve this problem, compliant control strategies dealing with non-cooperative objects have attracted substantial interest. The impedance controllers have demonstrated good performance in [2, 3]. A latter paper [4] used the disturbance observer to determine the contact force between the end joint and the spinning object, which is important for the impedance controller. In [5], an impedance control strategy is used to buff the impact and to realize compliant capture operation. In paper [6], researchers designed a coordination control to stabilize the space robot system based on impedance control, which is achieved with the parameter uncertainty of the model. Other efforts including coordinated motion control and contact model control have also been extensively studied [7, 8, 9, 10, 11]. In [12], the optimal impact control is employed to capture a space target with flexible dual-arm space robot. A novel coordinated control approach based on an adaptive algorithm for a free-floating flexible space robot is introduced in [13]. In [14], a capture method using the origami principle is proposed, which can capture various sizes objects without fixed contactpoints. In [15], a novel capture area computing algorithm is discussed through establishing the evaluation equation of capture area existence. The control strategy based on contact model control is designed to capture the object on-orbit by estimating contact force between the gripper and the space object to achieve soft contact [16; 17; 18]. The above research are all applied to rigid manipulators, and the interaction process is essentially a rigid contact. That is, there is no actual mechanical mechanism to output damping and spring forces to buffer the impact. Therefore, designing a new type of soft-docking mechanism to achieve compliant capture has become an effective means. In [19], a flexible continuous robot endowed with a multi-cut mechanism is proposed to ensure the temperature control and compliant capture in the space environment. In [20], a multidimensional damping mechanism with stiffness optimization is proposed to implant the momentum distribution and impact absorption during the on-orbit docking. A new type of topological polyhedron docking mechanism for space service is designed in [21]. The paper [22] designed a soft-capture arm with dual-mode to stabilize the attitude of the space robot. In [23], a series-wound flexible capturing mechanism with multi-dimensional controllable damper is developed, and an optimization control was realized based on the particle swarm optimization. In [24], a flexible net is employed as the capture mechanism which can quickly open or close, and the dynamics of flexible net are established to design the control method. A new adhesive capture mechanism is designed and the passive trigger mechanism is discussed in detail; contact-estimated modeling is proposed to take the failure of adhesive connection into account. The above studies demonstrate the superior performance of the soft-docking mechanism in dealing with the stabilization problem caused by contact forces during capturing. The introduction of the soft-docking mechanism will increase the complexity of the modeling of the spacecraft-manipulator system, which requires accurate modeling of the flexible joint mechanism. In [25], a dynamic model of the flexible robot is proposed by introducing the properties of friction in the flexible joints, and the characteristics of the planetary gear reducer are analyzed.