# Sampling-Based Motion Planning for Free-Floating Space Robot without Inverse Kinematics
## 1 Introduction  
Free-floating space robots (FFSRs) are composed of a manipulator and a base spacecraft. The base attitude and position control system is closed, and the base attitude is adjusted by joint motion. This mechanism has the advantages of saving fuel and prolonging system life. Therefore, FFSRs are widely employed for on-orbit services [1]. Motion planning is one of the fundamental technologies for FFSRs to achieve autonomy [2]. For a manipulator, it is required that the joint motion is planned so that the end-effector (EE) moves from the initial pose to the goal pose. The general motion planning framework for a manipulator consists of three steps [3]. First, inverse kinematics is used to map the goal EE's pose to a goal configuration. For a fixed base manipulator, the configuration space is the joint space, and the configuration space for FFSRs includes joint space and base attitude space. Then, the path from the initial configuration to the goal configuration is generated through a sampling-based planning algorithm or other algorithms. Finally, the generated path points are interpolated to obtain the trajectory. This framework works well for a base-fixed manipulator, while it is not suitable for FFSRs. FFSRs have nonholonomic characteristics, and a first-order differential relationship exists between joint angles and base attitude. In addition, this planning framework still has the following disadvantages. First, it is difficult to obtain the analytical inverse kinematics resolution. Second, the obtained goal configuration and the initial configuration may not be in the same connected domain. For the motion planning of an FFSR, scholars have studied the steering problem at an early stage, where obstacles were not considered in their methods. The FFSR can move from an initial configuration to a goal configuration by using action series generated by these steering methods. Based on the virtual manipulator (VM) model [4], [PERSON], [PERSON] et al. developed the self-correcting motions method [4] and the disturbance map (DM) method [5]. In the self-correcting motions method, periodic joint motions are used to adjust base attitude. In the DM method, the joint space is divided into grid points, and the joint motion directions with the largest and smallest base attitude disturbances are drawn at each point. Based on this, the path with less base attitude disturbance is selected. [PERSON], [PERSON] and [PERSON] [6] used Lie brackets and the Frobenius theorem to discuss the nonholonomic characteristics of FFSRs and proposed the bi-directional approach using the Lyapunov function. In this method, the base attitude and the joint position are simultaneously controlled by using only the motion of joints. [PERSON] et al. [7] proved that the cat-falling problem is equivalent to the nonlinear controllability problem. Then, they proposed the steering method of coupled rigid bodies and used this method to control the base of an FFSR. The above methods emphasize the nonholonomic characteristics of FFSRs. Joint motion is used to manipulate the base attitude in these methods. However, obstacles are not considered, and they did not discuss the situation where the initial configuration and the goal configuration are not in the same connected domain. The second method is to convert the motion planning of an FFSR into a nonlinear optimization problem through direct and indirect methods. [PERSON] [8] used the variational method to plan the joint path, and the base attitude can be arbitrarily changed in this method. [PERSON] and [PERSON] [9] extended [PERSON]'s method, and the spiral perturbation was used to approximate joint motions. The pose of EE and the base attitude can be arbitrarily changed by only controlling 6-degree-of-freedom joints in the method proposed by [PERSON] and [PERSON] In 2010, [PERSON] [10] studied the motion planning problem of capturing a spin target for space robots, and the problem was converted into a nonlinear optimization problem.