# Sampling-Based Motion Planning for Free-Floating Space Robot without Inverse Kinematics
## 1 Introduction
However, this framework also has the following problems. First, it is difficult to obtain an analytical inverse kinematics resolution for a manipulator. Second, the target configuration and the initial configuration may not be in the same connected domain [19]. In order to solve this problem, [PERSON], [PERSON] et al. [20] gave a solution based on the basic framework of RRTs and called this method Jacobian transpose-directed rapidly exploring random trees (JT-RRTs). The goal EE pose was used in goal guiding growth in JT-RRTs. Moreover, in order to deal with local planning in goal guiding growth, the error of the EE pose was mapped to the configuration space through the transpose of the Jacobian matrix. The JT-RRTs method is very powerful for the motion planning of a base-fixed manipulator, but it is not enough for the motion planning of FFSRs for the following two reasons. First, FFSR is a nonholonomic system with differential constraints, while JT-RRTs can only give a geometric path. Second, the local planning approach for goal guiding growth in JT-RRTs cannot ensure that there is no violation of base attitude constraints. Faced with these questions, this paper investigates a novel motion planning method based on RRT for an FFSR from an initial configuration to a goal EE pose. The main problem in motion planning of FFSRs is that it is a system with differential constraints, and the base attitude disturbance must be restricted in the final trajectory planned for it. The final trajectory is composed of several locally planned trajectories when using RRTs for motion planning. In order to meet the above requirements, the following specific local planners are designed. 1. For random configuration guiding growth, three local planning schemes can be found for the motion planning of robots with differential constraints. The first scheme selects a random action and integrates for a certain period of time from the node to be extended with this action. The selected action is treated as a constant during the integration. The second scheme solves a two-point boundary value problem. The third scheme gives several actions that are reasonably distributed in the action space and then integrates for a certain period of time from the node to be extended with these actions. The selected actions are also treated as constants during the integration. Finally, the action with an integration result that is closest to the guiding point is chosen. Obviously, the first and third schemes are not convenient for considering the base disturbance, and the second scheme is time-consuming. This paper proposes a control-based local planner for random configuration guiding growth of the tree. Actions are selected according to the error between the guiding point and the point to be expanded in this local planner. This local planner can achieve rapid local planning and restrict the base attitude disturbance. For goal EE pose guiding growth, the requirements of base attitude disturbance cannot be omitted. For JT-RRTs, only the error of EE needs to be considered in the local planning of goal EE pose guiding growth. In JT-RRTs, the DOF of the EE pose is 6, while the DOF of joint space is 7, which is redundant relative to the former. However, the local planner for FFSRs must deal with not only the error of EE but also the base disturbance, which has another 3 DOF. This paper proposes a control-based goal EE pose guiding local planner (CB-EEPG-LP) for goal EE pose guiding growth. Different from the local planner in JT-RRTs, CB-EEPG-LP can not only guide the tree toward the goal pose but also coordinate the base attitude when necessary. The actions are designed based on two kinds of errors: the first is the error between the goal EE pose and the EE pose corresponding to the configuration to be expanded, and the second is the error between the reference goal base attitude and the attitude corresponding to the configuration to be expanded. The proposed local planner can complete the goal EE pose guiding growth and avoid singularity as much as possible.